(*^ ::[ frontEndVersion = "Microsoft Windows Mathematica Notebook Front End Version 2.2"; microsoftWindowsStandardFontEncoding; fontset = title, "Times New Roman", 25, L0, center, nohscroll, R65280, cellOutline; fontset = subtitle, "Times New Roman", 17, L0, center, nohscroll, R6400, G6400, B6400; fontset = subsubtitle, "Times New Roman", 25, L0, center, nohscroll, R65280, cellOutline; fontset = section, "Times New Roman", 17, L0, nohscroll, R6400, G6400, B6400, grayBox; fontset = subsection, "Bookman Old Style", 17, L0, nohscroll, bold, R6400, G6400, B6400, blackBox; fontset = subsubsection, "Bookman Old Style", 17, L0, nohscroll, bold, R6400, G6400, B6400, whiteBox; fontset = text, "Times New Roman", 17, L0, nohscroll, B32768; fontset = smalltext, "Times New Roman", 17, L0, nohscroll; fontset = input, "Courier New", 12, L-2, nowordwrap, bold; fontset = output, "Courier New", 12, L-1, nowordwrap, B32768; fontset = message, "Courier New", 10, L-2, nowordwrap, R32768; fontset = print, "Courier New", 10, L-2, nowordwrap; fontset = info, "Courier New", 10, L-2, nowordwrap, B32768; fontset = postscript, "Courier New", 12, L0, nowordwrap; fontset = name, "Courier New", 10, L0, nohscroll; fontset = header, "Courier New", 10, L0, nohscroll; fontset = footer, "Courier New", 10, L0, center, nohscroll; fontset = help, "Courier New", 10, L0, nohscroll; fontset = clipboard, "Courier New", 10, L0, nohscroll; fontset = completions, "Courier New", 12, L0, nohscroll; fontset = graphics, "Courier New", 10, L0, nowordwrap, nohscroll; fontset = special1, "Times New Roman", 17, L0, nohscroll, R21760, G21760, B21760, whiteBox; fontset = special2, "Courier New", 10, L0, center, nohscroll, R6400, G6400, B6400; fontset = special3, "Courier New", 10, L0, nohscroll; fontset = special4, "Courier New", 10, L0, center, nohscroll; fontset = special5, "Courier New", 10, L0, center, nohscroll; fontset = leftheader, "Arial", 12, L0; fontset = leftfooter, "Arial", 12, L0; fontset = reserved1, "Courier New", 10, L0, nowordwrap, nohscroll;] :[font = title; inactive; preserveAspect; nohscroll; cellOutline; center; ] Mathematica Problem Set 1 :[font = input; nowordwrap; ] :[font = text; inactive; preserveAspect; nohscroll; ] 1. You enjoy both movies, M, and pizza, P. Your utility function for these two goods is: U = .6 log M + .4 log P :[font = text; inactive; preserveAspect; nohscroll; ] a) For a given quantity of pizzas, say P=2, plot your total utility function for movies. :[font = input; preserveAspect; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] Clear[f,M] f[M_] = .6 Log[M ] + .4 Log[2]; Plot[f[M],{M,0,10}, PlotRange->{0,2}, PlotStyle->{{Red,Thickness[0.015]}}, AxesLabel->{"Movies","U"}, PlotLabel->"Total utility"]; :[font = postscript; inactive; output; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 185; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0 0.309017 [ [(0)] .02381 0 0 2 Msboxa [(2)] .21429 0 0 2 Msboxa [(4)] .40476 0 0 2 Msboxa [(6)] .59524 0 0 2 Msboxa [(8)] .78571 0 0 2 Msboxa [(10)] .97619 0 0 2 Msboxa [(Movies)] 1.025 0 -1 0 Msboxa [(Total utility)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(0.25)] .01131 .07725 1 0 Msboxa [(0.5)] .01131 .15451 1 0 Msboxa [(0.75)] .01131 .23176 1 0 Msboxa [(1)] .01131 .30902 1 0 Msboxa [(1.25)] .01131 .38627 1 0 Msboxa [(1.5)] .01131 .46353 1 0 Msboxa [(1.75)] .01131 .54078 1 0 Msboxa [(2)] .01131 .61803 1 0 Msboxa [(U)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(10)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P [(Movies)] 1.025 0 -1 0 Mshowa p .002 w 0 0 m 1 0 L s P [(Total utility)] .5 .61803 0 -2 0 0 1 Mouter Mrotshowa p .002 w .02381 .07725 m .03006 .07725 L s P [(0.25)] .01131 .07725 1 0 Mshowa p .002 w .02381 .15451 m .03006 .15451 L s P [(0.5)] .01131 .15451 1 0 Mshowa p .002 w .02381 .23176 m .03006 .23176 L s P [(0.75)] .01131 .23176 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(1)] .01131 .30902 1 0 Mshowa p .002 w .02381 .38627 m .03006 .38627 L s P [(1.25)] .01131 .38627 1 0 Mshowa p .002 w .02381 .46353 m .03006 .46353 L s P [(1.5)] .01131 .46353 1 0 Mshowa p .002 w .02381 .54078 m .03006 .54078 L s P [(1.75)] .01131 .54078 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(2)] .01131 .61803 1 0 Mshowa p .001 w .02381 .01545 m .02756 .01545 L s P p .001 w .02381 .0309 m .02756 .0309 L s P p .001 w .02381 .04635 m .02756 .04635 L s P p .001 w .02381 .0618 m .02756 .0618 L s P p .001 w .02381 .09271 m .02756 .09271 L s P p .001 w .02381 .10816 m .02756 .10816 L s P p .001 w .02381 .12361 m .02756 .12361 L s P p .001 w .02381 .13906 m .02756 .13906 L s P p .001 w .02381 .16996 m .02756 .16996 L s P p .001 w .02381 .18541 m .02756 .18541 L s P p .001 w .02381 .20086 m .02756 .20086 L s P p .001 w .02381 .21631 m .02756 .21631 L s P p .001 w .02381 .24721 m .02756 .24721 L s P p .001 w .02381 .26266 m .02756 .26266 L s P p .001 w .02381 .27812 m .02756 .27812 L s P p .001 w .02381 .29357 m .02756 .29357 L s P p .001 w .02381 .32447 m .02756 .32447 L s P p .001 w .02381 .33992 m .02756 .33992 L s P p .001 w .02381 .35537 m .02756 .35537 L s P p .001 w .02381 .37082 m .02756 .37082 L s P p .001 w .02381 .40172 m .02756 .40172 L s P p .001 w .02381 .41717 m .02756 .41717 L s P p .001 w .02381 .43262 m .02756 .43262 L s P p .001 w .02381 .44807 m .02756 .44807 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .49443 m .02756 .49443 L s P p .001 w .02381 .50988 m .02756 .50988 L s P p .001 w .02381 .52533 m .02756 .52533 L s P p .001 w .02381 .55623 m .02756 .55623 L s P p .001 w .02381 .57168 m .02756 .57168 L s P p .001 w .02381 .58713 m .02756 .58713 L s P p .001 w .02381 .60258 m .02756 .60258 L s P [(U)] .02381 .61803 0 -4 Mshowa p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 1 0 0 r p .015 w s s s s s s s s s s s .08388 0 m .10317 .05187 L s .10317 .05187 m .14286 .12705 L .18254 .18039 L .22222 .22176 L .2619 .25557 L .30159 .28415 L .34127 .30891 L .38095 .33074 L .42063 .35028 L .46032 .36795 L .5 .38408 L .53968 .39892 L .57937 .41267 L .61905 .42546 L .65873 .43742 L .69841 .44866 L .7381 .45926 L .77778 .46929 L .81746 .4788 L .85714 .48784 L .89683 .49647 L .93651 .50471 L .97619 .5126 L s P P % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; nohscroll; ] b) Suppose the quantity of pizzas increases to 3, show how this would affect your total utility function. :[font = input; preserveAspect; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] Clear[f,f2,M] f[M_] = .6 Log[M ] + .4 Log[2]; f2[M_] = .6 Log[M ] + .4 Log[3]; Plot[{f2[M],f[M]},{M,0,10}, PlotRange->{0,2}, PlotStyle->{{Blue,Thickness[0.01]}, {Red,Thickness[0.01]}}, AxesLabel->{"Movies","U"}, PlotLabel->"Total utility"]; :[font = postscript; inactive; output; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 185; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0 0.309017 [ [(0)] .02381 0 0 2 Msboxa [(2)] .21429 0 0 2 Msboxa [(4)] .40476 0 0 2 Msboxa [(6)] .59524 0 0 2 Msboxa [(8)] .78571 0 0 2 Msboxa [(10)] .97619 0 0 2 Msboxa [(Movies)] 1.025 0 -1 0 Msboxa [(Total utility)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(0.25)] .01131 .07725 1 0 Msboxa [(0.5)] .01131 .15451 1 0 Msboxa [(0.75)] .01131 .23176 1 0 Msboxa [(1)] .01131 .30902 1 0 Msboxa [(1.25)] .01131 .38627 1 0 Msboxa [(1.5)] .01131 .46353 1 0 Msboxa [(1.75)] .01131 .54078 1 0 Msboxa [(2)] .01131 .61803 1 0 Msboxa [(U)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(10)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P [(Movies)] 1.025 0 -1 0 Mshowa p .002 w 0 0 m 1 0 L s P [(Total utility)] .5 .61803 0 -2 0 0 1 Mouter Mrotshowa p .002 w .02381 .07725 m .03006 .07725 L s P [(0.25)] .01131 .07725 1 0 Mshowa p .002 w .02381 .15451 m .03006 .15451 L s P [(0.5)] .01131 .15451 1 0 Mshowa p .002 w .02381 .23176 m .03006 .23176 L s P [(0.75)] .01131 .23176 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(1)] .01131 .30902 1 0 Mshowa p .002 w .02381 .38627 m .03006 .38627 L s P [(1.25)] .01131 .38627 1 0 Mshowa p .002 w .02381 .46353 m .03006 .46353 L s P [(1.5)] .01131 .46353 1 0 Mshowa p .002 w .02381 .54078 m .03006 .54078 L s P [(1.75)] .01131 .54078 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(2)] .01131 .61803 1 0 Mshowa p .001 w .02381 .01545 m .02756 .01545 L s P p .001 w .02381 .0309 m .02756 .0309 L s P p .001 w .02381 .04635 m .02756 .04635 L s P p .001 w .02381 .0618 m .02756 .0618 L s P p .001 w .02381 .09271 m .02756 .09271 L s P p .001 w .02381 .10816 m .02756 .10816 L s P p .001 w .02381 .12361 m .02756 .12361 L s P p .001 w .02381 .13906 m .02756 .13906 L s P p .001 w .02381 .16996 m .02756 .16996 L s P p .001 w .02381 .18541 m .02756 .18541 L s P p .001 w .02381 .20086 m .02756 .20086 L s P p .001 w .02381 .21631 m .02756 .21631 L s P p .001 w .02381 .24721 m .02756 .24721 L s P p .001 w .02381 .26266 m .02756 .26266 L s P p .001 w .02381 .27812 m .02756 .27812 L s P p .001 w .02381 .29357 m .02756 .29357 L s P p .001 w .02381 .32447 m .02756 .32447 L s P p .001 w .02381 .33992 m .02756 .33992 L s P p .001 w .02381 .35537 m .02756 .35537 L s P p .001 w .02381 .37082 m .02756 .37082 L s P p .001 w .02381 .40172 m .02756 .40172 L s P p .001 w .02381 .41717 m .02756 .41717 L s P p .001 w .02381 .43262 m .02756 .43262 L s P p .001 w .02381 .44807 m .02756 .44807 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .49443 m .02756 .49443 L s P p .001 w .02381 .50988 m .02756 .50988 L s P p .001 w .02381 .52533 m .02756 .52533 L s P p .001 w .02381 .55623 m .02756 .55623 L s P p .001 w .02381 .57168 m .02756 .57168 L s P p .001 w .02381 .58713 m .02756 .58713 L s P p .001 w .02381 .60258 m .02756 .60258 L s P [(U)] .02381 .61803 0 -4 Mshowa p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p 0 0 1 r p .01 w s s s s s s s s s s .07049 0 m .08333 .04865 L s .08333 .04865 m .10317 .10199 L .14286 .17717 L .18254 .23051 L .22222 .27188 L .2619 .30569 L .30159 .33427 L .34127 .35902 L .38095 .38086 L .42063 .4004 L .46032 .41807 L .5 .4342 L .53968 .44904 L .57937 .46278 L .61905 .47558 L .65873 .48754 L .69841 .49878 L .7381 .50938 L .77778 .5194 L .81746 .52891 L .85714 .53796 L .89683 .54659 L .93651 .55483 L .97619 .56272 L s P P p 1 0 0 r p .01 w s s s s s s s s s s s .08388 0 m .10317 .05187 L s .10317 .05187 m .14286 .12705 L .18254 .18039 L .22222 .22176 L .2619 .25557 L .30159 .28415 L .34127 .30891 L .38095 .33074 L .42063 .35028 L .46032 .36795 L .5 .38408 L .53968 .39892 L .57937 .41267 L .61905 .42546 L .65873 .43742 L .69841 .44866 L .7381 .45926 L .77778 .46929 L .81746 .4788 L .85714 .48784 L .89683 .49647 L .93651 .50471 L .97619 .5126 L s P P P % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; nohscroll; ] c) Graph your marginal utility functions for movies and pizza. :[font = input; preserveAspect; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] Plot[f'[M],{M,1,8}, PlotStyle->{{Red,Thickness[0.015]}}, AxesLabel->{"Movies","U"}, PlotLabel->"Marginal utility of movies"] :[font = postscript; inactive; output; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 185; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.119048 0.0147151 0.981006 [ [(2)] .2619 .01472 0 2 Msboxa [(4)] .5 .01472 0 2 Msboxa [(6)] .7381 .01472 0 2 Msboxa [(8)] .97619 .01472 0 2 Msboxa [(Movies)] 1.025 .01472 -1 0 Msboxa [(Marginal utility of movies)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(0.1)] .01131 .11282 1 0 Msboxa [(0.2)] .01131 .21092 1 0 Msboxa [(0.3)] .01131 .30902 1 0 Msboxa [(0.4)] .01131 .40712 1 0 Msboxa [(0.5)] .01131 .50522 1 0 Msboxa [(0.6)] .01131 .60332 1 0 Msboxa [(U)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .2619 .01472 m .2619 .02097 L s P [(2)] .2619 .01472 0 2 Mshowa p .002 w .5 .01472 m .5 .02097 L s P [(4)] .5 .01472 0 2 Mshowa p .002 w .7381 .01472 m .7381 .02097 L s P [(6)] .7381 .01472 0 2 Mshowa p .002 w .97619 .01472 m .97619 .02097 L s P [(8)] .97619 .01472 0 2 Mshowa p .001 w .07143 .01472 m .07143 .01847 L s P p .001 w .11905 .01472 m .11905 .01847 L s P p .001 w .16667 .01472 m .16667 .01847 L s P p .001 w .21429 .01472 m .21429 .01847 L s P p .001 w .30952 .01472 m .30952 .01847 L s P p .001 w .35714 .01472 m .35714 .01847 L s P p .001 w .40476 .01472 m .40476 .01847 L s P p .001 w .45238 .01472 m .45238 .01847 L s P p .001 w .54762 .01472 m .54762 .01847 L s P p .001 w .59524 .01472 m .59524 .01847 L s P p .001 w .64286 .01472 m .64286 .01847 L s P p .001 w .69048 .01472 m .69048 .01847 L s P p .001 w .78571 .01472 m .78571 .01847 L s P p .001 w .83333 .01472 m .83333 .01847 L s P p .001 w .88095 .01472 m .88095 .01847 L s P p .001 w .92857 .01472 m .92857 .01847 L s P [(Movies)] 1.025 .01472 -1 0 Mshowa p .002 w 0 .01472 m 1 .01472 L s P [(Marginal utility of movies)] .5 .61803 0 -2 0 0 1 Mouter Mrotshowa p .002 w .02381 .11282 m .03006 .11282 L s P [(0.1)] .01131 .11282 1 0 Mshowa p .002 w .02381 .21092 m .03006 .21092 L s P [(0.2)] .01131 .21092 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(0.3)] .01131 .30902 1 0 Mshowa p .002 w .02381 .40712 m .03006 .40712 L s P [(0.4)] .01131 .40712 1 0 Mshowa p .002 w .02381 .50522 m .03006 .50522 L s P [(0.5)] .01131 .50522 1 0 Mshowa p .002 w .02381 .60332 m .03006 .60332 L s P [(0.6)] .01131 .60332 1 0 Mshowa p .001 w .02381 .03434 m .02756 .03434 L s P p .001 w .02381 .05396 m .02756 .05396 L s P p .001 w .02381 .07358 m .02756 .07358 L s P p .001 w .02381 .0932 m .02756 .0932 L s P p .001 w .02381 .13244 m .02756 .13244 L s P p .001 w .02381 .15206 m .02756 .15206 L s P p .001 w .02381 .17168 m .02756 .17168 L s P p .001 w .02381 .1913 m .02756 .1913 L s P p .001 w .02381 .23054 m .02756 .23054 L s P p .001 w .02381 .25016 m .02756 .25016 L s P p .001 w .02381 .26978 m .02756 .26978 L s P p .001 w .02381 .2894 m .02756 .2894 L s P p .001 w .02381 .32864 m .02756 .32864 L s P p .001 w .02381 .34826 m .02756 .34826 L s P p .001 w .02381 .36788 m .02756 .36788 L s P p .001 w .02381 .3875 m .02756 .3875 L s P p .001 w .02381 .42674 m .02756 .42674 L s P p .001 w .02381 .44636 m .02756 .44636 L s P p .001 w .02381 .46598 m .02756 .46598 L s P p .001 w .02381 .4856 m .02756 .4856 L s P p .001 w .02381 .52484 m .02756 .52484 L s P p .001 w .02381 .54446 m .02756 .54446 L s P p .001 w .02381 .56408 m .02756 .56408 L s P p .001 w .02381 .5837 m .02756 .5837 L s P [(U)] .02381 .61803 0 -4 Mshowa p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 1 0 0 r p .015 w .14286 .60332 m .16022 .52841 L .17758 .47041 L .19494 .42418 L .2123 .38646 L .24702 .32864 L .28175 .28638 L .31647 .25415 L .35119 .22875 L .38591 .20823 L .42063 .1913 L .45536 .17709 L .49008 .165 L .5248 .15458 L .55952 .14552 L .59425 .13755 L .62897 .13051 L .66369 .12422 L .69841 .11859 L .73313 .1135 L .76786 .10889 L .80258 .10469 L .8373 .10085 L .87202 .09733 L .90675 .09408 L .94147 .09107 L .97619 .08829 L s P P % End of Graphics MathPictureEnd :[font = output; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form was saved for this expression. ;[o] -Graphics- :[font = input; preserveAspect; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] Plot[f'[P],{P,1,8}, PlotStyle->{{Blue,Thickness[0.015]}}, AxesLabel->{"Pizzas","U"}, PlotLabel->"Marginal utility of pizzas"]; :[font = postscript; inactive; output; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 185; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.119048 0.0147151 0.981006 [ [(2)] .2619 .01472 0 2 Msboxa [(4)] .5 .01472 0 2 Msboxa [(6)] .7381 .01472 0 2 Msboxa [(8)] .97619 .01472 0 2 Msboxa [(Pizzas)] 1.025 .01472 -1 0 Msboxa [(Marginal utility of pizzas)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(0.1)] .01131 .11282 1 0 Msboxa [(0.2)] .01131 .21092 1 0 Msboxa [(0.3)] .01131 .30902 1 0 Msboxa [(0.4)] .01131 .40712 1 0 Msboxa [(0.5)] .01131 .50522 1 0 Msboxa [(0.6)] .01131 .60332 1 0 Msboxa [(U)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .2619 .01472 m .2619 .02097 L s P [(2)] .2619 .01472 0 2 Mshowa p .002 w .5 .01472 m .5 .02097 L s P [(4)] .5 .01472 0 2 Mshowa p .002 w .7381 .01472 m .7381 .02097 L s P [(6)] .7381 .01472 0 2 Mshowa p .002 w .97619 .01472 m .97619 .02097 L s P [(8)] .97619 .01472 0 2 Mshowa p .001 w .07143 .01472 m .07143 .01847 L s P p .001 w .11905 .01472 m .11905 .01847 L s P p .001 w .16667 .01472 m .16667 .01847 L s P p .001 w .21429 .01472 m .21429 .01847 L s P p .001 w .30952 .01472 m .30952 .01847 L s P p .001 w .35714 .01472 m .35714 .01847 L s P p .001 w .40476 .01472 m .40476 .01847 L s P p .001 w .45238 .01472 m .45238 .01847 L s P p .001 w .54762 .01472 m .54762 .01847 L s P p .001 w .59524 .01472 m .59524 .01847 L s P p .001 w .64286 .01472 m .64286 .01847 L s P p .001 w .69048 .01472 m .69048 .01847 L s P p .001 w .78571 .01472 m .78571 .01847 L s P p .001 w .83333 .01472 m .83333 .01847 L s P p .001 w .88095 .01472 m .88095 .01847 L s P p .001 w .92857 .01472 m .92857 .01847 L s P [(Pizzas)] 1.025 .01472 -1 0 Mshowa p .002 w 0 .01472 m 1 .01472 L s P [(Marginal utility of pizzas)] .5 .61803 0 -2 0 0 1 Mouter Mrotshowa p .002 w .02381 .11282 m .03006 .11282 L s P [(0.1)] .01131 .11282 1 0 Mshowa p .002 w .02381 .21092 m .03006 .21092 L s P [(0.2)] .01131 .21092 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(0.3)] .01131 .30902 1 0 Mshowa p .002 w .02381 .40712 m .03006 .40712 L s P [(0.4)] .01131 .40712 1 0 Mshowa p .002 w .02381 .50522 m .03006 .50522 L s P [(0.5)] .01131 .50522 1 0 Mshowa p .002 w .02381 .60332 m .03006 .60332 L s P [(0.6)] .01131 .60332 1 0 Mshowa p .001 w .02381 .03434 m .02756 .03434 L s P p .001 w .02381 .05396 m .02756 .05396 L s P p .001 w .02381 .07358 m .02756 .07358 L s P p .001 w .02381 .0932 m .02756 .0932 L s P p .001 w .02381 .13244 m .02756 .13244 L s P p .001 w .02381 .15206 m .02756 .15206 L s P p .001 w .02381 .17168 m .02756 .17168 L s P p .001 w .02381 .1913 m .02756 .1913 L s P p .001 w .02381 .23054 m .02756 .23054 L s P p .001 w .02381 .25016 m .02756 .25016 L s P p .001 w .02381 .26978 m .02756 .26978 L s P p .001 w .02381 .2894 m .02756 .2894 L s P p .001 w .02381 .32864 m .02756 .32864 L s P p .001 w .02381 .34826 m .02756 .34826 L s P p .001 w .02381 .36788 m .02756 .36788 L s P p .001 w .02381 .3875 m .02756 .3875 L s P p .001 w .02381 .42674 m .02756 .42674 L s P p .001 w .02381 .44636 m .02756 .44636 L s P p .001 w .02381 .46598 m .02756 .46598 L s P p .001 w .02381 .4856 m .02756 .4856 L s P p .001 w .02381 .52484 m .02756 .52484 L s P p .001 w .02381 .54446 m .02756 .54446 L s P p .001 w .02381 .56408 m .02756 .56408 L s P p .001 w .02381 .5837 m .02756 .5837 L s P [(U)] .02381 .61803 0 -4 Mshowa p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 0 0 1 r p .015 w .14286 .60332 m .16022 .52841 L .17758 .47041 L .19494 .42418 L .2123 .38646 L .24702 .32864 L .28175 .28638 L .31647 .25415 L .35119 .22875 L .38591 .20823 L .42063 .1913 L .45536 .17709 L .49008 .165 L .5248 .15458 L .55952 .14552 L .59425 .13755 L .62897 .13051 L .66369 .12422 L .69841 .11859 L .73313 .1135 L .76786 .10889 L .80258 .10469 L .8373 .10085 L .87202 .09733 L .90675 .09408 L .94147 .09107 L .97619 .08829 L s P P % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; nohscroll; ] d) For total utility equal to 1.27, graph the relationship between M and P, measuring M on the vertical axis and P on the horizontal axis. This curve is called an indifference curve. :[font = input; preserveAspect; startGroup; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] f1[P_] = Exp[(1.27 - .4 Log[P])/.6] :[font = output; inactive; formatted; output; endGroup; nowordwrap; ] E^(1.666666666666667*(1.27 - 0.4*Log[P])) ;[o] 1.66667 (1.27 - 0.4 Log[P]) E :[font = input; preserveAspect; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] Plot[f1[P],{P,0,8}, PlotRange->{0,8}, PlotStyle->{{Blue,Thickness[0.015]}}, AxesLabel->{"Pizza","Movies"}, PlotLabel->"Indifference Curve"]; :[font = postscript; inactive; output; endGroup; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 185; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.119048 0 0.0772542 [ [(0)] .02381 0 0 2 Msboxa [(2)] .2619 0 0 2 Msboxa [(4)] .5 0 0 2 Msboxa [(6)] .7381 0 0 2 Msboxa [(8)] .97619 0 0 2 Msboxa [(Pizza)] 1.025 0 -1 0 Msboxa [(Indifference Curve)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(1)] .01131 .07725 1 0 Msboxa [(2)] .01131 .15451 1 0 Msboxa [(3)] .01131 .23176 1 0 Msboxa [(4)] .01131 .30902 1 0 Msboxa [(5)] .01131 .38627 1 0 Msboxa [(6)] .01131 .46353 1 0 Msboxa [(7)] .01131 .54078 1 0 Msboxa [(8)] .01131 .61803 1 0 Msboxa [(Movies)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .2619 0 m .2619 .00625 L s P [(2)] .2619 0 0 2 Mshowa p .002 w .5 0 m .5 .00625 L s P [(4)] .5 0 0 2 Mshowa p .002 w .7381 0 m .7381 .00625 L s P [(6)] .7381 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(8)] .97619 0 0 2 Mshowa p .001 w .07143 0 m .07143 .00375 L s P p .001 w .11905 0 m .11905 .00375 L s P p .001 w .16667 0 m .16667 .00375 L s P p .001 w .21429 0 m .21429 .00375 L s P p .001 w .30952 0 m .30952 .00375 L s P p .001 w .35714 0 m .35714 .00375 L s P p .001 w .40476 0 m .40476 .00375 L s P p .001 w .45238 0 m .45238 .00375 L s P p .001 w .54762 0 m .54762 .00375 L s P p .001 w .59524 0 m .59524 .00375 L s P p .001 w .64286 0 m .64286 .00375 L s P p .001 w .69048 0 m .69048 .00375 L s P p .001 w .78571 0 m .78571 .00375 L s P p .001 w .83333 0 m .83333 .00375 L s P p .001 w .88095 0 m .88095 .00375 L s P p .001 w .92857 0 m .92857 .00375 L s P [(Pizza)] 1.025 0 -1 0 Mshowa p .002 w 0 0 m 1 0 L s P [(Indifference Curve)] .5 .61803 0 -2 0 0 1 Mouter Mrotshowa p .002 w .02381 .07725 m .03006 .07725 L s P [(1)] .01131 .07725 1 0 Mshowa p .002 w .02381 .15451 m .03006 .15451 L s P [(2)] .01131 .15451 1 0 Mshowa p .002 w .02381 .23176 m .03006 .23176 L s P [(3)] .01131 .23176 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(4)] .01131 .30902 1 0 Mshowa p .002 w .02381 .38627 m .03006 .38627 L s P [(5)] .01131 .38627 1 0 Mshowa p .002 w .02381 .46353 m .03006 .46353 L s P [(6)] .01131 .46353 1 0 Mshowa p .002 w .02381 .54078 m .03006 .54078 L s P [(7)] .01131 .54078 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(8)] .01131 .61803 1 0 Mshowa p .001 w .02381 .01545 m .02756 .01545 L s P p .001 w .02381 .0309 m .02756 .0309 L s P p .001 w .02381 .04635 m .02756 .04635 L s P p .001 w .02381 .0618 m .02756 .0618 L s P p .001 w .02381 .09271 m .02756 .09271 L s P p .001 w .02381 .10816 m .02756 .10816 L s P p .001 w .02381 .12361 m .02756 .12361 L s P p .001 w .02381 .13906 m .02756 .13906 L s P p .001 w .02381 .16996 m .02756 .16996 L s P p .001 w .02381 .18541 m .02756 .18541 L s P p .001 w .02381 .20086 m .02756 .20086 L s P p .001 w .02381 .21631 m .02756 .21631 L s P p .001 w .02381 .24721 m .02756 .24721 L s P p .001 w .02381 .26266 m .02756 .26266 L s P p .001 w .02381 .27812 m .02756 .27812 L s P p .001 w .02381 .29357 m .02756 .29357 L s P p .001 w .02381 .32447 m .02756 .32447 L s P p .001 w .02381 .33992 m .02756 .33992 L s P p .001 w .02381 .35537 m .02756 .35537 L s P p .001 w .02381 .37082 m .02756 .37082 L s P p .001 w .02381 .40172 m .02756 .40172 L s P p .001 w .02381 .41717 m .02756 .41717 L s P p .001 w .02381 .43262 m .02756 .43262 L s P p .001 w .02381 .44807 m .02756 .44807 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .49443 m .02756 .49443 L s P p .001 w .02381 .50988 m .02756 .50988 L s P p .001 w .02381 .52533 m .02756 .52533 L s P p .001 w .02381 .55623 m .02756 .55623 L s P p .001 w .02381 .57168 m .02756 .57168 L s P p .001 w .02381 .58713 m .02756 .58713 L s P p .001 w .02381 .60258 m .02756 .60258 L s P [(Movies)] .02381 .61803 0 -4 Mshowa p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 0 0 1 r p .015 w s s s s s s s s s s s s s s s s s s s s s s .15028 .61803 m .1627 .57883 L s .1627 .57883 m .18254 .52953 L .22222 .45633 L .2619 .4041 L .30159 .36464 L .34127 .33358 L .38095 .30839 L .42063 .28747 L .46032 .26977 L .5 .25457 L .53968 .24134 L .57937 .22971 L .61905 .21938 L .65873 .21014 L .69841 .20182 L .7381 .19427 L .77778 .18739 L .81746 .1811 L .85714 .1753 L .89683 .16995 L .93651 .16498 L .97619 .16037 L s P P % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; nohscroll; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; plain; fontName = "Times New Roman"; fontSize = 12; ] :[font = text; inactive; preserveAspect; nohscroll; ] e) Repeat step d for utility levels 1.46 and 1.61, making an indifference map. :[font = input; preserveAspect; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] Clear[f2,P] f2[P_] = Exp[(1.46 - 0.4 Log[P])/.6]; f3[P_] = Exp[(1.61 - 0.4 Log[P])/.6]; Plot[{f1[P], f2[P], f3[P]},{P,0,8}, PlotRange->{0,10}, PlotStyle->{{Blue,Thickness[0.01]}, {Red,Thickness[0.01]}, {Green,Thickness[0.01]}}, AxesLabel->{"Pizza","Movies"}, PlotLabel->"Indifference Map"]; :[font = postscript; inactive; output; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 185; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.119048 0 0.0618034 [ [(0)] .02381 0 0 2 Msboxa [(2)] .2619 0 0 2 Msboxa [(4)] .5 0 0 2 Msboxa [(6)] .7381 0 0 2 Msboxa [(8)] .97619 0 0 2 Msboxa [(Pizza)] 1.025 0 -1 0 Msboxa [(Indifference Map)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(2)] .01131 .12361 1 0 Msboxa [(4)] .01131 .24721 1 0 Msboxa [(6)] .01131 .37082 1 0 Msboxa [(8)] .01131 .49443 1 0 Msboxa [(10)] .01131 .61803 1 0 Msboxa [(Movies)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .2619 0 m .2619 .00625 L s P [(2)] .2619 0 0 2 Mshowa p .002 w .5 0 m .5 .00625 L s P [(4)] .5 0 0 2 Mshowa p .002 w .7381 0 m .7381 .00625 L s P [(6)] .7381 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(8)] .97619 0 0 2 Mshowa p .001 w .07143 0 m .07143 .00375 L s P p .001 w .11905 0 m .11905 .00375 L s P p .001 w .16667 0 m .16667 .00375 L s P p .001 w .21429 0 m .21429 .00375 L s P p .001 w .30952 0 m .30952 .00375 L s P p .001 w .35714 0 m .35714 .00375 L s P p .001 w .40476 0 m .40476 .00375 L s P p .001 w .45238 0 m .45238 .00375 L s P p .001 w .54762 0 m .54762 .00375 L s P p .001 w .59524 0 m .59524 .00375 L s P p .001 w .64286 0 m .64286 .00375 L s P p .001 w .69048 0 m .69048 .00375 L s P p .001 w .78571 0 m .78571 .00375 L s P p .001 w .83333 0 m .83333 .00375 L s P p .001 w .88095 0 m .88095 .00375 L s P p .001 w .92857 0 m .92857 .00375 L s P [(Pizza)] 1.025 0 -1 0 Mshowa p .002 w 0 0 m 1 0 L s P [(Indifference Map)] .5 .61803 0 -2 0 0 1 Mouter Mrotshowa p .002 w .02381 .12361 m .03006 .12361 L s P [(2)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(4)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(6)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(8)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(10)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P [(Movies)] .02381 .61803 0 -4 Mshowa p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p 0 0 1 r p .01 w s s s s s s s s s s s s s s s s s s s s .11479 .61803 m .12302 .5795 L s .12302 .5795 m .14286 .51318 L .1627 .46306 L .18254 .42362 L .22222 .36506 L .2619 .32328 L .30159 .29171 L .34127 .26686 L .38095 .24671 L .42063 .22998 L .46032 .21582 L .5 .20366 L .53968 .19307 L .57937 .18377 L .61905 .1755 L .65873 .16811 L .69841 .16145 L .7381 .15542 L .77778 .14992 L .81746 .14488 L .85714 .14024 L .89683 .13596 L .93651 .13199 L .97619 .12829 L s P P p 1 0 0 r p .01 w s s s s s s s s s s s s s s s s s s s s s s s .16913 .61803 m .18254 .58144 L s .18254 .58144 m .22222 .50107 L .2619 .44372 L .30159 .40038 L .34127 .36628 L .38095 .33862 L .42063 .31565 L .46032 .29622 L .5 .27953 L .53968 .265 L .57937 .25223 L .61905 .24089 L .65873 .23074 L .69841 .2216 L .7381 .21332 L .77778 .20577 L .81746 .19885 L .85714 .19249 L .89683 .18661 L .93651 .18116 L .97619 .17609 L s P P p 0 1 0 r p .01 w s s s s s s s s s s s s s s s s s s s s s s s s s .23588 .61803 m .2619 .56975 L s .2619 .56975 m .30159 .5141 L .34127 .47032 L .38095 .4348 L .42063 .40531 L .46032 .38035 L .5 .35892 L .53968 .34027 L .57937 .32387 L .61905 .30931 L .65873 .29628 L .69841 .28454 L .7381 .27391 L .77778 .26421 L .81746 .25533 L .85714 .24716 L .89683 .23961 L .93651 .23261 L .97619 .2261 L s P P P % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; nohscroll; ] 2. Supppose the price of pizza is $3 and the price of a movie is $4. You have $25 per week to spend on pizzas and movies. Therefore, your budget constraint is: 25 = 3 P + 4 M :[font = text; inactive; preserveAspect; nohscroll; ] a) Graph your budget constraint with M on the vertical axis and P on the horizontal axis. :[font = input; preserveAspect; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] b1[P_] = (25 - 3 P)/4; Plot[b1[P],{P,0,10}, PlotRange->{0,8}, PlotStyle->{{Blue,Thickness[0.015]}}, AxesLabel->{"Pizza","Movies"}, PlotLabel->"Budget Line"]; :[font = postscript; inactive; output; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 185; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0 0.0772542 [ [(0)] .02381 0 0 2 Msboxa [(2)] .21429 0 0 2 Msboxa [(4)] .40476 0 0 2 Msboxa [(6)] .59524 0 0 2 Msboxa [(8)] .78571 0 0 2 Msboxa [(10)] .97619 0 0 2 Msboxa [(Pizza)] 1.025 0 -1 0 Msboxa [(Budget Line)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(1)] .01131 .07725 1 0 Msboxa [(2)] .01131 .15451 1 0 Msboxa [(3)] .01131 .23176 1 0 Msboxa [(4)] .01131 .30902 1 0 Msboxa [(5)] .01131 .38627 1 0 Msboxa [(6)] .01131 .46353 1 0 Msboxa [(7)] .01131 .54078 1 0 Msboxa [(8)] .01131 .61803 1 0 Msboxa [(Movies)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(10)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P [(Pizza)] 1.025 0 -1 0 Mshowa p .002 w 0 0 m 1 0 L s P [(Budget Line)] .5 .61803 0 -2 0 0 1 Mouter Mrotshowa p .002 w .02381 .07725 m .03006 .07725 L s P [(1)] .01131 .07725 1 0 Mshowa p .002 w .02381 .15451 m .03006 .15451 L s P [(2)] .01131 .15451 1 0 Mshowa p .002 w .02381 .23176 m .03006 .23176 L s P [(3)] .01131 .23176 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(4)] .01131 .30902 1 0 Mshowa p .002 w .02381 .38627 m .03006 .38627 L s P [(5)] .01131 .38627 1 0 Mshowa p .002 w .02381 .46353 m .03006 .46353 L s P [(6)] .01131 .46353 1 0 Mshowa p .002 w .02381 .54078 m .03006 .54078 L s P [(7)] .01131 .54078 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(8)] .01131 .61803 1 0 Mshowa p .001 w .02381 .01545 m .02756 .01545 L s P p .001 w .02381 .0309 m .02756 .0309 L s P p .001 w .02381 .04635 m .02756 .04635 L s P p .001 w .02381 .0618 m .02756 .0618 L s P p .001 w .02381 .09271 m .02756 .09271 L s P p .001 w .02381 .10816 m .02756 .10816 L s P p .001 w .02381 .12361 m .02756 .12361 L s P p .001 w .02381 .13906 m .02756 .13906 L s P p .001 w .02381 .16996 m .02756 .16996 L s P p .001 w .02381 .18541 m .02756 .18541 L s P p .001 w .02381 .20086 m .02756 .20086 L s P p .001 w .02381 .21631 m .02756 .21631 L s P p .001 w .02381 .24721 m .02756 .24721 L s P p .001 w .02381 .26266 m .02756 .26266 L s P p .001 w .02381 .27812 m .02756 .27812 L s P p .001 w .02381 .29357 m .02756 .29357 L s P p .001 w .02381 .32447 m .02756 .32447 L s P p .001 w .02381 .33992 m .02756 .33992 L s P p .001 w .02381 .35537 m .02756 .35537 L s P p .001 w .02381 .37082 m .02756 .37082 L s P p .001 w .02381 .40172 m .02756 .40172 L s P p .001 w .02381 .41717 m .02756 .41717 L s P p .001 w .02381 .43262 m .02756 .43262 L s P p .001 w .02381 .44807 m .02756 .44807 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .49443 m .02756 .49443 L s P p .001 w .02381 .50988 m .02756 .50988 L s P p .001 w .02381 .52533 m .02756 .52533 L s P p .001 w .02381 .55623 m .02756 .55623 L s P p .001 w .02381 .57168 m .02756 .57168 L s P p .001 w .02381 .58713 m .02756 .58713 L s P p .001 w .02381 .60258 m .02756 .60258 L s P [(Movies)] .02381 .61803 0 -4 Mshowa p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p 0 0 1 r p .015 w .02381 .48284 m .06349 .4587 L .10317 .43456 L .14286 .41041 L .18254 .38627 L .22222 .36213 L .2619 .33799 L .30159 .31385 L .34127 .2897 L .38095 .26556 L .42063 .24142 L .46032 .21728 L .5 .19314 L .53968 .16899 L .57937 .14485 L .61905 .12071 L .65873 .09657 L .69841 .07243 L .7381 .04828 L .77778 .02414 L s .81746 0 m .77778 .02414 L s s s s s s P P % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; nohscroll; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; plain; fontName = "Times New Roman"; fontSize = 12; ] :[font = text; inactive; preserveAspect; nohscroll; ] b) Increase the budget to 30 and add this new constraint. :[font = input; preserveAspect; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] b2[P_] = (30 - 3 P)/4; Plot[{b1[P],b2[P]},{P,0,10}, PlotRange->{0,8}, PlotStyle->{{Blue,Thickness[0.01]},{Green,Thickness[0.01]}}, AxesLabel->{"Pizza","Movies"}, PlotLabel->"Budget Lines"]; :[font = postscript; inactive; output; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 185; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0 0.0772542 [ [(0)] .02381 0 0 2 Msboxa [(2)] .21429 0 0 2 Msboxa [(4)] .40476 0 0 2 Msboxa [(6)] .59524 0 0 2 Msboxa [(8)] .78571 0 0 2 Msboxa [(10)] .97619 0 0 2 Msboxa [(Pizza)] 1.025 0 -1 0 Msboxa [(Budget Lines)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(1)] .01131 .07725 1 0 Msboxa [(2)] .01131 .15451 1 0 Msboxa [(3)] .01131 .23176 1 0 Msboxa [(4)] .01131 .30902 1 0 Msboxa [(5)] .01131 .38627 1 0 Msboxa [(6)] .01131 .46353 1 0 Msboxa [(7)] .01131 .54078 1 0 Msboxa [(8)] .01131 .61803 1 0 Msboxa [(Movies)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .21429 0 m .21429 .00625 L s P [(2)] .21429 0 0 2 Mshowa p .002 w .40476 0 m .40476 .00625 L s P [(4)] .40476 0 0 2 Mshowa p .002 w .59524 0 m .59524 .00625 L s P [(6)] .59524 0 0 2 Mshowa p .002 w .78571 0 m .78571 .00625 L s P [(8)] .78571 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(10)] .97619 0 0 2 Mshowa p .001 w .0619 0 m .0619 .00375 L s P p .001 w .1 0 m .1 .00375 L s P p .001 w .1381 0 m .1381 .00375 L s P p .001 w .17619 0 m .17619 .00375 L s P p .001 w .25238 0 m .25238 .00375 L s P p .001 w .29048 0 m .29048 .00375 L s P p .001 w .32857 0 m .32857 .00375 L s P p .001 w .36667 0 m .36667 .00375 L s P p .001 w .44286 0 m .44286 .00375 L s P p .001 w .48095 0 m .48095 .00375 L s P p .001 w .51905 0 m .51905 .00375 L s P p .001 w .55714 0 m .55714 .00375 L s P p .001 w .63333 0 m .63333 .00375 L s P p .001 w .67143 0 m .67143 .00375 L s P p .001 w .70952 0 m .70952 .00375 L s P p .001 w .74762 0 m .74762 .00375 L s P p .001 w .82381 0 m .82381 .00375 L s P p .001 w .8619 0 m .8619 .00375 L s P p .001 w .9 0 m .9 .00375 L s P p .001 w .9381 0 m .9381 .00375 L s P [(Pizza)] 1.025 0 -1 0 Mshowa p .002 w 0 0 m 1 0 L s P [(Budget Lines)] .5 .61803 0 -2 0 0 1 Mouter Mrotshowa p .002 w .02381 .07725 m .03006 .07725 L s P [(1)] .01131 .07725 1 0 Mshowa p .002 w .02381 .15451 m .03006 .15451 L s P [(2)] .01131 .15451 1 0 Mshowa p .002 w .02381 .23176 m .03006 .23176 L s P [(3)] .01131 .23176 1 0 Mshowa p .002 w .02381 .30902 m .03006 .30902 L s P [(4)] .01131 .30902 1 0 Mshowa p .002 w .02381 .38627 m .03006 .38627 L s P [(5)] .01131 .38627 1 0 Mshowa p .002 w .02381 .46353 m .03006 .46353 L s P [(6)] .01131 .46353 1 0 Mshowa p .002 w .02381 .54078 m .03006 .54078 L s P [(7)] .01131 .54078 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(8)] .01131 .61803 1 0 Mshowa p .001 w .02381 .01545 m .02756 .01545 L s P p .001 w .02381 .0309 m .02756 .0309 L s P p .001 w .02381 .04635 m .02756 .04635 L s P p .001 w .02381 .0618 m .02756 .0618 L s P p .001 w .02381 .09271 m .02756 .09271 L s P p .001 w .02381 .10816 m .02756 .10816 L s P p .001 w .02381 .12361 m .02756 .12361 L s P p .001 w .02381 .13906 m .02756 .13906 L s P p .001 w .02381 .16996 m .02756 .16996 L s P p .001 w .02381 .18541 m .02756 .18541 L s P p .001 w .02381 .20086 m .02756 .20086 L s P p .001 w .02381 .21631 m .02756 .21631 L s P p .001 w .02381 .24721 m .02756 .24721 L s P p .001 w .02381 .26266 m .02756 .26266 L s P p .001 w .02381 .27812 m .02756 .27812 L s P p .001 w .02381 .29357 m .02756 .29357 L s P p .001 w .02381 .32447 m .02756 .32447 L s P p .001 w .02381 .33992 m .02756 .33992 L s P p .001 w .02381 .35537 m .02756 .35537 L s P p .001 w .02381 .37082 m .02756 .37082 L s P p .001 w .02381 .40172 m .02756 .40172 L s P p .001 w .02381 .41717 m .02756 .41717 L s P p .001 w .02381 .43262 m .02756 .43262 L s P p .001 w .02381 .44807 m .02756 .44807 L s P p .001 w .02381 .47898 m .02756 .47898 L s P p .001 w .02381 .49443 m .02756 .49443 L s P p .001 w .02381 .50988 m .02756 .50988 L s P p .001 w .02381 .52533 m .02756 .52533 L s P p .001 w .02381 .55623 m .02756 .55623 L s P p .001 w .02381 .57168 m .02756 .57168 L s P p .001 w .02381 .58713 m .02756 .58713 L s P p .001 w .02381 .60258 m .02756 .60258 L s P [(Movies)] .02381 .61803 0 -4 Mshowa p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p 0 0 1 r p .01 w .02381 .48284 m .06349 .4587 L .10317 .43456 L .14286 .41041 L .18254 .38627 L .22222 .36213 L .2619 .33799 L .30159 .31385 L .34127 .2897 L .38095 .26556 L .42063 .24142 L .46032 .21728 L .5 .19314 L .53968 .16899 L .57937 .14485 L .61905 .12071 L .65873 .09657 L .69841 .07243 L .7381 .04828 L .77778 .02414 L s .81746 0 m .77778 .02414 L s s s s s s P P p 0 1 0 r p .01 w .02381 .57941 m .06349 .55526 L .10317 .53112 L .14286 .50698 L .18254 .48284 L .22222 .4587 L .2619 .43456 L .30159 .41041 L .34127 .38627 L .38095 .36213 L .42063 .33799 L .46032 .31385 L .5 .2897 L .53968 .26556 L .57937 .24142 L .61905 .21728 L .65873 .19314 L .69841 .16899 L .7381 .14485 L .77778 .12071 L .81746 .09657 L .85714 .07243 L .89683 .04828 L .93651 .02414 L .97619 0 L s P P P % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; nohscroll; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; plain; fontName = "Times New Roman"; fontSize = 12; ] :[font = text; inactive; preserveAspect; nohscroll; ] c) Repeat step b for a budget of $35. :[font = input; preserveAspect; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] b3[P_] = (35 - 3 P)/4; Plot[{b1[P],b2[P],b3[P]},{P,0,12}, PlotRange->{0,10}, PlotStyle->{{Blue,Thickness[0.01]}, {Green,Thickness[0.010]},{Red,Thickness[0.01]}}, AxesLabel->{"Pizza","Movies"}, PlotLabel->"Budget Lines"]; :[font = postscript; inactive; output; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 185; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0793651 0 0.0618034 [ [(0)] .02381 0 0 2 Msboxa [(2)] .18254 0 0 2 Msboxa [(4)] .34127 0 0 2 Msboxa [(6)] .5 0 0 2 Msboxa [(8)] .65873 0 0 2 Msboxa [(10)] .81746 0 0 2 Msboxa [(12)] .97619 0 0 2 Msboxa [(Pizza)] 1.025 0 -1 0 Msboxa [(Budget Lines)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(2)] .01131 .12361 1 0 Msboxa [(4)] .01131 .24721 1 0 Msboxa [(6)] .01131 .37082 1 0 Msboxa [(8)] .01131 .49443 1 0 Msboxa [(10)] .01131 .61803 1 0 Msboxa [(Movies)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .18254 0 m .18254 .00625 L s P [(2)] .18254 0 0 2 Mshowa p .002 w .34127 0 m .34127 .00625 L s P [(4)] .34127 0 0 2 Mshowa p .002 w .5 0 m .5 .00625 L s P [(6)] .5 0 0 2 Mshowa p .002 w .65873 0 m .65873 .00625 L s P [(8)] .65873 0 0 2 Mshowa p .002 w .81746 0 m .81746 .00625 L s P [(10)] .81746 0 0 2 Mshowa p .002 w .97619 0 m .97619 .00625 L s P [(12)] .97619 0 0 2 Mshowa p .001 w .05556 0 m .05556 .00375 L s P p .001 w .0873 0 m .0873 .00375 L s P p .001 w .11905 0 m .11905 .00375 L s P p .001 w .15079 0 m .15079 .00375 L s P p .001 w .21429 0 m .21429 .00375 L s P p .001 w .24603 0 m .24603 .00375 L s P p .001 w .27778 0 m .27778 .00375 L s P p .001 w .30952 0 m .30952 .00375 L s P p .001 w .37302 0 m .37302 .00375 L s P p .001 w .40476 0 m .40476 .00375 L s P p .001 w .43651 0 m .43651 .00375 L s P p .001 w .46825 0 m .46825 .00375 L s P p .001 w .53175 0 m .53175 .00375 L s P p .001 w .56349 0 m .56349 .00375 L s P p .001 w .59524 0 m .59524 .00375 L s P p .001 w .62698 0 m .62698 .00375 L s P p .001 w .69048 0 m .69048 .00375 L s P p .001 w .72222 0 m .72222 .00375 L s P p .001 w .75397 0 m .75397 .00375 L s P p .001 w .78571 0 m .78571 .00375 L s P p .001 w .84921 0 m .84921 .00375 L s P p .001 w .88095 0 m .88095 .00375 L s P p .001 w .9127 0 m .9127 .00375 L s P p .001 w .94444 0 m .94444 .00375 L s P [(Pizza)] 1.025 0 -1 0 Mshowa p .002 w 0 0 m 1 0 L s P [(Budget Lines)] .5 .61803 0 -2 0 0 1 Mouter Mrotshowa p .002 w .02381 .12361 m .03006 .12361 L s P [(2)] .01131 .12361 1 0 Mshowa p .002 w .02381 .24721 m .03006 .24721 L s P [(4)] .01131 .24721 1 0 Mshowa p .002 w .02381 .37082 m .03006 .37082 L s P [(6)] .01131 .37082 1 0 Mshowa p .002 w .02381 .49443 m .03006 .49443 L s P [(8)] .01131 .49443 1 0 Mshowa p .002 w .02381 .61803 m .03006 .61803 L s P [(10)] .01131 .61803 1 0 Mshowa p .001 w .02381 .02472 m .02756 .02472 L s P p .001 w .02381 .04944 m .02756 .04944 L s P p .001 w .02381 .07416 m .02756 .07416 L s P p .001 w .02381 .09889 m .02756 .09889 L s P p .001 w .02381 .14833 m .02756 .14833 L s P p .001 w .02381 .17305 m .02756 .17305 L s P p .001 w .02381 .19777 m .02756 .19777 L s P p .001 w .02381 .22249 m .02756 .22249 L s P p .001 w .02381 .27193 m .02756 .27193 L s P p .001 w .02381 .29666 m .02756 .29666 L s P p .001 w .02381 .32138 m .02756 .32138 L s P p .001 w .02381 .3461 m .02756 .3461 L s P p .001 w .02381 .39554 m .02756 .39554 L s P p .001 w .02381 .42026 m .02756 .42026 L s P p .001 w .02381 .44498 m .02756 .44498 L s P p .001 w .02381 .46971 m .02756 .46971 L s P p .001 w .02381 .51915 m .02756 .51915 L s P p .001 w .02381 .54387 m .02756 .54387 L s P p .001 w .02381 .56859 m .02756 .56859 L s P p .001 w .02381 .59331 m .02756 .59331 L s P [(Movies)] .02381 .61803 0 -4 Mshowa p .002 w .02381 0 m .02381 .61803 L s P P 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath p p 0 0 1 r p .01 w .02381 .38627 m .06349 .36309 L .10317 .33992 L .14286 .31674 L .18254 .29357 L .22222 .27039 L .2619 .24721 L .30159 .22404 L .34127 .20086 L .38095 .17768 L .42063 .15451 L .46032 .13133 L .5 .10816 L .53968 .08498 L .57937 .0618 L .61905 .03863 L .65873 .01545 L s .68519 0 m .65873 .01545 L s s s s s s s s s P P p 0 1 0 r p .01 w .02381 .46353 m .06349 .44035 L .10317 .41717 L .14286 .394 L .18254 .37082 L .22222 .34764 L .2619 .32447 L .30159 .30129 L .34127 .27812 L .38095 .25494 L .42063 .23176 L .46032 .20859 L .5 .18541 L .53968 .16223 L .57937 .13906 L .61905 .11588 L .65873 .09271 L .69841 .06953 L .7381 .04635 L .77778 .02318 L .81746 0 L s s s s s P P p 1 0 0 r p .01 w .02381 .54078 m .06349 .5176 L .10317 .49443 L .14286 .47125 L .18254 .44807 L .22222 .4249 L .2619 .40172 L .30159 .37855 L .34127 .35537 L .38095 .33219 L .42063 .30902 L .46032 .28584 L .5 .26266 L .53968 .23949 L .57937 .21631 L .61905 .19314 L .65873 .16996 L .69841 .14678 L .7381 .12361 L .77778 .10043 L .81746 .07725 L .85714 .05408 L .89683 .0309 L .93651 .00773 L s .94974 0 m .93651 .00773 L s s P P P % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; nohscroll; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 0; fontColorGreen = 0; fontColorBlue = 32768; plain; fontName = "Times New Roman"; fontSize = 17; ] 3. Add your budget lines from part 2 to your indifference map in part 1. Are there any points of tangency? The points of tangency are your income expansion path. :[font = input; preserveAspect; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] Plot[{f1[P],f2[P],f3[P],b1[P],b2[P],b3[P]},{P,0,13}, PlotRange->{0,13}, PlotStyle->{{Blue,Thickness[0.01]}, {Red,Thickness[0.01]}, {Green,Thickness[0.01]}, {Yellow,Thickness[0.01]},{Purple,Thickness[0.01]}, {Black,Thickness[0.01]}}, AxesLabel->{"Pizza","Movies"}, PlotLabel->"Income Expansion Path"]; :[font = postscript; inactive; output; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 185; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0732601 1.04083e-17 0.0475411 [ [(0)] .02381 0 0 2 Msboxa [(2)] .17033 0 0 2 Msboxa [(4)] .31685 0 0 2 Msboxa [(6)] .46337 0 0 2 Msboxa [(8)] .60989 0 0 2 Msboxa [(10)] .75641 0 0 2 Msboxa [(12)] .90293 0 0 2 Msboxa [(Pizza)] 1.025 0 -1 0 Msboxa [(Income Expansion Path)] .5 .61803 0 -2 0 0 1 Mouter Mrotsboxa [(2)] .01131 .09508 1 0 Msboxa [(4)] .01131 .19016 1 0 Msboxa [(6)] .01131 .28525 1 0 Msboxa [(8)] .01131 .38033 1 0 Msboxa [(10)] .01131 .47541 1 0 Msboxa [(12)] .01131 .57049 1 0 Msboxa [(Movies)] .02381 .61803 0 -4 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .02381 0 m .02381 .00625 L s P [(0)] .02381 0 0 2 Mshowa p .002 w .17033 0 m .17033 .00625 L s P [(2)] .17033 0 0 2 Mshowa p .002 w .31685 0 m .31685 .00625 L s P [(4)] .31685 0 0 2 Mshowa p .002 w .46337 0 m .46337 .00625 L s P [(6)] .46337 0 0 2 Mshowa p .002 w .60989 0 m .60989 .00625 L s P [(8)] .60989 0 0 2 Mshowa p .002 w .75641 0 m .75641 .00625 L s P [(10)] .75641 0 0 2 Mshowa p .002 w .90293 0 m .90293 .00625 L s 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Suppose the price of pizza falls to $2, while your budget remains at $25 and the price of movies at $4 a.) Graph the old and new budget lines. :[font = input; preserveAspect; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] b4[P_] = (25 - 2 P)/4; Plot[{b1[P],b4[P]},{P,0,13}, PlotRange->{0,10}, PlotStyle->{{Blue,Thickness[0.01]}, {Red,Thickness[0.01]}}, AxesLabel->{"Pizza","Movies"}, PlotLabel->"Budget Lines"]; :[font = postscript; inactive; output; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 185; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0732601 0 0.0618034 [ [(0)] .02381 0 0 2 Msboxa [(2)] .17033 0 0 2 Msboxa [(4)] .31685 0 0 2 Msboxa [(6)] .46337 0 0 2 Msboxa [(8)] .60989 0 0 2 Msboxa [(10)] .75641 0 0 2 Msboxa [(12)] .90293 0 0 2 Msboxa [(Pizza)] 1.025 0 -1 0 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.00375 L s P p .001 w .19963 0 m .19963 .00375 L s P p .001 w .22894 0 m .22894 .00375 L s P p .001 w .25824 0 m .25824 .00375 L s P p .001 w .28755 0 m .28755 .00375 L s P p .001 w .34615 0 m .34615 .00375 L s P p .001 w .37546 0 m .37546 .00375 L s P p .001 w .40476 0 m .40476 .00375 L s P p .001 w .43407 0 m .43407 .00375 L s P p .001 w .49267 0 m .49267 .00375 L s P p .001 w .52198 0 m .52198 .00375 L s P p .001 w .55128 0 m .55128 .00375 L s P p .001 w .58059 0 m .58059 .00375 L s P p .001 w .63919 0 m .63919 .00375 L s P p .001 w .6685 0 m .6685 .00375 L s P p .001 w .6978 0 m .6978 .00375 L s P p .001 w .72711 0 m .72711 .00375 L s P p .001 w .78571 0 m .78571 .00375 L s P p .001 w .81502 0 m .81502 .00375 L s P p .001 w .84432 0 m .84432 .00375 L s P p .001 w .87363 0 m .87363 .00375 L s P p .001 w .93223 0 m .93223 .00375 L s P p .001 w .96154 0 m .96154 .00375 L s P p .001 w .99084 0 m .99084 .00375 L s P [(Pizza)] 1.025 0 -1 0 Mshowa p .002 w 0 0 m 1 0 L s P [(Budget Lines)] 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.53968 .16867 L .57937 .15193 L .61905 .13519 L .65873 .11846 L .69841 .10172 L .7381 .08498 L .77778 .06824 L .81746 .0515 L .85714 .03476 L .89683 .01803 L .93651 .00129 L s .93956 0 m .93651 .00129 L s s P P P % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; nohscroll; ] b) Add the indifference curves for utility levels 1.27 and 1.44. Are there points of tangency? :[font = input; preserveAspect; startGroup; nowordwrap; backColorRed = 65280; backColorGreen = 65280; backColorBlue = 65280; fontColorRed = 65280; fontColorGreen = 0; fontColorBlue = 0; bold; fontName = "Courier New"; fontSize = 12; ] f4[P_] = Exp[(1.44 - .4 Log[P])/.6] Plot[{f1[P],f4[P],b1[P],b4[P]},{P,0,13}, PlotRange->{0,13}, PlotStyle->{{Green,Thickness[0.01]}, {Yellow,Thickness[0.01]},{Blue,Thickness[0.01]}, {Red,Thickness[0.01]}}, AxesLabel->{"Pizza","Movies"}, PlotLabel->"Consumer Choice"]; :[font = output; inactive; formatted; output; nowordwrap; ] E^(1.666666666666667*(1.44 - 0.4*Log[P])) ;[o] 1.66667 (1.44 - 0.4 Log[P]) E :[font = postscript; inactive; output; endGroup; BITMAP; PostScript; pictureLeft = 100; pictureTop = 0; pictureWidth = 300; pictureHeight = 185; nowordwrap; ] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0732601 1.04083e-17 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