Limits, Alternatives, and Choices

The economic perspective

Lesson Overview

Goals

Students will be able to describe the relationships presented by the budget line.

Students will be able to describe the relationships presented with the Production Possibilities curve.

Students will be able to calculate a table and display a Production Possibilities curve.

Instructor Presentation

Micro-Economics and the Budget Line

In both the study of micro and macro Economics, we study how we deal with limited resources and the decisions we make on how to use the resources.  The terms used between Micro and Macro economics for these tradeoffs takes different names.  When studying Micro-Economics, we study choosing to consume one item (DVDs) versus consuming the other item ( Books ).  This tradeoff is what is called Budget Line.

data={{6,0},{5,2},{4,4},{3,6},{2,8},{1,10},{0,12}};
header = {"Units of DVDs","Units of Books"};
fulldata = Prepend[data,header];
TableForm[fulldata,TableAlignments->Center]
ListPlot[data,Joined->True,AxesLabel->{"Units of DVD's","Units of Book's"},Filling->Axis]

Reference:  McConnell  & Brue, Economics, Principles, Problems and Policies, Boston, McGraw - Hill, 7 th Edition, 2008

Figure 1.1  The budget line shows all the combinations of any two products that can be purchased given the prices of the products and the consumer' s money income.

Instructor Presentation

Macro-Economics Scarcity and Choice

Economics deals with limited resources and the decisions we make on how to use the resources.  When we choose to produce one item (Robots, for example), limited resources prevent us from producing the other item ( Pizzas ).  This tradeoff is what is called Opportunity Costs.

w=Graphics[{PointSize[0.03],Point[{{4.2,7.5}},VertexColors->{Green}]},Axes->True,AxesLabel->{"Pizza (thousands)",Robots}];
pts=Graphics[{{PointSize[0.02],
Point[{{0,10},{1,9},{2,7},{3,4},{4,0}}]},Text[Style["Attainable",16,Bold,Red],{2,2}],
Text[Style["Unattainable",16,Bold,Red],{7,8}],
Text[Style["W", 12,Green],{4.6,7.5}],
Text[Style["A", 12,Black,Bold],{0.2,10.3}],
Text[Style["B", 12,Black,Bold],{1.3,9.3}],
Text[Style["C", 12,Black,Bold],{2.2,7.2}],
Text[Style["D", 12,Black,Bold],{3.2,4.2}],
Text[Style["E", 12,Black,Bold],{4.1,0.4}]
},Axes->True,AxesLabel->{Pizza,Robots}];
lns=Plot[10-0.5x-0.5x^2,{x,0,4},Filling->Axis];

Show[{w,lns,pts}]

Reference :  McConnell  & Brue, Economics, Principles, Problems and Policies, Boston, McGraw - Hill, 7 th Edition, 2008

Figure 1.2  The production possibilities curve.  Each point on the production possibilities curve represents some maximum combination of two products that can be produced if resource are fully employed.  When an economy is operating on the curve, the economy is said to be efficient.  When the economy is operating within the curve, the economy is not 100 % efficient.  Points outside the curve, say W are Unattainable.

Concept Exploration

Law of Increasing Opportunity Cost

The Law of Increasing Opportunity Cost states that as we increase production on a particular product with each incremental increase, the opportunity cost to produce it rises. l

w=Graphics[{PointSize[0.03],Point[{{4.2,7.5}},VertexColors->{Green}]},Axes->True,AxesLabel->{"Pizza (thousands)",Robots}];
pts=Graphics[{{PointSize[0.02],
Point[{{0,10},{1,9},{2,7},{3,4},{4,0}}]},Text[Style["Attainable",16,Bold,Red],{2,2}],
Text[Style["Unattainable",16,Bold,Red],{7,8}],
Text[Style["W", 12,Green],{4.6,7.5}],
Text[Style["A", 12,Black,Bold],{0.2,10.3}],
Text[Style["B", 12,Black,Bold],{1.3,9.3}],
Text[Style["C", 12,Black,Bold],{2.2,7.2}],
Text[Style["D", 12,Black,Bold],{3.2,4.2}],
Text[Style["E", 12,Black,Bold],{4.1,0.4}]
},Axes->True,AxesLabel->{Pizza (thousands),Robots}];
lns=Plot[10-0.5x-0.5x^2,{x,0,4},Filling->Axis];

Show[{w,lns,pts}]

In the above example, to produce the first thousand pizzas, we have to give up producing 1 Robot. This can be identified as moving from point A to point B on the curve.  To produce the second thousand pizzas, we have to give up 2 additional Robots.  Moving from point B to point C on the curve.  This continues until, we find that to produce the 4 th thousands pizzas, we will have to give up 4 additional Robots.  This is a great illustration of Law of Increasing Opportunity Cost.

Unemployment and Growth

Any point inside the Production Possibilities Curve represents an inefficiency of the economy.  Point U in the below graph might be caused by unemployment of the potential work force.

w=Graphics[{PointSize[0.03],Point[{{1.0,4.0}},VertexColors->{Black}]},Axes->True,AxesLabel->{"Pizza (thousands)",Robots}];
pts=Graphics[{{PointSize[0.02],Point[{{0,10},{1,9},{2,7},{3,4},{4,0}}]},
Text[Style["Attainable",16,Bold,Red],{2,2}],
Text[Style["Unattainable",16,Bold,Red],{7,8}],
Text[Style["U",12,Black],{1.3,3.2}],
Text[Style["A", 12,Black,Bold],{0.2,10.3}],
Text[Style["B", 12,Black,Bold],{1.3,9.3}],
Text[Style["C", 12,Black,Bold],{2.2,7.2}],
Text[Style["D", 12,Black,Bold],{3.2,4.2}],
Text[Style["E", 12,Black,Bold],{4.1,0.4}],
Text[Style["↑",64,Green],{1.0,5.0}],
Text[Style["→",64,Green],{2.0,4.0}],
Text[Style["↗",64,Green],{2.0,5.0}]
},Axes->True,AxesLabel->{Pizza,Robots}];
lns=Plot[10-0.5x-0.5x^2,{x,0,4},Filling->Axis];

Show[{w,pts,lns}]

An economy in growth will move from point U toward the Production Possibility Curve.  This movement, represented by the green arrows, is determined through buyer demand.  The net is that the economy becomes more efficient.

A Growing Economy

In the real world, quantity and quality of resources and technology are not always fixed. New technologies allow us to substitute different resources to accomplish similar results, new sources of resources are found, demand changes allowing different resource allocation.  The net is that the economy then has the ability to expand

w=Graphics[{PointSize[0.03],Point[{{1.0,4.0}},VertexColors->{Black}]},Axes->True,AxesLabel->{"Pizza (thousands)",Robots}];
pts=Graphics[{{PointSize[0.02],Point[{{0,10},{1,9},{2,7},{3,4},{4,0}}]},
Text[Style["Attainable",16,Bold,Red],{2,2}],
Text[Style["Unattainable",16,Bold,Red],{7,8}],
Text[Style["U",12,Black],{1.3,3.2}],
Text[Style["A", 12,Black,Bold],{0.2,10.3}],
Text[Style["B", 12,Black,Bold],{1.3,9.3}],
Text[Style["C", 12,Black,Bold],{2.2,7.2}],
Text[Style["D", 12,Black,Bold],{3.2,4.2}],
Text[Style["E", 12,Black,Bold],{4.1,0.4}],
Text[Style["↑",64,Green],{2.0,10.0}],
Text[Style["→",64,Green],{6.0,2.0}]
},Axes->True,AxesLabel->{Pizza,Robots}];
lns=Plot[10-0.5x-0.5x^2,{x,0,4},Filling->Axis];
lns2=Plot[14-0.75x-0.125x^2,{x,0,8}];

Show[{w,pts,lns,lns2}]

Quick Quiz 1.2

Page 12:  McConnell and Brue

a: The production possibilities curve is bowed out from the origin.  Why?
		a1.  the marginal benefits of pizzas decline as more pizzas are consumed.
	      a2.  the curve gets steeper as we move from E to A.
	      a3.  it reflects the law of increasing opportunity costs.
	      a4.  resources are scarce.

b: The marginal opportunity cost of the second unit of pizza is:
		b1. 2 units of robots
	      b2. 3 units of robots
	      b3. 7 units of robots
	      b4. 9 units of robots

c: The total opportunity cost of 9 units of robots is:
		c1. 1 unit of pizza
	      c2. 2 units of pizza
	      c3. 3 units of pizza
	      c4. 4 units of pizza

d: All the points on this production possibilities curve necessarily represent:
		d1. society's optimal choice.
	      d2. less than full use of resources.
	      d3. unattainable levels of output.
	      d4. full employment.

Example 1

Suppose you won $15 on a lotto ticket at the local 7-Eleven and decide to spend all the wining on candy bars and bags of peanuts.  The price of candy bars is $0.75 and the price of peanuts is $1.50.

Construct a table showing the alternative combinations of the two products that are available:

data =Table[{peanuts,((15-1.50peanuts)/(.75)) },{peanuts,0,10}];
headers={"Peanuts","Candy Bars"};
fulldata=Prepend[data,headers];
TableForm[fulldata,TableAlignments->Center]

Plot the data in your table as a budget line in a graph:

ListPlot[data,Joined->True,AxesLabel->{"Peanuts","Candy Bars"},Filling->Axis]

Example 2

Below is a production possibilities table for consumer goods (automobiles) and capital goods (forklifts).

data={{0,30},{2,27},{4,21},{6,12},{8,0}};
header = {"Automobiles","Forklifts"};
fulldata=Prepend[data,header];
TableForm[fulldata,TableAlignments->Center]

Define the curve that represents the data set above.

FindFit[data,a s^2 + b s + c,{a,b,c},s]

Show these data graphically.  Upon what specific assumptions is this production possibilities curve based?

curve=Plot[-0.375 x^2 + -.75 x + 30,{x,0,8},Filling->Axis];
w=Graphics[{PointSize[0.08],Point[{{6.0,12}},VertexColors->{Red}]},Axes->True,AxesLabel->{"Automobiles","Forklifts"}];
Show[{w,curve}]

What are the assumptions that the production possibilities curve based?

If the economy is functioning at the red point on the chart, What is the cost of one more automobile? Two more automobiles?  How does the law of increasing opportunity costs effect your results?

If you were told that the economy is functioning by producing 3 Automobiles and 20 Forklifts, what could you conclude about the use of available resources?

Examples Answer Key

Example 2

What are the assumptions that the production possibilities curve based?

full employment.  Fixed resources and fixed technology.  Two products are all that can be produced.

If the economy is functioning at the red point on the chart, What is the cost of one more automobile? Two more automobiles?  How does the law of increasing opportunity costs effect your results?

curve=Plot[-0.375 x^2 + -.75 x + 30,{x,0,8},Filling->Axis];
x=7;
y7=-0.375 x^2 + -.75 x + 30;
x=8;
y8=-0.375 x^2 + -.75 x + 30;
w6=Graphics[{PointSize[0.08],Point[{{6.0,12}},VertexColors->{Red}]},Axes->True,AxesLabel->{"Automobiles","Forklifts"}];
w7=Graphics[{PointSize[0.08],Point[{{7.0,y7}},VertexColors->{Green}]}];
w8=Graphics[{PointSize[0.08],Point[{{8.0,y8}},VertexColors->{Yello}]}];
Show[{w6,w7,w8,curve}]

If you were told that the economy is functioning by producing 3 Automobiles and 20 Forklifts, what could you conclude about the use of available resources?

ppc=Plot[-0.375 x^2 + -.75 x + 30,{x,0,8}];
w=Graphics[{PointSize[0.08],Point[{{2.0,20}},VertexColors->{Red}]},Axes->True,AxesLabel->{"Automobiles","Forklifts"}];
Show[{w,ppc}]