EconS 404, Week 1 Answers

Tracking the Economy - Historical Statistics:

• Using the data on real GDP as an estimate of the overall level of economic activity, explain what has happened to the PPF from 1960 to 1995.

The PPF shifted out, because real GDP has grown.

• Discuss what has happened to the relative position on the PPF which shows a tradeoff between government and other sectors of the economy.

The government share of the economy has fallen, meaning we've moved towards more private goods and less government goods as a share of the economy.

• Unemployment is a measure of efficiency - are we on the PPF or not. In which year did the economy shown the least inefficiency? In what year did it show the most inefficiency?

2000 - least inefficiency.  1975 - most inefficiency

PPF Application

The issue of the spotted owl was one of jobs versus environment.  Soceity sometimes faces a constraint where to preserve the environment jobs are lost.  In terms of this issue, many economist see the tradeoff as shown in the picture below.  We can choose point 1, more jobs and less environment, or point 2, more environment (spotted owls) and fewer jobs (thus fewer other goods).  Thus the cost of preserving the spotted owls is, in terms of opportunity cost, J1-J2 jobs, and the other goods associated with those jobs.

Technical Problems:

1.  Suppose you are policy maker faced with deciding how many public health nurses to employ.  The following table shows Total Benefit and Total Cost from different levels of employment.  Fill in the table, and answer the questions:

a)  What level of employment maximizes total benefit?  What level maximizes average benefit?  What level maximizes marginal benefit?  10, 1, 1.

b)  What level of employment maximizes total cost?  What level maximizes average cost?  What level maximizes marginal cost? 10, 10, 10

c)  What level of employment maximizes net benefit?  What is the relationship between marginal benefit and marginal cost at this level of employment?  Is there a relationship between average benefit and average cost at this level of employment? 7.  When employment is 7, MB exceeds MC, but if employment is 8, MB is less than MC, so when employment is 7, we essentially have MB equal to MC.  No.

d)  Why is cost 10 even when employment is zero?  We call this fixed cost.  If there were no fixed costs, all costs would be reduced by 10.  Does the presence of fixed costs change the optimal employment level?  Explain why or why not.  Cost is 10 even when employment is zero because there are costs the firm incurs even if no workers are employed.  The presence of fixed cost does not change the optimal employment level, since all total costs would reduce  by 10, but the MC (the change in total cost) would remain the same.

2.  Suppose as production manager you know that total revenue, R(Q) and total cost, C(Q) are given by the following functions, where Q is the output set (in thousands of units):

R(Q) = 1500Q - 4Q²     and     C(Q)=50+Q²

a)  Find the functions for profit (revenue - cost), marginal cost and marginal revenue.

Profit = 1500Q-4Q² -50-Q²  = -50+1500Q-5Q²

MC = 2Q

MR = 1500-8Q

b) Find the output which maximizes profit.  Find the value for marginal revenue and marginal cost at this output.  How are they related?

To maximize profit you set MR=MC, i.e., 2Q=1500-8Q.  Solving this for Q gives Q=150.

c)  Find the functions for average revenue, R(Q)/Q, and average cost, C(Q)/Q.  One of your staffers argues that output should continue until average revenue = average cost.  Why is this incorrect?

AR=1500-4Q and AC=50/Q + Q.  Suppose we set these equal, so 1500-4Q=50/Q+Q.  This is a quadratic function.  Multiplying through by Q gives 1500Q-4Q²=50+Q² which can be rewritten 5Q²-1500Q+50=0.  Using the quadratic formula, you can find that Q=0.0333337 or Q=299.9666667.  Although it is not exactly the answer, let's round these to 0 and 300.  Using 300, since the output of 0 is really irrelevant, we find that MC=600 and MR=-900, sot he additional profit from producing the last unit where AR=AC is -1500, which means profit goes down at with that unit.  The staffer is incorrect because this approach ignores marginal analysis.

3.  As a resource recovery expert you have been appointed your firm's recycling "czar".  The benefits to this program include a cleaner environment (social benefit), goodwill to your company, and direct revenue from the sales of certain recyclables.  The costs include direct labor and capital costs, and some costs associated with goods for which there is really no market for recycling.  In fact, sometimes you have to pay to get something recycled.  Your firm is interested in maximizing its net benefit from recycling.

a)  Using marginal analysis, explain what you would consider in setting up the program.

You should consider whether the marginal gain to your company exceeds the costs.

b)  Explain why society would probably want your firm to recycle more than it does.

A lot of the benefits from your company recycling fall outside direct gain to your company -- it falls to members of society from less resource use, etc.  Thus, societal gain exceeds the gain to your company, while all the costs fall on your company.  If the company recycles until MB=MC, it will be less than if recycling occurs until the social marginal benefit=MC.

4.  Related to question 5, suppose we have the following functions.  Q is the amount of recycling your firm does.

Social benefit from recycling:  S(Q) = 20Q

Firm's (private) benefit:  B(Q) = 80Q - 2Q²

Firm's cost:  C(Q) = 10 + 2Q²

a)  Determine the amount of recycling society would like to see your firm do.  Now find the amount it will actually do.  Why do they differ?

Total (societal) benefit = social benefit + firm benefit = 100Q-2Q² while the firm's benefit = 80Q-2Q².  From society's perspective MB=100-4Q while for the firm MB=80-4Q.  We show no societal cost, so in both cases MC=4Q.

Society:  100-4Q=4Q  implies Q=12.5

Firm:  80-4Q=4Q implies Q=10.

b)  Suppose tax credits lower the cost of recycling by 10 for each unit of Q.  How would that change your answers to a)? 

The firms cost function becomes 10+2Q²-10Q so its MC becomes 4Q-10.  Since the true cost of recycling hasn't changed, society's optimum remains the same.  But for the firm,

80-4Q=4Q-10 implies that Q=11.25.  What the firm would choose to recycle moves closer to what society would like.

c)  If instead of a tax credit lowering cost, the government directly paid your company 10 for each unit recycled, would it change your answer to the b)?  Explain.

No difference.  either way it lowers the MC (or increases the MB) by 10 per unit.