Economics 172

Fall 2007

Due Friday October 26

Homework 7

 

Chapter 8

 

Questions  2,  6,  8,  11, (You do not need to draw graphs for any of these in your answers, although you will need to think about average costs and doodle around with them to answer them correctly.)

 

2.   Suppose the marginal cost curve hit the price line at 2 different output levels .  If the MC curve is decreasing and it crosses the price line, by increasing output, MC would be falling and would be less than price.  The firm should expand. 

When the MC curve is rising and crosses the price line, if it produced more MC would be higher than price.  The firm should not expand production.

 

Using calculus:  Π(q) = R(q) – C(q)

Differentiate with respect to q:   Π’(q) = R’(q) – C’(q) where ’ means first derivative.

Profit maximization requires   Π’(q) = R’(q) – C’(q) = 0 or R’(q) = C’(q)

Now take the second derivative:    Π’’(q) = R’’(q) – C’’(q) 

Remember from calculus that a relative maximum occurs when f’’(x) < 0 and a relative minimum is when f’’(x) >0; that is, the function is at a relative maximum if the second derivative is negative and a minimum if it is positive.

So if R’’(q) - C’’(q) < 0, then profits will be maximized.  So when is R’’(q) < C’’(q)  ?  When the rate of change of MR is less than the rate of change of MC.  When MC crosses MR or price when MC is rising,  then R’’(q) =0 and C’’(q) >0. 

 

 

6.  The French government gives cheese producers a fixed amount regardless of how much cheese they produce.  This is like a reduction in fixed costs.  Firms in France will make a profit and entry will occur until there is no more profit to be made.  Since there are more firms, more cheese is produced and the LR supply curve of cheese will shift to the right.  More cheese, unlike this.

The answer to this problem is similar to Solved Problem 8.3 in the text, except it works in reverse.

8.  If the government passes a law requiring six month’s notice before shutting down a plan, that means that there are fewer short run variable costs for the firm.  This increases the firm’s uncertainty as to whether it should start producing at all.   Some firms may not enter the market even if there are short run profits to be earned.  Think this is fanciful?  Just look at what’s happened in France.  President Sarkozy wants to change the law to make it much easier to lay off new workers (those under 25) without any reason.  Unemployment rates among youth in France are about 25%.  Firms are reluctant to hire workers because it is nearly impossible to lay them off.  This increases the uncertainty to firms and they don’t hire as many people.

11.  If Arizona puts a tax per orange on its orange producers (and California does not), then the marginal and average variable cost curves for Arizona orange producers will rise.  Some Arizona producers will go out of business.  Orange prices will rise and that will attract entry into the California orange industry, since California producers will now be making economic profits.   Assuming no change in the cost of land in California, entry will occur until there are no more profits to be made.  In the limit, all Arizona firms will leave the market and only California firms will be left.  Then the long run industry supply curve is horizontal.    If California entry raises land prices in California, then the long run industry supply curve will be upward sloping and entry will continue until there are no more economic profits.  There will still be some Arizona orange production in this case.

 

 

 

1.  The ballpoint pen industry is a competitive industry in long run equilibrium and all pens sell for $2. 

a.  Assume that all firms have normally shaped average and marginal cost curves.  Show, using all relevant graphs the initial long run equilibrium situation for a representative firm in the ballpoint pen industry.  Be sure to show output level and all relevant costs. 

 

 

 

 

 

Ballpoint pens are manufactured in numerous factories all over the U.S. and can be easily shipped.  One of the companies that manufacture these pens, ClevePens is located in Cleveland, Ohio.   In order to raise revenue, the Cleveland City Council decides to put a tax of 20 cents per pen on the production of pens in factories located in the city.  

 

b. Show graphically and briefly discuss how this tax will affect the market price and quantity of ballpoint pens in the United States.

 

 

 

 

c. Show and briefly discuss how this tax will affect the price, quantity, and profits of ClevePens in the short run. 

 

Output will fall from q1 to q2.  The price ClevePens can charge in the market is unchanged because it is in a competitive market.   Profits will fall and be negative since AC>Price.

 

d.  Show graphically and briefly discuss how this tax will affect the price, quantity, and profits of ClevePens in the long run. 

 

2. (15) 7.  Overheard in a restaurant:  “My firm loses $2 on each unit of output we produce.  But we produce so much that we make up for that loss in volume.  Consequently we earn profits.”  Comment on the economic validity of this statement using graphical and verbal analysis.

 

If the P<ATC by $2, the firm is losing $2 on each unit of output.  Total profit must be average profit times the number of units produced, Q.  Q x -$2 must be negative.   The guy in the restaurant doesn’t know what he’s talking about. Graphically, it is part b of the above question.

 

Chapter 9 questions.

Questions 2, 6, 11

 

2.  The initial consumer surplus is the area bounded by gd and then over to the vertical axis and up to g.  The initial producer surplus is from d to h and up to where the dotted line intersects the y axis.

The new consumer surplus is gacf and producer surplus is fch.

The price ceiling (pc) on gasoline reduces welfare by the areas abd + bcd.

                  

           

 

 

6. The welfare loss due to the minimum wage is area abc. When the minimum is instituted, employment falls to L1 from L0. Because labor supply at the new higher wage increases to L2, unemployment is increased by the institution of the minimum. Because of the excess supply, less experienced workers are likely to be losers with the new policy. In addition, if discrimination exists on the basis of age, gender, or race, those workers in the less desired group are also likely to be hurt by the minimum wage.  Initial consumer surplus is wocw  (w is where the D curve intersects the vertical axis.  Initial producer surplus is woc to where the S curve intersects the y axis.  The new consumer surplus is ŵaw and producer surplus is ŵab to the y axis. 

                

           

 

 

1.  In the market for organs for transplant, such as kidneys and hearts, the price is constrained by law to equal zero.  Opposition to any type of remuneration for donating organs has been all but absolute from most physicians and legislators.  In no state can organs be sold or purchased.  Reliance on altruism, however, does not appear to be working.  (For more information about the problems that result, and how many people are waiting for transplants, go to UNOS.)   Relying on graphs, explain the effect that banning the sale or purchase of human organs has on producer surplus and consumer surplus.

 

 

Under the current system, the quantity of organs available is constrained to be Q1.  If there was a market, the quantity would be Q2.  The current consumer surplus is the triangle above the P1 line and the consumer surplus if there was a market would be the triangle above P2.