Economics 172

Spring 2006

Due Friday March 31

Homework 7

Chapter 8

 

Questions  2,  6,  8,  11,  13

2.  It is possible to have the MC curve hitting the price line at two different output levels.  When the MC is downward sloping and crosses the price line, increasing output means MC<MR, and the firm should expand output.  When the MC curve is upward sloping expanding output beyond MC = P (or MR) will reduce profit since MC>MR.

 

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 maxium 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.  A French government subsidy will not shift the marginal cost curve since the subsidy is a fixed amount independent of the output level.  It will shift the average total cost curve downward but not the average variable cost curve.  There will now be more cheese produced in the world than before at any price (the lower costs and higher profits attracts entry in France).  The worldwide supply curve of cheese shifts to the right and cheese prices fall.

 

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 happening in France today.  The government wants to pass a law making 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 Arizone 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.

 

13.  Start with the California price of p* and G*.  The tax raises the price to p* + 0. 15 but none is supplied since the California refineries can produce the reformulated version at p*.  Now a disaster hits the refineries and supply shifts to S’.  The equilibrium price will now be p’ if there is no tax and quantity would be GNI  (no imports).  But with the tax (which allows normal gas to be imported into California subject to a 15 cent tax) it is now cheaper to bring in the imported normal gas and pay the 15 cent tax than it is to pay the p’ price for the reformulated gas.  So consumers will pay p* plus 0.15.  The quantity demanded will be G’.   The new supply curve will be the S’ supply curve from the y axis up until it hits the S’ supply curve, then the supply curve is the horizonal line.  So California producers still produce some gas, but imports make up most of the sales of gas in California.

 

 

 

1.  In long run equilibrium, each firm in a perfectly competitive industry earns zero profit.  Why would anyone ever want to start a business in a perfectly competitive industry? 

 

If an entrepreneur thought she could produce the product at lower marginal (and average) costs than any other competitor, entry would occur because of the attempt to earn economic profits.

 

2.  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.

 

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