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Problem 1


A perfectly competitive firm has total revenue and total cost curves given by:

TR = 100Q

TC = 5,000 + 2Q + 0.2 Q2

a.       Find the profit-maximizing output for this firm.


b.      What profit does the firm make?



Answer: The profit function is given by




We differentiate to get:




The maximum profit is



The profit function is shown below:




Problem 2:

Assume that the demand curve for bicycles in New York City during the Fall is given by the following equation ; and the supply curve for bicycles in NYC during the Fall is given by the following curve,  


a)      What is the choke price? What is the slope of the demand curve? What is the slope of the supply curve?


Answer: In order to find the choke price we solve:




The slope of the demand curve is , and the slope of the supply curve is .



b)      Graph the supply and demand curves for the market of bicycles in NYC during the Fall.


Answer: We have the following graph:




c)      What is the equilibrium price and quantity in the market for bicycles in New York during the Fall?


Answer: By intersecting the demand and supply curve we get:




The equilibrium quantity is computed as






d)      Fall has started in NYC. Unexpectedly, the weather turns out to be quite warm. Happy New Yorkers decide to spend more time biking around. As result, the original demand curve for bicycles in the Fall increases by 4 bicycles at every price. What is the new demand curve? Show it in the graph in (a).


Answer: The new demand is




In the new graph we have



e)      What is the new equilibrium price and quantity?


Answer: Now we solve:




The new equilibrium quantity is




f)        Why doesn't the new equilibrium quantity you found in (e) also increase by 4 bicycles? Briefly explain in words.


Answer: The new equilibrium will not be obtained in general by adding the amounts of units that demand was shifted, because it also depends on the interaction with the supply curve.



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