Problem Set 6. Competitive Market
EconS 526
1. Farmers produce corn from labor, a variable input, and land, a fixed input. The labor cost in
dollars to produce y bushels of corn is 𝑐𝑐(𝑦𝑦) = 𝑦𝑦 2 . There are 100 identical farms which all behave
competitively.
a. What is the individual farmer’s supply equation of corn?
b. What is the market supply of corn?
c. Suppose the demand curve of corn is 𝐷𝐷(𝑝𝑝) = 200 − 50𝑝𝑝. What is equilibrium price and
quantity of corn? How much does each individual firm produce?
d. Assume that the market price you calculate in (c) is the long run equilibrium price. What is
the equilibrium rental value of land?
2. On a tropical island there are 100 boat builders, numbered 1 through 100. Each builder can build
up to 12 boats a year and each builder maximizes profit given the market price. Let y denote the
number of boats built per year by a particular builder. The cost function for boat builder i is
𝑐𝑐(𝑦𝑦) = 11 + 𝑖𝑖𝑖𝑖 such that the first builder has a cost function 𝑐𝑐(𝑦𝑦) = 11 + 1𝑦𝑦, the second
builder has a cost function 𝑐𝑐(𝑦𝑦) = 11 + 2𝑦𝑦, etc. Assume that the quasi-fixed cost $11 is only
paid id the firm produces a positive amount of output. If the price of boats is 25, how many
builders will choose to produce a positive amount of output? If the price of boats is 25, how
many boats will be built per year in total?
3. US consumers have a demand function for umbrellas which has the form 𝐷𝐷(𝑝𝑝) = 90 − 𝑝𝑝.
Umbrellas are supplied by US firms and UK firms. For simplicity, assume that there is a single
representative firm in each country that behaves competitively. The cost function for producing
umbrellas is given by 𝑐𝑐(𝑦𝑦) = 0.5𝑦𝑦 2 in each country.
a. What is the aggregate supply function for umbrellas?
b. What is the equilibrium price and quantity sold?
c. Now the domestic industry lobbies for protection and Congress agrees to put a $3 tariff on
foreign umbrellas. What is the new U.S. price for umbrellas paid by the consumers?
d. How many umbrellas are supplied by foreign firms and how many are supplied by domestic
firms?
Deadline: November4, 2015 beginning of class. See syllabus for penalty due to late submissions.