NAME..... SOLUTIONS......................
ECON 201/Zenginobuz
Koç University/Spring 2014
Final Exam
(120 minutes)
A- TRUE or FALSE. Briefly explain your answer.
1. (5 pts) If the long run supply curve of a competitive firm is q = 3p, then it cannot have
constant returns to scale.
2. (5 pts) A competitive, cost-minimizing firm has the production function f (x, y) = x + 2y
and uses positive amounts of both inputs. If the price of x doubles and the price of y
triples, then the cost of production will more than double.
3. (5 pts) If somebody is buying 10 units of x and the price of x falls by $3, then that
person’s net consumer’s surplus must increase by at least $30.
B- PROBLEMS
1) (15 pts) Jülide, Erdal, and Kağan are all buyers of cameras. Jülide’s demand function is
QJ = 520 - 13p, Erdal’s demand function is QE = 40 - p, and Kağan’s demand function is
QK = 200 - 5p. Together these three constitute the entire demand for cameras. At what
price will the price elasticity of market demand be equal to 1?
2) (20 pts) A competitive firm has a production function described as follows:
Output is the square root of the minimum of the number of units of capital and the number
of units of labor employed.
Suppose that in the short run this firm must use 16 units of capital but can vary its amount
of labor freely.
a) Write down a formula that describes the marginal product of labor in the short run as a
function of the amount of labor used.
b) If the wage rate is w = 1 and the price of output is p = 4, how much labor will the firm
use in the short run?
c) How much labor will the firm use in the short run if w = 1 and p = 1?
d) Write down an equation for the firm’s short-run demand for labor as a function of w
and p.
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3) (20 pts) Cass consumes cocoa and cheese. Cocoa is sold in an unusual way. There is only
one supplier, and the more cocoa you buy from him, the higher the price you have to pay
per unit. In fact y units of cocoa will cost Cass y2 dollars. Cheese is sold in the usual way
at a price of 2 dollars per unit. Cass’ income is 20 dollars and his utility function is
𝑈 𝑥, 𝑦 = 𝑥 + 2𝑦, where x is his consumption of cheese and y is his consumption of
cocoa.
a) Write down Cass’ budget set, and show it on a diagram.
b) Calculate the amount of cheese and the amount of cocoa that Cass demands at these
prices and this income.
c) Sketch some of his indifference curves on and label the point that he chooses.
4) (20 pts) A monopolist can produce at a constant average (and marginal) cost of $5 per
unit. The market (inverse) demand for the firm’s output is p = 53 - y, where p is the price
charged by the monopolist and y is the quantity of output.
a) Calculate the profit maximizing price and quantity for this monopolist.
b) Suppose a second firm enters the market. Market demand is now given by
p = 53− ( y1 + y2 ), where y1 and y2 are the quantities of output of firms 1 and 2.
Assuming that the second firm has the same cost function as the first, how much will
each firm produce at the Cournot equilibrium of this market? (Cournot competition is
where firms compete by choosing how much quantity they will produce.)
c) The monopolist considers paying the owners of the second firm not to enter the market
to compete as a Cournot competitor. What is the minimum amount the owners of the
second firm would accept to stay out? What is the maximum amount the monopolist
would be willing to pay? Would such a deal occur between the two?
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