Intermediate Microeconomics 301
Final Exam
Thursday, May 5, 2005
Time: 2 hours.
Instructions. To obtain credit, you must give arguments to support your answer. The numbers
in brackets at the start of each question are the numbers of points the questions are worth.
Exercise 1 [15]:Consumer theory
Jacob’s utility function is
U= 10XY 2
The price of Xis pX= $10 and the price of Yis pY= $5, and his income is m= $150. What is
his optimal consumption bundle? Show in a graph.
Exercise 2 [25]:Producer theory
Suppose a production function is given by f(K; L) = KL1
3, and that the price of capital is $10
and the price of labor is $16. The capital is …xed at the level K= 4.
1. What is the quantity of labor that minimizes the cost of producing any given output?
2. What is the minimum cost of producing yunits of output ?
3. What are the marginal cost of production and the average total cost, average variable cost
and the average …xed cost?
4. Derive the …rm’s short run supply curve.
Exercise 3 [20]:Supply and Demand
The supply curve for T-shirt is given by the equation P= 6Q. The demand curve is given by
the equation p= 18 3Q.
1. What is the equilibrium price and quantity?
2. At a price of $18, will there be a surplus? Indicate by how much.
3. At a price of $6, will there be a surplus? Indicate by how much.
Exercise 4 [15]: Nash Equilibrium
1. In the following game, players must move simultaneously. What are the Nash equilibria of the
game? How many are there?
1n2 L M
L 3,8 5,0
M 2,3 7,4
2. Which equilibrium will occur if players play sequentially and player 1 makes her decision …rst?
Why? Give an extensive representation of the game (tree).
3. Which equilibrium will occur if players play sequentially and player 2 makes her decision …rst?
Why? Give an extensive representation of the game (tree).
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