I True or false（2points*10）.
1.Since a monopoly charges a price higher than marginal cost, it will produce an
inefficient amount of output.
2. A duopoly in which two identical firms are engaged in Bertrand competition will
not distort prices from their competitive levels.
3.The change in producer's surplus when the market price changes from p1to p2is
half of the area to the left of the marginal cost curve between p1and p2.
4.If the production function is f(x1;x2) = min(x1 ,x2); then the cost function is
c(w1;w2;y) =min(w1;w2;y )
5. A monopolist with constant marginal costs faces a demand curve with a constant
elasticity of demand and does not practice price discrimination. If the government imposes a tax of $1 per unit of goods sold by the monopolist, the monopolist will increase his price by more than $1 per unit.
6.John purchases two goods, x and y. Good x is an inferior good for some range of
income, there must be another range of income for which good x is a normal good.
7.Ambrose’s utility function is U(x,y)=x+4y1/2. The price of x is 1 and the price of y
is 2. If his income rises from 100 to 150, his consumption of y increases by more than 10% but less than 50%.
8.Bill Katz prefers more of good 1 to less and he prefers less of good 2 to more. Bill
has convex preferences. If we draw his indifference curves with good 1 on the horizontal axis and good 2 on the vertical axis, then his indifference curves have positive slope but get steeper as they rise.
9.In a competitive pure exchange economy, if the total value of excess demand for
all types of food is zero, then the total value of excess demand for all nonfood commodities must be zero.
10.In Nash equilibrium, each player is making an optimal choice for herself, given
the choices of the other players.
II Fill in the blanks for the following questions（2points*10）: (1)Professor Stern's colleague, Dr. Schmertz, gives one midterm exam and a Final
exam. He weights the final twice as heavily as the midterm to determine the course grade. No grades can be dropped. If the midterm score is represented on the horizontal axis and the final score on the vertical axis, and if a student in Dr.
Schmertz's class cares only about her course grade, her indifference curve is a line with slope ___________.
(2)Casper's utility function is y
3; where x is his consumption of cocoa and y is
x+
his consumption of cheese. If the total cost of x units of cocoa is 2x; if the price of cheese is 10, and Casper's income is $260, how many units of cocoa will he consume?____________
(3)Brand X is one of many firms in a competitive industry where each firm has a
constant marginal cost of 2 dollars per unit of output. If marginal cost for Brand X rises to 4 dollars per unit and marginal costs of all other firms in the industry stay constant, by how much does the price in the industry increase?____________________
(4)An industry has two _rms. The inverse demand function for this industry
is q
=. Both firms produce at a constant unit cost of $32 per unit. What is p2
92-
the Cournot equilibrium price for this industry? _________________________ (5)One unit of zinc and one unit of copper are needed to produce a unit of brass. The
world's supply of zinc and the world's supply of copper are owned by two different monopolists. For simplicity assume that it costs nothing to mine zinc and copper, that no other inputs are needed to produce brass and that the brass industry operates competitively. Then the price of a unit of brass equals the cost of the inputs used to make it. The demand function for brass is p
=where p is
900-
q2 the price of brass. The zinc and copper monopolists each set a price, believing that the other monopolist will not change his price. What is the equilibrium price of brass? ___________________
III. Calculation (25 points)
1. For a typical Cobb-Douglas technology, use calculus to derive the cost function of the firm.(10 points)
2. Smith is the owner of a sole mineral water spring in an isolated economy. It costs Smith $2 per gallon to get his water bottled. The inverse demand curve for Smith’s water is p = 20 - q / 5 , where p is the price per gallon and q is the number of gallon sold.
a. Write down an expression π(q ) for profits as a function of q. Find the
profit-maximizing choice of q for Smith, and the corresponding price and profit.
