05 Jun Question 1. Assume for the moment that both agents have the same utility function U ( xi , y i ) xi y i4 and that there
Question
1. Assume for the moment that both agents have the same utility function
U ( xi , y i ) xi y i4 and that there is no production.
a) Show that the MRS for each consumer at every PE point is the same and that
the number is a function of the fixed level of production for each good.
b) Now assume that there are production options defined by the PPF 8000 = x 2
+ y2 which has a RPT = x/y.
i) Explain why (80,40) is on the PPF but there is no PE allocation at that
level of production. (1 point)
ii) Explain why there are multiple PE allocations if total production is
(40,80) (1 point)
c) Now keep the same PPF but now we are going to change the preferences:
6
Assume that person A has the utility function U ( x A , y A ) x A y A and person B
6
has the utility function U ( x B , y B ) x B y B . Find the PE allocation of goods when
total production is (40,80) and when total production is (80,40) (2 points)
2. A competitive market has 30 identical firms each with a short-run cost of
SC(q) = 3/2q 2 + 15q + 150. The market demand for the good is P =105 1/5Q D.
a) Find the equation for the market supply curve P = S(Q S) and use that to find
the equilibrium price. Show that this price is a LR equilibrium price. Also find the
total consumer surplus in the market. You wont need an integral for this, just
geometry. (2 points)
b) Now assume that these firms are merged into 1 giant firm so that the MC of
this new monopoly is the market supply when the market was perfectly
competitive.
i) Explain why Q2/20 + 15Q + 4500 is the cost function for the monopolist.
(1 point)
ii) Find the monopolists profit maximizing output and profit. Find the
Cosumer surplus at the monopolist P and Q. Compare Cons. Surplus +
profit in the competitive case and the monopoly case. Does this result
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