An economy has 2,000 people. 1,000 of them have utility function U(x, y) = x + y
and 1,000 of them have utility function U(x, y) = min(2x, y) . Everybody has an initial
allocation of 1 unit of x and 1 unit of y . Find the competitive equilibrium prices and
consumptions for each type of person. (10 分)
A natural monopolist has the total cost function c(q) = 350 + 20q , where q is its
output. The inverse demand function for the monopolist’s product is p = 100 − 2q .
Government regulations require this firm to produce a positive amount and to set price
equal to average costs. What amount will this firm produce to comply with these
requirements? (10 分)
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