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econ11_08_ps8

econ11_08_ps8 - Eco11 Fall 2008 Simon Board Economics 11...

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Eco11, Fall 2008 Simon Board Economics 11: Practice Problems 8 (Weeks 9–10) December 3, 2008 1. First Welfare Theorem There are two goods ( x and y ) and two agents (A and B). The agents’ utility functions are u A = v A ( x ) + y u B = v B ( x ) + y where v A = 2ln( x ) and v B ( x ) = 4 x 1 / 2 , The agents have incomes m A = 10 and m B = 10. The price of good y is p y = 1; the price of good x is to be determined. A single firm produces good x . It has cost function c ( q ) = q 2 / 2. (a) Show that p = 2 is an equilibrium price. Find the equilibrium allocations ( x A ,x B ,q ). (b) Suppose a social planner chooses ( x A ,x B ,q ) to maximise the total surplus, v A ( x A ) + v B ( x B ) - c ( q ) subject to q = x A + x B . Verify your allocations from part (a) satisfy the FOCs from this optimisation problem. 2. Shifts in Supply Functions Suppose the supply function is q = p , and the demand function is q = 10 - p . (a) Find the equilibrium price and quantity.
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econ11_08_ps8 - Eco11 Fall 2008 Simon Board Economics 11...

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