w6 - e) Draw the relationship between MC and AC. Prove that...

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Economics 11: Microeconomic Theory 1 Professor Christian Hellwig Exercises Week 6 1) In a two period world, Mark has an income of $50 today and $20 tomorrow. He has the following production technology: Q 2 =20*I 1 1/2 , where I 1 is the investment today and Q 2 is the gross return of the investment. a) Suppose that Mark wants to consume $60 tomorrow. How much should he consume and invest today? b) Suppose that the interest rate is 100% and his utility function is U(C 1 , C 2 )=C 1 1/2 C 2 1/2 . Find the optimal investment and consumption. 2) Digging clams by hand in Sunset Bay requires only labor input. The total number of clams obtained per hour (q) is given by: q = 100(L) 1/2 Where L is he labor input per hour. a) Graph the relationship between q and L b) Find the marginal and average product of labor. 3) Suppose that the cost function of X is given by: C = 100 -10X + 5X 2 a) Find the variable cost b) Find the fixed cost c) Find the average cost. d) Find the marginal cost
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Unformatted text preview: e) Draw the relationship between MC and AC. Prove that they always intersect at the minimum AC 4) Sam is thinking about starting a new business. He wants to produce shirts and sell them in a local market. The technology he faces is given by the following production function: Q=F(L)=10L 1/2 , where L is the number of people needed to produce Q shirts. Sam is a price taker not only in the shirt market but also in the labor market. The market price of shirts is estimated to be P=6 and the market wage rate is w=3. Compute the profit-maximizing number of shirts and how many people Sam should hire to produce them. (Don’t forget to check that profits are positive.) 5) Let 3 / 1 3 / 1 L K X ! = . Assume that both factors are variable. a) Derive the cost function. b) Find the amount of K and L necessary to produce X=100 when w=2 and r=1. c) Find the marginal and average cost functions....
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This note was uploaded on 04/05/2009 for the course ECON 11 taught by Professor Cunningham during the Spring '08 term at UCLA.

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