Department of Economics Econ 2750A H.W. #4 Prof. K.C. Tran Due Date: Wednesday March 18, 2009 1. Consider the following production function: Q ( K 2 L2 ), K , L 0 (a) Find the marginal products of K and L. (b) Is this production function exhibits diminishing returns? (Note: Diminishing returns mean that when either K or L increases, the marginal product of K or marginal product of L eventually declines. Thus to do this you need to calculate the own second-order partial derivatives) (c) Compute the two output partial elasticities. That is, compute Q , K and Q , L . 2. Find the derivative of the following functions: (i) y f ( x) (2 x 1 / 2 3)( 4 x 2 / 3 1) (ii) y f ( x) 2 x ( x 2 1) (iii) y f ( x1 , x 2 ) 2 x2 x1 1 (iv) y f ( x1 , x 2 ) ln( 2 x1 1) x2 2 1/ 4 3. (a) Given the average-cost function AC (Q) Q 2 4Q 174 . Find the marginal-cost function. Is the given function more appropriate as a long-run or short-run function? Why? (b) Given a monopolist demand curve Q 15 1 P . Find total revenue (TR), 4 average revenue (AR), marginal revenue (MR) and price elasticity of demand when P = 4. Compare the slope of AR function to the MR function, what can you conclude about their relative slopes?