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?