estion One

A. The production function of a firm is given as = 200

2

2

. Where: Q is output; L is

labor and K is capital. If each unit of labor cost 200 shillings and each unit of capital cost 400

shillings and the firm has only 300,000 shillings at its disposal.

i. Set up a constrained output maximization problem to determine the optimal values

capital and labour to be employed

ii. Determine the maximum amount of output to be produced.

iii. Determine the value of the Lagrange multiplier and give an Interpretation?

iv. What would be the firm's output be if there was no resource constraint?

QUESTION TWO

A. Find the First derivatives (dy/dx) of the following functions

i. =

ii. = (

+ 1)( + 2)(

4 + 3)

iii. () =

(+1)

(

+2)

B. Find point price elasticity of demand when q = 10 if = (120 2)

0.5

Question Three

A. Evaluate:

(

)

B. Given the following supply function: =

2 + + 3. Determine the producer's surplus

for a market of P