2.Consider a production function for a firm: Q = 2K^I/2 where Q is output, K is capital, and L is labor. MPK= K^-1/2 and MP =(1/2) L^-1/2. Let r and w be the prices of capital and labor respectively. P is the price of the output.

a. Find the optimal input bundle.

b. Find the cost function.

c. Given K is fixed at 25 units in the short run, find the short run cost function.

d. Show that the technology exhibits decreasing return to scale.

2. {20 marks] Consider a production function for a rm: o = 2s\"2 + L\"2 where Q is output, K is capital, and L is labor. Mm: Km and MPL=[1;'2] L'm. Let r and w be the prices of capital and labor respectively. P is the price of the output. a. Find the optimal input bundle. 1). Find the cost function. c. |Bitten K is xed at 25 units in the short run, nd the short run cost function. d. Show that the technologyr exhibits decreasing return to scale