Question 4: Given production function:

Q = L 3/4 . K1/4

Find out the optimal quantities of the two factors using Lagrangian method, if it is given that

price of labor is Rs.6 and price of capital is Rs.3 and total cost is equal to Rs.120.

Question 5: Given the cost function is

TC = 6L + 3K

Find out the optimal quantities of the two factor using Lagrangian method, if it is given that output is equal to 13.46 = L3/4 . K1/4.

Question 6: Suppose that the production function of the firm is:

Q = 100L1/2.K1/2

K= 100, P = $1, w = $30 and r = $40. Determine the quantity of labor that the firm should hire in order to maximize the profits. What is the maximum profit of this firm?

Question7: Solve the above problem for w = $50.

Question 8: Given TC = 100 + 60Q - 12Q2 + Q3. Find

a. The equations of the TVC, AVC, and MC functions.

b. The level of output at which AVC and MC are minimum, and prove that the AVC and MC curves are U-shaped.

c. Find the AVC and MC for the level of out