Question

2. The production function is given as Q=LK1/2 with K fixed at 4 units. Note K1/2 is same as the square root of K.

a. Draw the total, average and marginal product associated with this function.

b. Write down the equations for total cost, total fixed and total variable cost when w=2 and r=3, and draw the respective diagrams.

c. Write down the equations for AFC, AVC, MC and ATC corresponding to the values of w and r as in part b, and draw the respective diagrams.

d. Using duality, answer to part a, and words, explain the shapes of AVC and MC drawn in part c.

e. If r = 4, which of the cost curves (TC, TFC, TVC, AFC, AVC, AC and MC) will change and why? (4 points)

Answer 1

a)Q= LK1/2, K is fixed at 4. So, Q= 2L

Average product=Q/L= 2L/L= 2

Marginal product= dQ/dL= 2

b) Total cost= Fixed cost + variable cost. Fixed cost is cost of capital and variable cost is cost of labor. Cost of capital is r=3 and variable cost is w=2. So, Tc= 3*2+ 2*L= 6+2L or 6+Q

Total fixed cost= r*K= 3*2=6

Total variable cost= w*L= 2L or Q

c) Average fixed cost= TFC/Q= 6/Q

Average variable cost= TVC/Q= 2L/Q= 2L/2L= 1

Marginal cost= dTC/dQ= 1

Average total cost= AFC+AVC= 6/Q+1

d) Marginal cost and average variable cost is constant and equal to 1. This is because of fact that K is fixed, so only L varies. Furthermore, L is linear function of Q.

e) If r is changed, then cost of capital is chnaging. Since capital is fixed, it would include in fixed cost. Total fixed cost in turn affects Total cost, Average fixed cost and Average total cost