Question

248 PROFIT MAXIMIZATION (Ch. 20) 20.1 (0) The short-run production function of a competitive firm is given by f(L)62/3, where L is the amount of labor it uses. (For those who do not know calculus-if total output is al, where a and b are constants, and where L is the amount of some factor of production. then the marginal product of L is given by the formula abL- The cost per unit of labor is w-6 and the price per unit of output is p 3 (a) Plot a few points on the graph of this firm's production function and sketch the graph of the production function, using blue ink. Use black ink to draw the isoprofit line that passes through the point (0, 12), the isoprofit line that passes through (0,8), and the isoprofit line that passes through the point (0,4). What is the slope of each of the isoprofit lines? How many points on the isoprofit, line through (0, 12) consist of input-output points that are actually possible? Make a squiggly line over the part of the isoprofit line through (0, 4) that consists of outputs that are actually possible. (b) How many units of labor will the firm hire?How much output will it produce? will its total profits be?. If the firm has no other costs, how much Output 48 36 24 Labor input (c) Suppose that the wage of labor falls to 4, and the price of output remains at p. On the graph, use red ink to draw the new isoprofit line for the firm that passes through its old choice of input and output. Whn the firm increase its output at the new price?Explain why

Answer 1

a.

1. Slope of isoprofit lines= 2

Reason- slope of isoprofit = w/p=6/3=2

2. How many points on isoprofit line (0,12) are actually possible?

Answer- None

Reason- As this isoprofit is not tangent to the production function.

3. Squiggly line is from point A to B

B. Firm will hire 8 units of Labor. It will produce 24 units of output. Total profits will be 24.

Reason- Profit maximizing equation=

π=3(6L^2/3) -6L

To find optimal level of Labour, we differentiate the equation and equate it to zero.

dπ/dL= 12/L^(1/3)-6 =0

Labor= L=8

Output= 6L^2/3= 6(8)^2/3= 24

π=profit =3(6L^2/3) -6L= π=3(6(8)^2/3) -6(8)= 24

(Point C in the diagram)

C. Yes, firm will increase its output at new price level because the firm can reach higher isoprofit line by increasing the output. Look at the red line in the diagram.

48 BLACK LINE 3b RED LIN 24 /3 3 SquiGGYいん BUUE LINE 12. 1 6 20 2y abour In put วา

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