Question

2. To produce 18 units of output a firm can hire either 9 workers or 3 machines. a. Let L denote workers and K denote machines. Write down a production function that represents this firm's production technology. (2 points) b. Let w denote the wage rate and r denote the rental rate of capital. Suppose wir = 0.4. Derive the firm's long run factor demand functions for labor and capital and the firm's long run cost function. (4 points) C. A different firm (using a different technology of production) has the following long run cost function: Clw.rg) = 29222 What is the minimum cost the firm must incur to produce q = 36 if w = 4 and r = 25? (2 points) d. By how much does the firm's costs change (in dollars) if w increases to 9 and r falls to 16? Do total costs rise, fall, or remain the same? (3 point) e. Derive the firm's factor demand functions for labor and capital. (4 points)

Answer 1

Prodh funch is of perfect substitutes type. |q (kil) = 2L+GKA 80 that for q=18 L=912=9. & K = 916=3. 6.) wir, who=04, then as MRTS = MPL = 2/6 = 1/3 =:33 MPK 80. I MRTS (w/r. MAL MPK , so only is used in prod". 80. K* =q16. L"=O. LRTC= WLA + 8k= LRTC = c.) c= 29" 2 Wh2alla q=36, W=4,8=25 G=2 /36 ſq 125 = 2x6x 2x5 = $120 Ang

d.) And -('= QxJ6 x Jax JT6 = 2x6x3 x4 = $144 . So total costs rise from shephard Lemma factor dd func, K=0C = 292 w ar 250 e u tine