Question

5) A firm producing hockey sticks has a production function given by F(L,K) = 2 LK . In the short-run, the firm's amount of capital equipment is fixed at K = 100. The rental rate of capital is r=$1, and the wage rate of labor is w=$4. a. Derive the firm's short-run total cost curve. What is the short-run average total cost? What is the short-run average variable cost? b. Find the short-run marginal cost function. What are the total cost, average total cost and marginal cost for the firm if it produces 25 hockey sticks? Two hundred hockey sticks? c. Where do the short-run marginal cost and short-run average total cost intersect? d. In the long run, the firm can change the level of K. What is the optimal capital/labor (K/ L) ratio if the firm wants to minimize the total cost of producing at any level of output? e. Calculate the firm's long-run cost function. f. Calculate the long-run marginal cost and average cost functions.

Answer 1

- y = FCL, k) = 2 J2k y= 250 Sk K = 100 y = 2/ 1100 y= 250 (10) y= zout L= y² 400 SRTC = = Wht.rk uly² ) + (0) (100) 400 = y2 + + 100 100 100 SRATC SRIC ( 100) = te onthou VCE y? . 100 SRAUCE SRAUCE here = $(42) SRAVC no. Y to 100

dSRTC dy Mc = 9 Now, y= 25 SRICE SRICE 4? + 100 (25?+ 100 = 6.25 + 100 760 SRAICE = 106.95 YO + leto SRATC = 0.25+ 4 = y = 25 = 50 50 4.25 0.5 SRmc = Now. y = 200 SRTC = (2002 + 100 = 200 X-900 too - +100 500 SRAT 2+0.5 = 2.5 SRMC = 200 50

) SRMC= l y SRAYC y 100 SRMC = SRAVC 24-y 100 zo intersect Then, - at Srme & SRAUC y=o y= 2JI ST Long run 2y = 2 (ar) ok = MPL = Skle ay - MP = 2 JI (bk) = Jlra MRTS = JIJ VI/Sk mie = Ę optimal choice MRTS = w

| (e) 수쁨 는 쁩 K 1붉) put k= W L in prodh fh ge 2STE g=2 볼음 블용 위블흡 K 볼9% ce WL + rk = 블5 이볼 c=y[WS c = [ IMF) c= vwrry

dc = mc = wir Mc = Twr AC = Olgo 9Jт AC = wir