Question

just answer e,f,g,h,i,j.

(a) (3 points) To begin, assume that a firm is producing using q = h(K, L) = K(1/3) L (1/3). Suppose the firm currently owns 128 machines, the price of the good is P = $96, the rental rate of capital is r = $4, and the wage rate is w = $16. What level of Labour would be hired? How much would be produced? Would the firm make a profit or a loss? Suppose there are two other methods of production using the same machines: 9 = 9(K, L) = min{{K, ŽL} or q = f(K, L) = K(1/4) L(3/4) (b) (2 points) Using production g(K, L), if the capital remains fixed and the firm wants to keep output the same, what level of labour would be hired? What are the profits made here? (c) (3 points) Continuing to use production g(K, L) with the capital fixed, how much would the firm produce if the did not keep output the same? What are the profits here? (d) (2 points) Would the firm ever be willing to switch from using h(K, L) to using 9(K, L) with capital at 128 machines? Explain. (e) (2 points) Using production f(K, L), if the capital remains fixed and the firm wants to keep output the same, what level of labour would be hired? What are the profits made here? (f) (3 points) Continuing to use production f(K, L) with the capital fixed, how much would the firm produce if the did not keep output the same? What are the profits here?

Answer 1

ce) 4 L Production function: q = f(KgL)= kra level of production : 42 16 capital : (28 u з KL Уз ... ขV3 2 (16)** ( аз у'з :. К = 8 946 If they do not maintain ор - Уз (6) q/3k L Уз 43 то 4x128 1% x(12в = 6 x (28) Avas ", MC Р: ме = 46 А4 е с отлет 3 6 Хо - 6 х (зв'я, 2 х (tasyҮз 2 الم (1664 x 128 3 2 K 2 та 425

(9) earen Yes. Griven the market price P=96, the firm more profit with fck, h) than & h (K ,L). Hence firm will switch the process. h) and q f(K, L) For Let q=h (K, L) q=ka LB equilibrium : At MPL MPK 312 ß kali 지도 ak Вк LL 212 지 ) a daß q= ßr dw ßr ßr aw a+B :. LRTC = WL Ark +

A+ .: +L K - र) : १ -) ofw +B ßr .'. LRTE WL TK o18 %3D (v)- १ (EE ) ( (4) २ <+8 at B १- (A) ( - in (K) , - at For ~ MP 16 LRTC = 21 A (K) For 3/A :, LRTCE 3 [05 (1) के %3D ཅད 2 १.859 For १ (Kmin , +K L ... १ - YAK = FL ..KEL < : ११, L:58 . .'. LRTC : ११

LRTC cis LR AC 9 LRACE lorq for q: le (K, L) s q= g(K,-) LRAC = 96 19.85 q=f(k, L); LRAC = (jo Loing profit : h (K3L) 60 312 a6 q 16 FOC : Boss ак aq 96 16 x na Y2 A الم = 16 r/o K = (4 * (16) 128 (proved) For gek, 2) there are infinite number of ow the firm can produce at pa is a possibility with q=32 Then ab, wo 16, K* = 128