Question

2. Consider a firm producing pizza with production function q = KL, that faces input prices w= $10 and r = $100 for labor and capital, respectively. a. Derive the isoquant equation. Find the isoquant of an output q = 1. Draw it in a figure with l in the horizontal axis and k in the vertical axis. b. Does this firm's production exhibit increasing, decreasing or constant returns to scale? Briefly explain c. Find the labor demand, and the capital demand, as a function of d. Find the firm's total cost function. TC (9) e. Find the firm's average cost function, AC(q) and its long-run marginal cost function, MC(q). wat een output level

Answer 1

las 9 = KL = K = 91 - Equation of isog. when q = 1 = K = Ź 21-Q 0.5,22 it toll, 12 - 2005) aist - - - - 2 =KL K= tk and L=th where t > So, q'= (Łk 2C+L) = ťkl = tq So, power of t is a which is > . Thus, there are retuns to scale. c) Optimal input demand is determined where MRTS = w Nerrame So, MRTS = M = 2/22 = ♡ =ķ MPK Barak =Telok 7 aqjak ce) q=kl = K CIOK) = 10*? =) *' = -)/* = and 1 = lok = 10 - Toq =)=1109] d teca) = WLtok = 10 (Joq) + 100 g - lodioq + lovioq => Tecq) = Vottorin > Kcq) = - 20 min = s[acca) - Boeing MC(q) = dic&q ca am (un, 197 = 105F ! Alcq) = 109/ AC09) = 20 To va Scanne M Gifh- CamScanner