Question

6. A market consists of 10 identical consumers and 10 identical firms. Consumers have preferences U(91,92) = 9192. They all have income Y = 10. Since we will focus on the market for good 1, assume that p2 = 1. a. Write an expression for one consumer's utility maximization problem. b. Use whichever method you prefer to maximize utility and derive an expression for one consumer's demand for good 1:qı(P1). C. What are the market demand and inverse demand curves, Q“ (p) and pa(Q)? Each of the 10 firms has the production function q = VKL. The wage is 5 and the rent on capital is 10. Assume we are in the long run, so firms can vary both factors. d. Write an expression for one firm's cost minimization problem. e. Use whichever method you prefer to minimize cost and derive an expression for one firm's total cost: TC(qı) f. Compute one firm's marginal cost and derive the inverse supply curve for one firm and the inverse supply curve for the market. What is the elasticity of supply? g. Use your answers to parts (c) and (f) to find the equilibrium quantity and price. 4

please answer this question! I really need to check answers before tmrw 8am/PST. I'll even venmo the first person $15 for it... just include your account name

Answer 1

BL: (9,822 z 12192 Piqit P2q2 = y Plq t ( 22 =10 Piqt q2 =10 max sit u = Saa2 Pleit Z2 = 20 DEL Do z = muz = dei MRS = mu - 22 Jaz mu muz 2 Jei Jei 2 Je2 MRS 2 AL optimal choice MRS = put 91 22 = Piz 92= PIZ, in B2 equ. Piqi + 22 = 10 Piqi+ Pizi = to 2P121 =10 q = 10 2P

2) = c) market dd, Q9CP) = n . of 5) inverse mk ad, P = 50 a VE VL Now proan au q = w =5 8 =10 (= wh trk (= 5L + lok min c= 52+ lok Sit q = UK ir e

MPL = 8e = 5 MRIS - met MRTS = K . At cost minimizing MRTS = condition ť I= zk put = 2k q= q= in production to DIJK 2K SK

q= Jak Ik = 2 L = 2K L= 21 22 IL= 122 c = 5L + lok = 5529 & 10192 5/2q +5 tora = 552q+ 5522 10522 c =

(f) c= 1052e = 102 Mc = 1052 given by supply Р = P = fh м is с 1052 Thes, for a firm is inverse .: P = is the 10 12 inverse industry ss uruce 10/2 n P = tor 18 re . IP =

19) - In dd: equilibrium ad ess p= 50 , SS: P = r2 √20 = 50 o= 2552 } P =