answers to 2 decimal places. 7 points) Production. A factory has the production
ID: 1130624 • Letter: A
Question
answers to 2 decimal places. 7 points) Production. A factory has the production function K a) (11 points) Find the MPL. Calculate the value when L = 10 and K = 10. w all your work! Calcuiate numerical 1. (27 Explain the meaning of the result. ) (16 points) Calculate the MRTS for the Q = 10 isoquant when L = 5 Explain the meaning of the result. 2. (45 points) Market in short-run. The market is competitive. Suppose a firm has production function q a) (4 points) Capital in use is K K" Show that the marginal cost function is MC 2.5wg 1.5K1 For the rest of question 2 assume w=2 r=15 K* = 5 there are 10 identical firms in the market market supply function is p-la) (K. 1.5 b) (5 points) Market demand is P-Find the compeitive market ecuilibrium. c) (10 points) Suppose the competitive market equilibrium is Q = 5623 and P-1334 d) (8 points) Suppose the competitive market equilibrium is Q = 5623 and P-1334 e) (7 points) The heads of the 10 firms consider forming a cartel. f) (11 points) Suppose the monopoly market equilibrium is Q 39.76 and P Calculate demand elasticity at the equilibrium and explain its meaning. Will a firm earn a profit? If not, should it keep operating? Find the monopoly market equilibrium that would result. if one of the cartel firms cheats, find its profit maximizing output = 1586 caiculate the cheating firm's profit (or loss).Explanation / Answer
1. a) MPL = 0.4L(0.4 - 1). K0.4
MPL = 0.4L-0.6. K0.4
MPL = 0.4(10)-0.6. (10)0.4 = 0.4 x 10-0.2 = 0.4/100.2 = 0.4/1.58 = 0.25
MPL shows how much product of firm changes when there is additional unit of labor is hired.
b) MRTS = MPL/MPK
MPL = 0.4L-0.6. K0.4
MPK = 0.4K-0.6. L0.4
MRTS = K/L
Q = L0.4.K0.4
10 = 50.4.K0.4
10 = 1.9 K0.4
K0.4 = 5.26
K = 63.45
MRTS = K/L = 63.45/5 = 12.69
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