Question

Consider a firm with the following production function y = 20K21 For the whole exercise let the price of a unit of capital be $200, the price of a unit of labor be $150 and consider the case where capital is fixed at K = 1. a) Calculate the short run profit of the firm when the price of output is $300. (5 points) b) Calculate the short run cost function. (5 points) c) On the same graph, plot the short run average variable cost, average fix cost and marginal cost. (5 points) d) What is the price at which the firm will shut down in the short run (e.g. produce y=0)? (5 points)

Answer 1

Qeves y = 20 k e ²/2 8 = $200 $150 y = gol102, 2 M2 ya n 2012 -10) 30 L ㅈ TR Te Piy نامه ) ㄴ + gle) = Py 20 (wit 200119) (1504 + 200) = 300g K = 3004 154 (42 + 200 Islan 300 29 dy () - 0 jos 3w = 2y ( herba 20 of 30 x 4020 X5 x2 7 quo 400 =y Egy CS Scanned with CamScanner

2 L () 3 ?, = 20 step go L ) yo T7 T = TR = Py (wl tok) 30040) - (150 (400) † 20011 0(1) (600 12oow Gooot 206 = 1200 - 60200 s9800 b Short Run Lost function CZ wa tre = 130 ( ? † 2011) 3 top to y 2 it a co 8 To A 3y2 + goo CS Scanned with CamScanner

AVC(y) = Tve(9) یا = 2 y2 8 y AVC (y) داره 9 AFC (y) TAC (3) 5 200 =) AFC (y) y (9) ہے Mely) = dy 3(24) By = 3 प y CS Scanned with CamScanner

colle & 1:50 1:05 50 Output 50 100

d ) firm will shut down Whove p = minh AVC of how, hre AVC 2 J AIC O در ايح dy hence To Is fue sunt down point CS Scanned with CamScanner