Question

A firm's production function isx = k0-220.6. We have p=100,w=18 and r=18. What is long-run firm output when the government imposes a tax of 11.1% on labor that the firm has to pay (i.e. the cost of labor to the firm is 1.111*w).Round to the nearest integer.

Answer 1

A firmis Production fruction is : x = k0.2006 NOW, labor? e Marginal Product of MPO - ax - 0.6k O al and Marginal product of capital : MPK n - 0.2 k-0.8 10.6it LITTLITLLLLLLL Now, when the govnnment imposu a tan of T11% on labor the the firm has to pay then new wage rate will be W*: 11111 w Now inital wage W. 18 ! - this, wat = 1.1 (18) .:19.99.8. J and r = 18 Now optimal input mir condition will be MPL - w² MPK 0.6k 0.28014 19.998 a0-26-08806 Scanned with CamScanner

3K- 1, | 3) 3% 3, 1.111 lis) Dia (a) K e 0.37€ Libre Now substituting k= 0.37 l in the fins production function ac qut' x= k0.2006 = - (0.37 l) l0.6 0.37 I 1.62 1 a / 1.6 4.0 l (037) 240.625 e J.861 =) X 0.63 - 108.611 =) x 0.63 l e= 0.53 70.63 as k= 0.37 l 2) K = 0.37 / 20.631 1. 86 _Now 1.86 0.19 x 0.63 Huce long run out but of the by substituting value of k Production function. firm will be found and l in the Scanned with CamScanner

Xe ko. 1 0-6 = о 14 xo63) 16:53 " - (0.53 хрууд: б. 33 х = 24 б. +1+ o.S "} SOH+ ) ҳ0.5 с во, - -) xo's A 0:487 1 , — ) х = | o-187) - о. 23 + = O 24 ч. Huce, long ren firm's output will be Д) -ач "us. Pue Scanned with -- CamScanner. .