Answered: ree competition company produces a good…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Related questions

Question

Free competition company produces a good Y with the following product functions

Y=1/2*L^1/2, where L is labor

a) How large is the company profit, calculate and illustrate it graphically.

b) The salary is doubled to 20kr, how will this affect the company's demand and adjustment in the market? Show graphic and mathematically.

Expert Solution

Step 1

If the wage is W, then cost L units of labour is WL.

To obtain the cost function, we just need to express C=WL as a function of Y, since there is only one input.

So,

$C = W L Y = \frac{1}{2} \sqrt{L} \Rightarrow \sqrt{L} = 2 Y \Rightarrow L = 4 Y^{2} H e n c e, t h e \cos t f u n c t i o n i s, C = W L = 4 W Y^{2} . O r, C (Y) = 4 W Y^{2} N o w w e c a n s o l v e f o r t h e p r o f i t m a x i m i z i n g l e v e l : L e t p b e t h e p r i c e . T h e n p r o f i t i s : π = p Y - C (Y) . T h a t i s m π = pY - 4 {WY}^{2} Maximizing wrt Y : \frac{d π}{d Y} = p - 8 WY = 0 \Rightarrow Y = \frac{p}{8 W} . This is the supply function .$