Question

A profit-Maximising competitive firm uses Just one input, ac. It's production function is g = 40012 The price of output is t12 and the factor price is t3 al. What is the profit-maximising quantity of the input? b) What is the profit-Maximising quantity of output ? c) what is the maximum profit achieved

Answer 1

A)the profit Maximizing quantity of input is ,where, Marginal revenue product of input= price /cost of input

Marginal revenue product=Marginal product of input* price of product

Marginal product of input=4/2*√x=2/√X

Price of good=12

Marginal revenue product=(2/√x)*12=24/√x

Price of input=3

Profit Maximizing condition,

3=24/√x.

√x=24/3=8

X=8^2=64

B) putting profit Maximizing quantity of input into production function,

Q=4*√x=4*√64=4*8=32

C) profit = total revenue- total cost

Total revenue=p* Q=12*32=384

Total cost =price of input* quantity of input=3*64=192

Profit=384-192=192