Question

6. Suppose that the price per unit of input A is 12 euros and the price per unit of input B is 6 euros. What is the minimum cost of producing 120 units of output Y for the firm if the firm’s production function is Y = 4A + 2B, where Y denotes the quantity of output Y produced, A denotes the quantity of input A used and B denotes the quantity of input B used? (10 points)

Answer 1

the optimum input is used at MPL/w=MPK/r

MPA=dY/dA=4

MPB=dY/dB=2

MPA/cost of A=4/12=1/3

MPB/cost of B=2/6=1/3

the production function is linear, and the per dollar output is the same from both the inputs so the firm can use any time of any product

It can use maximum of A=total output/MPA=120/4=30

It can use a maximum of B =120/2=60 units

the cost =30*12=60*6=$360

the minimum cost is $360; it is same at any quantity of A and B as the firm is indifferent between both inputs.