Question

7. Suppose that the price per unit of input C is 10 euros and the price per unit of input K is 8 euros. What is the minimum cost of producing 40 units of output Y for the firm if the firm’s production function is Y = min {C/2 ; 4K}, where Y denotes the quantity of output Y produced, C denotes the quantity of input C used and K denotes the quantity of input K used? (10 points)

Answer 1

Given

Price of Input C=w=10 euro

Price of Input K=r=8 euros

Desired Output level Y*=40 units

Production Function Y=min{C/2,4K}

Let we assume we use C input to produce output so Y*=C/2

C=2*Y*=2*40=80 units

So cost of 80 units of C will be =80*10=800 euros

Let we assume we use K input to produce output so Y*=4*K

K=Y*/4=40/4=10 units

So cost of 10 units of K will be =10*8 =80 euros

So minimum cost of producing 40 units of output is 80 euros.( We will use input K for production)