Bhen and Geri have changed their production methods and are now producing ice cr

Question

Bhen and Geri have changed their production methods and are now producing ice cream according to the production function,

Y=KL,

1. The price of a machine is R= 2 dollars and a laborer costs W= 1 dollar, the expenditure level E=$8, Determine the slope of the iso-expenditure curve

2. By setting the MRTS equal to the slope of the iso-expenditure curve, determine the rm'scost-minimizing capital-labor ratio (K/L) with R=2 and W=1. Given that the firm wants to produce Y=8 units of output, what is the optimal level of capita and labor for the firm? what is the cost-minimizing level of expenditure E when the firm produces Y=8 pints of ice cream?

3.Suppose the price of a laborer goes up to W=2.What are the new cost-minimizing evels of capital and labor given that Bhen and Geri are still producing Y=8 pints of ice cream?What is the new cost-minimizing level of expenditure

Explanation / Answer

1. The iso-cost curve will be as follows

C=wl+rk

8=l+2k

Or

L+2K=8

The slope is equal to –w/r

Which is -1/2

2. Lagr =KL+L*(c-wl-rk)

FOC

D(Lagr)/dK =L-rL* = 0    

Or L=rL*                                               (1)

D(Lagr)/dL =K-wL* =0

Or K=wL*                                            (2)

D(Lagr)/dL* =(c-wl-rk) =0

C-wL-rK=0                                           (3)

Dividing (1) by (2)

L/K = r/w or rK =Lw

Putting these values in (3)

C-wL-wL=0

C=2wL=2rK

8=2*1*L = 2L

or L=4

2rK=2L

2*2K=8

K=2

K/L=1/r =2

C=1*4+2*2

C=8

(c) the price of a laborer goes up to W=2

C=2*4+2*2

=12

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