Consider a firm using labor and capital as its only inputs. The price of capital
ID: 1101204 • Letter: C
Question
Consider a firm using labor and capital as its only inputs. The price of capital is $40 where the price of labor (wage) is $60. Using 500 units of labor and 500 units of capital the firm is producing 1200 units of output. At this mix of input the firm's MPL is 10 while its MPK is 5.
a. Write the firm's isocost equation. What is the slope of the isocost?
b. Determine if the firm's mix of inputs is optimal. Explain.
c. If your answer to "b" is no, what should the firm do to improve its performance? Explain.
d. Now suppose as a result of a mandated increase in the minimum wage the wage increases to $80. What would be the implication of this change for this firm?
Explanation / Answer
question) Consider a firm using labor and capital as its only inputs. The price of capital is $40 where the price of labor (wage) is $60. Using 500 units of labor and 500 units of capital the firm is producing 1200 units of output. At this mix of input the firm's MPL is 10 while its MPK is 5.
a. Write the firm's isocost equation. What is the slope of the isocost?
----> isocost equation is 60*L+40*K =C
---->as given at L=500, K=500 output(Y) =1200, so L=500 and K=500 lie on isocost, hence
60*500+40*500 =C
--->C =30,000+20,000 = 50,000
---->so isocost function is 60*L+40*K = 50,000
--->slope of this isocost = -60/40 =-1.5.
b. Determine if the firm's mix of inputs is optimal. Explain.
----> for optimum, condition is:-
MPL/MPK = w/r
--->as MPL/MPK = 10/5 =2
but w/r = 60/40 =3/2 =1.5
--->so as both are not equal, hence it is not optimum mix.
c. If your answer to "b" is no, what should the firm do to improve its performance? Explain.
--->from b we understand that, it is not optimum.
--->To improve performance w/r ratio must be increased to 2 from 1.5.
---->hence firm should increase wage rate to 80 or must decrease price of capital to $30, so that w/r =2 making equal to MPL/MPK.
d. Now suppose as a result of a mandated increase in the minimum wage the wage increases to $80. What would be the implication of this change for this firm?
---> if wage increases to $80,then
w/r = 80/40 =2 which is equal to MPL/MPK =10/5 =2 , making optimum mix and improving firm's performance.
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