Question

In: Economics

q(L,K)=L+2K=100w=30v=40find, graph, and explain cost-minimizing solution (L*,K*)

q(L,K)=L+2K=100

w=30

v=40

find, graph, and explain cost-minimizing solution (L*,K*)

Solutions

Expert Solution


Ans. Q = L + 2K

Marginal product of L, MPL = dQ/dL = 1

Marginal product of K, MPK = dQ/dK = 2

=> Marginal Rate of Substitution, MRS = MPL/MPK = 1/2

At cost minimizing output level,

MRS = w/v

But here,

MRS (=1/2) < w/v (=3/4)

So, only K will be used and no L.

Thus, for production of 100 units,

100 = 0 + 2K

=> K = 50 units
Thus, K* = 50 units and L* = 0 units

So, Minimum Cost = wL* + vK* = 30*0 + 40*50 = $2000

Thus, minimum cost is $2000.

Rahul Sunny answered 2 years ago
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