Question

Suppose a firm makes use of a technology in which Labor and Capital are perfect complements, and which is represented by the production function: ?(?, ?) = ???{?, 2?}. Given inputs’ prices w=r=1, which of the following combinations of inputs is cost minimizing for the output target y = 10:

a. (? = 20, ? = 10);

b. (? = 10, ? = 5);

c. (? = 2, ? = 1);

d. (? = 20, ? = 20);

e. (? = 10, ? = 0).

Answer 1

Here Production function is given by : f(K,L) = min{K,2L}

We can see from above that this producer cansider K and L to be perfect complements(like a leontief function). For such function in order to minimize cost a producer hires that combination of inputs at which Kink of the isoquants will occur.

For this Function, isoquant will occur when K = 2L

Thus we have K = 2L and we want Q = f(K,L) = 10 => f(K,L) = min{K,2L} = 10 and K = 2L

=> min{2L,2L} = 10 => 2L = 10

=> L = 5 and thus K = 2L = 10

Hence the correct answer is (b) (K = 10, L = 5)