Question

Suppose that a hot dog vendor uses a cart (K) and his time (L) to make and sell hot dogs. The vendor's production function is , where Q is the number of hot dogs per day. Suppose that the rental on hot dog carts is $50 per day and that the vendor wants to produce 500 hot dogs per day. The demand for labor is ____.

Answer 1

L = 2084.75 W^-0.3

Step-by-step explanation:

The computation of the demand of the labor is shown below:

At the optimum input

As we know that

MRTS = MPL ÷ MPK = w ÷ r

0.7(K ÷ L)^0.3 ÷ 0.3(L ÷ K)^0.7 = w ÷ 50

7K ÷ 3L = w ÷ 50

K = (3 ÷ 350)wL

Now apply the production function

Q = K^0.3L^0.7

500 = ((3 ÷ 350)wL)^0.3 L^0.7

500 = (3 ÷ 350)^0.3 × w^0.3 × L

L = 2084.75 × w^-0.3.