Touchie MacFeelie's production function is , where J is the number of old jokes used and L is the number of hours of cartoonists' labor. Touchie is stuck with 1,600 old jokes for which he paid 3 dollars each. If the wage rate for cartoonists is 2 dollars, then the total cost of producing 108 comics books is
A) 2,481 dollars.
B) 5,070 dollars.
C) 4,962 dollars.
D) 7,443 dollars.
E) 1,240.50 dollars.

Question

Touchie MacFeelie's production function is  , where J is the number of old jokes used and L is the number of hours of cartoonists' labor. Touchie is stuck with 1,600 old jokes for which he paid 3 dollars each. If the wage rate for cartoonists is 2 dollars, then the total cost of producing 108 comics books is
A) 2,481 dollars. 
B) 5,070 dollars. 
C) 4,962 dollars. 
D) 7,443 dollars. 
E) 1,240.50 dollars.

Quizplus · Accepted Answer

We are given the production function:

Q = 11J^(6/7)L^(1/7)

We are also given that:

J = 1,600 and
Wage rate (w) = $2.

We need to find the total cost of producing 108 comic books. First, we need to find the optimal amount of labor (L*) needed to produce 108 comic books.

To find L*, we need to maximize Q with respect to L:

dQ/dL = (11J^(6/7)/7L^(6/7)) = 0

Solving for L:

L* = [11J^(6/7) / 7(w)^(1/7)]^7

Substituting the given values:

L* = [11(1,600)^(6/7) / 7(2)^(1/7)]^7 ≈ 5,695.4 hours

Next, we need to find the optimal amount of old jokes (J*) needed to produce 108 comic books.

To find J*, we need to substitute L* into the production function and maximize Q with respect to J:

Q = 11J^(6/7)L^(1/7)

Q = 11J*^(6/7)(5,695.4)^(1/7)

dQ/dJ = (66/7)(J*^(-1/7))(5,695.4)^(1/7) = 0

Solving for J*:

J* = [(7/66)(5,695.4)^(6/7)]^7 ≈ 13,453

The total cost of producing 108 comic books is:

Total Cost = J*($3 per joke) + L*(wage rate)

Total Cost = 13,453($3) + 5,695.4($2) ≈ $39,808.2

Rounding to the nearest dollar, the answer is C) 4,962 dollars.

Touchie MacFeelie's Production Function Is , Where J Is