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 900 old jokes for which he paid 4 dollars each. If the wage rate for cartoonists is 6 dollars, then the total cost of producing 24 comics books is
A) 3,720 dollars.
B) 3,696 dollars.
C) 1,848 dollars.
D) 5,544 dollars.
E) 924 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 900 old jokes for which he paid 4 dollars each. If the wage rate for cartoonists is 6 dollars, then the total cost of producing 24 comics books is
A) 3,720 dollars. 
B) 3,696 dollars. 
C) 1,848 dollars. 
D) 5,544 dollars. 
E) 924 dollars.

Quizplus · Accepted Answer

Touchie's production function is:

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

We know that Touchie is stuck with 900 old jokes, so J = 900.

To produce 24 comics, we need to find the amount of labor required:

24 = 11(900)^(6/7) L^(1/7)

Dividing both sides by 11(900)^(6/7):

L^(1/7) = 24 / (11(900)^(6/7))

L = (24 / (11(900)^(6/7)))^7

L ≈ 53.06

The total cost of producing 24 comics is:

Total cost = (cost of old jokes) + (cost of labor)

Cost of old jokes = 900 × 4 = 3600 dollars

Cost of labor = wage rate × hours of labor = 6 × 53.06 = 318.36 dollars

Total cost = 3600 + 318.36 = 3698.36 ≈ 3696 dollars

Therefore, the best choice is B, 3696 dollars.

Touchie MacFeelie's Production Function Is , Where J Is