Rabelaisian Restaurants has a monopoly in the town of Upper Glutton. Its production function is Q = 10L, where L is the amount of labor it uses and Q is the number of meals produced. Rabelaisian Restaurants finds that in order to hire L units of labor, it must pay a wage of 10 + .1L per unit of labor. The demand curve for meals at Rabelaisian Restaurants is given by P =. The profit-maximizing output for Rabelaisian Restaurants is

Question

Rabelaisian Restaurants has a monopoly in the town of Upper Glutton. Its production function is Q = 10L, where L is the amount of labor it uses and Q is the number of meals produced. Rabelaisian Restaurants finds that in order to hire L units of labor, it must pay a wage of 10 + .1L per unit of labor. The demand curve for meals at Rabelaisian Restaurants is given by P  =. The profit-maximizing output for Rabelaisian Restaurants is

Quizplus · Accepted Answer

To find the profit-maximizing output, we need to set marginal revenue (MR) equal to marginal cost (MC). Since Rabelaisian Restaurants has a monopoly, its MR is the price for each additional meal, which is given by the demand curve. The MC for the restaurant is the wage rate per unit of labor divided by the marginal product of labor:

MC = (10 + 0.1L)/10

To find the profit-maximizing level of labor, we solve for L at MR = MC:

11 - 0.0002Q = (10 + 0.1L)/10
110 - Q = 100 + L
L = 10 - Q

Substituting L back into the production function, we get:

Q = 10(10 - Q)
Q = 100 - 10Q
11Q = 100
Q = 9.09

Since Q must be a whole number, the profit-maximizing output is 10,000 meals (Q=10,000). Therefore, the answer is C.

Rabelaisian Restaurants Has a Monopoly in the Town of Upper