Rabelaisian Restaurants has a monopoly in the town of Upper Glutton. Its production function is Q = 40L, 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 40 + .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 = 40L, 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 40 + .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 for Rabelaisian Restaurants, we need to find the level of output where marginal revenue (MR) equals marginal cost (MC).

The demand curve for meals gives us the marginal revenue function: 
MR = P = 100 - Q/120

The production function gives us the total product function: 
Q = 40L

Taking the derivative of the total product function, we get the marginal product of labor: 
MP = dQ/dL = 40

Now we can find the marginal cost function. The wage rate is given by 40 + 0.1L, so the total cost of labor is: 
TC = (40 + 0.1L)L = 40L + 0.1L^2

The marginal cost (MC) of labor is then: 
MC = dTC/dL = 40 + 0.2L

To find the profit-maximizing level of output, we need to equate MR and MC: 
100 - Q/120 = 40 + 0.2L

Substituting Q = 40L, we get: 
100 - 40L/120 = 40 + 0.2L

Simplifying: 
100 - L/3 = 40 + 0.2L 
60 = 1.2L 
L = 50

So the profit-maximizing level of labor is L = 50, and the corresponding level of output is: 
Q = 40L = 40(50) = 2000

Therefore, the profit-maximizing output for Rabelaisian Restaurants is 2000 meals, which corresponds to choice (C), 6000 meals (since each meal serves three customers).

Rabelaisian Restaurants Has a Monopoly in the Town of Upper