Using the following information to complete questions 8 - 11.
Top-It-Off Inc. produces gold pen and pencil sets for executives' desks. Revenue and labor productivity data are given in the following table. The components cost $15.00. The wage rate is constant at $7.50 per hour.
-Given the above information, how much output should the firm produce and at what price?
A) Q = 85, P = 20
B) Q = 85, P = 45
C) Q = 75, P = 45
D) Q = 75, P = 60
E) None of the Above

Question

Using the following information to complete questions 8 - 11.
Top-It-Off Inc. produces gold pen and pencil sets for executives' desks. Revenue and labor productivity data are given in the following table. The components cost $15.00. The wage rate is constant at $7.50 per hour. 
-Given the above information, how much output should the firm produce and at what price?
A) Q = 85, P = 20 
B) Q = 85, P = 45 
C) Q = 75, P = 45 
D) Q = 75, P = 60 
E) None of the Above

Quizplus · Accepted Answer

To maximize profit, the firm should produce where marginal cost equals marginal revenue. 
From the table, we can find that to produce one set, it costs $15 for components and 0.25 hours of labor, which amounts to $1.875 with a constant wage rate of $7.50 per hour. Therefore, the total cost of producing Q sets is TC = 15Q + 1.875Q^2. 
The marginal cost of producing Q sets is MC = dTC/dQ = 15+3.75Q. 
The firm's revenue function is R = PQ, where P is the price and Q is the level of output. 
The marginal revenue of producing Q sets is MR = dR/dQ = P.
Equating MC and MR, we get 15+3.75Q = P, or P = 15+3.75Q.
Substituting this expression for P into the revenue function, we get 
R = Q(15+3.75Q) = 15Q + 3.75Q^2.
To find the level of output that maximizes profit, we need to find the level of output where marginal revenue equals marginal cost, which is:
15+3.75Q = 15
3.75Q = 0
Q = 0
Since the level of output cannot be zero, we need to consider the second-order condition for profit maximization, which is: 
d^2(π)/dQ^2 = d^2(R-TC)/dQ^2 = dMC/dQ > 0
From the given data, we know that dMC/dQ = 3.75, which is positive. Therefore, the second-order condition is satisfied, confirming that Q = 75 is the profit-maximizing level of output. 
To find the price that maximizes profit, we can substitute Q=75 into the expression for P: 
P = 15+3.75Q = 15+3.75(75) = $345.
Therefore, the firm should produce 75 sets at a price of $45 to maximize profit.

Using the Following Information to Complete Questions 8 - 11