Question

Use the following information in answering questions 1 - 9. Assume persons of type 1 value quality level z and the product itself such that the inverse demand for the product is given by P1 = 10 - Q1 + 2z. Similarly, for a person of type 2 the inverse demand for the product is given by P2 = 24 - 2Q2 + 6z. The AC and MC of producing the product with quality z is MC = AC= 2 + 4z. Assume that z can be either equal to 0 or 1

5. The profit maximizing quantity to sell to a person of type 2 when z=1 is
a. 4
b. 3
c. 6
d. 2
e. 5

Answer 1

c. 6

Step-by-step explanation:

The maximun profit is determined by the point where the Marginal Revenue (MR) is equal to the Marginas Cost (MC).

Solving for person of type 2 and considering Z=1.

The marginal cost equation:

MC = 2 + 4z

MC = 2 + 4(1)

MC = 6

The demand equation:

P2 = 24 - 2Q2 + 6z

P2= 24 - 2Q2 + 6

P2= 30 - 2Q2

To calculate the Marginal Revenue, we calculate, at first, the total profit:

Total profit=P*Q2

TP=(30-2Q2)*Q2

TP=30Q2 - 2Q2^2

Taking the derivative of the total profit, we obtain the Marginal Revenue

MR = 30 - 4Q2

Finally, set the MR and MC, and solve for Q2

30 - 4Q2 = 6

24 = 4Q2

Q2 = 6