Answer to Question #120235 in Microeconomics for lamesa

Question

1. Suppose that a monopolist firm has the following information
Q= 50-0.1P
TC= 25+10Q+0.5Q2
P=250- 2.5Q
A. Find the profit maximizing output (5 points)
B. Find the profit maximizing price (5points)
2. Assume that a project requires an initial investment of Br. 60,000 and the rate of return is 10%. The after taxes cash flows (or net cash flows) are as follows: (5 marks)
Year 1 = 8000 Year 4 = 20,000
Year 2 = 15,000 Year 5 = 20,000
Year 3 = 22,000
A. Calculate the payback period (PBP)
B. Calculate the Net present value (NPV)

Answer 1

Question 1: 

A. Find the profit maximizing output (5 points)

Monopolies maximize profits by setting MR = MC

We have the cost function as:

$$TC= 25+10Q+0.5Q^2$$

From the cost function, the marginal cost is:

$$MC = 10 + Q$$

We have the demand curve as:

$$P=250- 2.5Q$$

This gives the total revenue as:

$$TR = PQ = 250 - 2.5Q^2$$

And the marginal revenue as:

$$MR = 250 - 5Q$$

Equating marginal revenue to marginal cost:

$$10 + Q = 250 - 5Q$$

Solving for Q:

$$6Q = 240\\[0.3cm] \color{red}{Q_m = 40}$$

B. Find the profit maximizing price

$$P=250- 2.5Q\\[0.3cm] P_m = 250 - 2.5Q_m\\[0.3cm] P_m = 250 - 2.5(40)\\[0.3cm] \color{red}{P_m = \$150}$$

Question 2:

Assume that a project requires an initial investment of Br. 60,000 and the rate of return is 10%. The after taxes cash flows (or net cash flows) are as follows: (5 marks)

Year 1 = 8000

Year 2 = 15,000

Year 3 = 22,000

Year 4 = 20,000

Year 5 = 20,000

A. Calculate the payback period (PBP)

The payback period gives the period at which it takes for the initial cost to be recovered from the project.

From the table above, the payback period is 5 years since it is at this year that the project recovers its initial cost.

B. Calculate the Net present value (NPV)

The NPV formula is:

$$NPV = -C + \sum\dfrac{CF_t}{(1 + r)^t}$$

The table below shows the PV, which is equal to:

$$PV=\sum\dfrac{CF_t}{(1 + r)^t}$$

Therefore, the NPV is:

$$NPV = -60000 + 62277.04\\[0.3cm] \color{red}{NPV = 2,227.04}$$