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:

Suppose that a monopolist firm has the following information TC= 25+10Q+0.5Q2 P=250- 2.5Q

A. Find the profit maximizing output (5 points)

Monopolist will maximize its profits by producing where MR = MC

MR=MC

The demand curve is:

$$P=250- 2.5Q$$

And the total cost is:

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

From the total cost:

$$MC = 10 + Q$$

From the demand curve:

$$MR = 250 + 5Q$$

Equating MR to the MC and solving for Q:

$$10 + Q=250 - 5Q\\[0.3cm] 6Q = 240\\[0.3cm] \color{red}{Q^* = \dfrac{240}{6} = 40}$$

B. Find the profit maximizing price (5points)

Simce optimal quantity is 40, the optimal price is:

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

Question 2:

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 table below shows the cumulative cash flows.

From the table, the payback period is 5 years since it it after this period that the project recovers its cost.

B. Calculate the Net present value (NPV)

The NPV is calculated as:

$$NPV = -C_0 + \sum\dfrac{CF_i}{(1 + r)^i}$$

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The present value for each year and the total present value is shown in the table below

The initial cost is $C_0 = 60,000$ . Therefore, the net present value is:

$$NPV = -60,000 + 62,277.04\\[0.3cm] \color{red}{NPV = 2,277.04}$$