Answer to Question #120996 in Microeconomics for lamesa

Question

. 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)
Expert's answer

Answer 1

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)

We have the total cost as

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

And the inverse demand curve as:

$$P=250- 2.5Q$$

Monopolist will .maximize profits where:

$$MR = MC$$

From the cost function, we have:

$$MC = 10 + Q$$

Since marginal revenue is twice as steep as the demand curve, then:

$$MR =250 - 5Q$$

Equating MR to the MC and solving for Q:

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

B. Find the profit maximizing price (5points)

Using the inverse demand curve and the optimal quantity, the profit maximizing price is:

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

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, we can see that the payback period is year 5. At this year, all the start-up cost for the project will have recovered.

B. Calculate the Net present value (NPV)

We calculate the net present value as:

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

The table below shows the present values for each year.

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

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