Question

Please show all your work.

Your firm has total costs equal to 40Q₁ and at this point you are the only firm in the

market. The demand you face is P=4000-5Q. (Any type of Q will do!). What is your

output and profits? What is the deadweight loss?

Answer 1

Output:

Since there is only one firm in the market, it is under the monopoly structure. The condition of equilibrium is as below:

MR = MC

MR is the derivative of TR, which is calculated as below:

P = 4000 – 5Q

TR = P × Q = 4000Q – 5Q^2

MR = Derivative of (4000Q – 5Q^2)

       = 4000 – 10Q

Given, TC = 40Q^1

MC = Derivative of TC with respect to Q

       = 40

Now, MR = MC

4000 – 10Q = 40

10Q = 4000 – 40

10Q = 3960

Q = 396

Answer: Required output is 396 units.

Profit:

Profit = TR – TC

            = (P × Q) – (40Q)

            = (40 × 396) – (40 × 396)

            = 15,840 – 15,840

            = 0 (Answer)

Deadweight loss:

Since this is not a competitive market, there is deadweight loss.

P = MC

4000 – 5Q = 40

5Q = 3960

Q = 792 = New quantity

New price is still 40.

Deadweight loss = 0.5 × Difference in price × Difference in quantity

                            = 0.5 × (40 – 40) × (792 – 396)

                            = 0.5 × 0 × 396

                            = 0 (Answer)