Question

Dalia owns a small coffee roasting firm in Manchester. She is in a monopolistically competitive market and so has some market power. The inverse demand function that she faces is given by

P=20 - 0.6 Q

where P is the price per kilo and Q is the kilos of coffee demanded and her total costs are given by

TC = 23 + 7 Q + 0.2 Q2

(a) What is the marginal revenue function of this firm? Use capital letters in your response (i.e. Q not q).

MR=__________

(b) What is the marginal cost function of this firm? Use capital letters in your response (i.e. Q not q)

MC=__________

(c) Which of the following best describes what the marginal cost means in words?

	(a)	The cost of producing a given level of output.
	(b)	The cost of producing more output.
	(c)	The average cost of all the output and it depends on the total level of output.
	(d)	It is the cost Dalia will have to pay to produce another kilo of coffee and this cost is always the same.
	(e)	It is the cost Dalia will have to pay to produce another kilo of coffee and it depends on the total level of output.

(d) How many kilos of coffee should Dalia roast if she wants to maximize her profits? Give your answer to within one decimal place (e.g. 4.1). Make sure you round correctly.

To within one decimal place (e.g. 2.3), she will produce __________kgs of coffee to maximize profits.

(e) To within one decimal places (e.g. 7.1), How much profit does she make? Make sure you round correctly.

She makes £__________ of profit.

(f) How many kilos would she produce and what price would she charge if the coffee market was perfectly competitive? Give your answer to within one decimal place (e.g. 11.4).

She would make __________ kg of coffee and charge £__________  per kg.

(g) Calculate the social cost (deadweight loss) of Dalia's market power (hint: its the area of a triangle). Give your answer to within one decimal place (e.g. 1.3).

The deadweight loss is £__________ .

Answer 1

P =20 - 0.6Q

TC = 23 +7Q + 0.2Q^2

A) Marginal revenue = d/dq ( Total revenue)

Total revenue (TR) = P*Q

TR = (20 - 0.6Q)* Q

TR = 20Q - 0.6Q^2

MR = 20 - 1.2Q

B) Marginal cost = d/dq(Total cost)

= 7 + 0.4Q

C) It is the cost Dalia will have to pay to produce another kilo of coffee and it depends on the total level of output

D) Monopolist profit maximization condition;

MR = MC

20 - 1.2Q = 7+ 0.4Q

1.6Q = 20 - 7

1.6 Q = 13

Q = 8.12

E) Profit = Total revenue - Total cost

= PQ - TC

P = 20 - 0.6Q

P = 20 - 0.6*8.12

P = 20 - 4.87

Monopoly (P) = 15.13

Profit = 15.13*8.12 - ( 23 + 7*8.12 + 0.2(8.12)^2) )

profit = 122.85 - (23 + 56.84 + 0.2*65.93)

Profit = 122.85 - ( 23 + 56.84 + 13.18)

Profit = 122.85 - 93.02

Profit = 29.83

F) Comptetive market equlibirium

Price = Marginal cost

20 -0.6Q = 7 +0.4Q

Comptetive Q = 13

P = 20 -0.6Q

P = 20 - 0.6*13

P = 20 -7.8

Comptetive P = 12.2

G) Social cost or dead weight loss

Monopoly (P) = 15.13 , Q = 8.12

Comptetive P = 12.2, Comptetive Q = 13

DWL = 1/2 ( Monopoly price - comptetive price)*(Comptetive quantity - monopoly quatity)

= 1/2 (15.13 - 12.2)(13-8.12)

= 1/2(2.93)(1.8)

= 1/2*5.27

= 2.63