Question

In: Economics

Example 4: Suppose that the monopolist faces a demand curve for its widgets as q =...

Example 4:

Suppose that the monopolist faces a demand curve for its widgets as q = 9 - 0.2p. The firm’s marginal revenue and cost functions are: MR(q) = 45 – 10q and MC(q) = 15 + 5q. The firm’s total cost function is C(q) = 2.5q² + 15q + 3.

How many widgets should the firm produce and sell so that the monopolist can maximize its profits?
How much should the firm charge to each of its customers so that the firm can maximize its profits?
How much will the firm earn in total sales (or total revenues)?
How much will the firm earn in total profits?

Solutions

Expert Solution

q = 9 - 0.2p

0.2p = 9 - q

p = 45 - 5q

TR = pq

TR = (45 - 5q)q

TR = 45q - 5q²

dTR/dq = 45 - 10q

MR = 45 - 10q

C(q) = 2.5q² + 15q + 3

MC = 5q + 15

Profit Maximising condition

MR = MC

45 - 10q = 5q + 15

45 - 15 = 5q + 10q

30 = 15q

q = 2

Therefore the firm should sell 2 widgets to maximise its profit.

p = 45 - 5q

p = 45 - 5(2)

p = 45 - 10

p = 35

So the firm should charge $ 35 to maximise its profit.

TR = pq

TR = 35(2)

TR = 70

The firm will earn $70 in total sale or total revenue.

Total profit = TR - C(q)

= pq - 2.5q² - 15q - 3

= 35(2) - 2.5(2)² - 15(2) - 3

= 70 - 10 - 30 - 3

= 27

The firm will earn $ 27 in total profits.

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Monopco is a monopolist in the market for widgets, Q. The market demand curve for widgets...

Monopco is a monopolist in the market for widgets, Q. The market demand curve for widgets is given by p=24-Q, and its marginal revenue curve is MR=24-2Q. It also has average total cost curve ATC=Q and marginal cost curve MC=2Q. (a)Draw an accurate diagram showing Monopco’s D, MR, MC and ATC curves. (b) Find how many widgets Monopco produces, and the price it charges per widget. Compare these to the “efficient” price and quantity. (c) Calculate the profits earned by...

Suppose the firm is a monopolist. It faces a downward-sloping demand curve, P(Q). If it also...

Suppose the firm is a monopolist. It faces a downward-sloping demand curve, P(Q). If it also has non-negative marginal cost, will it choose a quantity on the demand curve where the price elasticity of demand is less than, greater than, or equal to -1? Explain. Two Hints: First, recall that R(Q) = P(Q) times Q, and that the price elasticity of demand is defined as . Second, recall the condition MR = MC. Think about how the firm’s revenue will...

Suppose a monopolist faces a market demand curve Q = 50 - p. If marginal cost...

Suppose a monopolist faces a market demand curve Q = 50 - p. If marginal cost is constant and equal to zero, what is the magnitude of the welfare loss? If marginal cost increases to MC = 10, does welfare loss increase or decrease? Use a graph to explain your answer

Suppose a monopolist faces a market demand curve Q= 120 - 2p. a. If marginal cost...

Suppose a monopolist faces a market demand curve Q= 120 - 2p. a. If marginal cost is constant and equal to zero, what is the magnitude of the welfare loss? b. If marginal cost increases to MC= 10, does welfare loss increase or decrease? Use a graph to explain your answer.

Suppose a monopolist faces the following demand curve: Q = 200 – 5P Also, the long...

Suppose a monopolist faces the following demand curve: Q = 200 – 5P Also, the long run total cost of the monopolist is given by TC = 20 + 2Q - .5Q2 a. What the monopolist’s MC function? (1/2 Point) b. What is the monopolist’s MR function? (1/2 Point) c. What is the monopolist’s profit maximizing level of output? (1/2 Point) d. What is monopolist’s profit maximizing level of price? (1/2 Point) e. How much profit is this monopoly...

A monopolist faces a market (inverse) demand curve P = 50 − Q . Its total...

A monopolist faces a market (inverse) demand curve P = 50 − Q . Its total cost is C = 100 + 10Q + Q2 . a. (1 point) What is the competitive equilibrium benchmark in this market? What profit does the firm earn if it produces at this point? b. (2 points) What is the monopoly equilibrium price and quantity? What profit does the firm earn if it produces at this point? c. (2 points) What is the deadweight...

A monopolist faces a demand curve of P = 120 – Q, and has costs of...

A monopolist faces a demand curve of P = 120 – Q, and has costs of C = 50 + 20Q. The monopolist sets a uniform price to maximize profits. Group of answer choices a) All of the answers are correct. b)The profit-maximizing price is 70. c)Deadweight loss is 1250. d) Producer surplus is 2500.

A monopolist with the cost function C(q) = q faces the market demand curve p =...

A monopolist with the cost function C(q) = q faces the market demand curve p = 101 -2q. What is the maximum amount the monopolist is willing to pay for advertising that shifts its demand curve to p = 101-q?

A monopolist faces the inverse demand for its output: p = 30 − Q. The monopolist...

A monopolist faces the inverse demand for its output: p = 30 − Q. The monopolist also has a constant marginal and average cost of $4/unit. (a) (10 points) What is the monopolist’s profit-maximizing level of output? What is the monopolist’s profit at this level of output? (b) (10 points) Calculate the consumer surplus and show it in a graph along with the monopolist’s equilibrium; label the monopolist’s equilibrium e M. (c) (2.5 points) What would the competitive equilibrium be...

Question 3B. (5 Point) CLO3 Suppose a monopolist faces the following demand curve: Q = 200...

Question 3B. (5 Point) CLO3 Suppose a monopolist faces the following demand curve: Q = 200 – 5P Also, the long run total cost of the monopolist is given by TC = 20 + 2Q - .5Q2 a. What the monopolist’s MC function? (1/2 Point) b. What is the monopolist’s MR function? (1/2 Point) c. What is the monopolist’s profit maximizing level of output? (1/2 Point) d. What is monopolist’s profit maximizing level of price? (1/2 Point) e. How much...

Subjects