Suzanne is the monopoly seller of an illegal product in a particular city. Her marginal cost is $11 per unit and she has no other costs. She faces a demand curve of P = 121–q, and she charges a linear (or single) price to her clients. What is the profit-maximising price Suzanne charges?
Question
Suzanne is the monopoly seller of an illegal product in a particular city. Her marginal cost is $11 per unit and she has no other costs. She faces a demand curve of P = 121–q, and she charges a linear (or single) price to her clients. What is the profit-maximising price Suzanne charges?
Solution
To find the profit-maximizing price, we first need to find the quantity where marginal cost (MC) equals marginal revenue (MR).
-
The demand curve is P = 121 - q. We can rewrite this as q = 121 - P.
-
The total revenue (TR) is Pq = P(121 - P).
-
The marginal revenue (MR) is the derivative of the total revenue with respect to quantity, which is d(TR)/dq.
-
To find MR, we first need to find the derivative of TR with respect to P, which is 121 - 2P.
-
Then, we find the derivative of q with respect to P, which is -1.
-
So, MR = (121 - 2P)*(-1) = 2P - 121.
-
Set MR = MC to find the profit-maximizing quantity: 2P - 121 = 11.
-
Solve for P: P = (121 + 11)/2 = $66.
So, the profit-maximizing price Suzanne charges is $66.
Similar Questions
Barbara has estimated the demand and marginal revenue for her product.They are P = 84 - 2Q (quantity) and MR = 84 - 4Q, respectively.She also experiences a constant marginal cost of $16.What is Barbara’s profit-maximising quantity and price?Question 4Answera.Q = 12; P = $50b.Q = 12; P = $40c.Q = 17; P = $50d.Q = 17; P = $40
A profit-maximising firm in a monopolistic competition setup will seek to produce the quantity Q where (X), and charge the price indicated by the firm’s (Y) curve at quantity Q. Identify X and Y.X = marginal cost equals marginal revenue; Y = marginal cost X = average cost is more than average revenue; Y = average total cost X = marginal cost equals marginal revenue; Y = demand X = average cost is more than average revenue; Y = demand
A monopoly has the following pricing and revenue structure.If the firm’s marginal cost per customer is $30, and the firm wants to follow the profit-maximizing rule, what would be the firm’s quantity of customers and price charged per customer?Click or tap a choice to answer the question.The quantity of customers is 4,000, and the price is $60.The quantity of customers is 3,000, and the price is $70.The quantity of customers is 4,000, and the price is $30.The quantity of customers is 3,000, and the price is $30.
A monopolist faces a demand curve given by P = 30-Q and has constant marginal (and average cost) of $19. What is the economic profit made by this profit-maximising monopolist when practicing perfect price discrimination? [Round your answer to 2 decimal places where necessary]
The total cost function of our monopolist HPW is TC = 300 + 10Q + Q2/2 (as in question 6, tutorial 9) where Q is the number of visitors to HPW. The demand curve for visits to HPW is given by P = 259 - 2Qd where P is the market price.What is the profit-maximising price charged by our (single-price) monopolist HPW? [Round your answer to one decimal place]
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.