A monopolist in a small market has a weekly total cost of TC(Q)=0.05Q^2+20Q+500. Q is measured in units per week and total cost is measured in dollars per week. The market demand is Qd = 880-20P a) What is the monopolist's minimum efficient scale? What is the monopolist's Average Cost when producing at minimum efficient scale? b) Find the monopolist's marginal revenue function. c) Find the profit maximizing level of output (QM) and the monopolist price (PM). d) What are consumer surplus and producer surplus in this market? e) Compute the monopolist's accounting profit. What is the difference between the monopolist's producer surplus and its accounting profit? f) Compute the price elasticity of demand when Q = QM. And show that the monopolist price and output solve MC(QM) = PM (1+1/eD) g) Find the level of output where P = MC and label it QPC. h) Find the industry total surplus when output is QPC and the deadweight loss due to the monopoly. Suppose the market was not a monopoly and that three identical price-taking firms each with total costs equal to TC(q)=0.05q^2+20q+500 were selling the product. i) Find the supply curve of each individual firm. k) Find the market supply curve. 1) Find the short run equilibrium price and quantity in this market. m) Find the amount of output that each firm produces each week. Is the firm earning accounting profits? n) Should the typical firm remain open in the short run? Why? o) In the long run, should the typical firm eventually go out of business? Why?
Added by Jessica M.
Close
Step 1
The total revenue can be found by multiplying the monopolist's price (P) by the quantity sold (QM). The total cost is given by the TC(Q) function. Total Revenue = P * QM Total Cost = TC(QM) Accounting Profit = Total Revenue - Total Cost (f) To compute the price Show more…
Show all steps
Your feedback will help us improve your experience
Rashmi Sinha and 70 other Microeconomics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Suppose that each firm in a competitive industry has the following costs: $$\mathrm{Total cost}:\quad TC=50 +{1\over2},q^2$$ $$\mathrm{Marginal cost}: MC=q$$ where $q$ is an individual firm's quantity produced. The market demand curve for this product is $$\mathrm{Demand}: Q^D=120-P$$ where $P$ is the price and $Q$ is the total quantity of the good. Currently, there are 9 firms in the market. a. What is each firm's fixed cost? What is its variable cost? Give the equation for average total cost. b. Graph average-total-cost curve and the marginal-cost curve for $q$ from 5 to 15. At what quantity is average-total-cost curve at its minimum? What is marginal cost and average total cost at that quantity? c. Give the equation for each firm's supply curve. d. Give the equation for the market supply curve for the short run in which the number of firms is fixed. e. What is the equilibrium price and quantity for this market in the short run? f. In this equilibrium, how much does each firm produce? Calculate each firm's profit or loss. Is there incentive for firms to enter or exit? g. In the long run with free entry and exit, what is the equilibrium price and quantity in this market? h. In this long-run equilibrium, how much does each firm produce? How many firms are in the market?
Assume that a monopolist faces a demand curve for its product given by: p=120−1q Further assume that the firm's cost function is: TC=580+11q Use calculus and formulas to find a solution. Round the optimal quantity to the nearest hundredth before computing the optimal price, which you should also round to the nearest hundredth. Use these rounded values to compute optimal profit. Note: Non-integer quantities may make sense when each unit of q represents a bundle of many individual items. Hint 1: Define a formula for Total Revenue using the demand curve equation. Hint 2: The first derivative of the total profit function, which is cumulative, is the marginal profit function, which is incremental. The lecture and formula summary explain how to compute the derivative. Set the marginal profit equal to zero to define an equation for the optimal quantity q. Hint 3: When computing the total profit for a candidate quantity, use the total profit function you define (rather than summing the marginal profits using the marginal profit function). 1. How much output should the firm produce? 2. What price should the monopolist choose to maximize profits? 3. What is the profit for the firm at the optimal quantity and price?
Supreeta N.
Akash M.
Recommended Textbooks
Principles of Economics
Principles of Microeconomics for AP® Courses
Economics
Watch the video solution with this free unlock.
EMAIL
PASSWORD