Lesson 1 - Integration Activity W5L1 - A (a) A firm's marginal cost function is MC = Q² + 2Q +4 Find the total cost function if the fixed costs are 100_
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- Based on market research, a film production company in Ectenia obtains the following information about the demand and production costs of its new DVD Demand :P =1000-10Q Total Revenue : TR=1000Q-10Q2 Marginal Revenue: MR=1000-20Q Marginal Cost: MC=100+10Q Where Q indicates the number of copies sold and P is the price in Ectenian dollasrs. a. Find the price and quantity that maximize the company's profit b. Find the price and quantity that would maximize social welfare c. Calculate the deadweight loss from monpoly. d. Suppose in addition to the costs above. the director of the film has to be paid. The company is considering four options i. a flat fee of 2000 Ectenian dollars ii. 50 percent of the profits. iii. 150 Ectenian dollars per unit sold iv. 50 percent of the revenue. For each option, calculate the profit-maximizing price and quantity. Which if any of these compensation schemes would alter the deadweight loss from monopoly. Explain.The monopolist faces the demand curve D(p) = 100 – 2p. Its cost function is c(y) = 2y. What is your optimal level of production and prices? Solve mathematically and graphSuppose you are a monopolist in the market for a specific Q video game. Your demand curve is given by P = 80- - and 2 your marginal cost curve is MC = Q. Your fixed cost is $400. i) Derive the marginal revenue curve. ii) Calculate the equilibrium price and quantity. iii) What is the profit?
- A monopolist's demand function is given by D(p) = 90 – 2p. This - monopolist is facing a cost function, C(y) = (1/2)y² + 600. (a) Is this a natural monopoly? Explain. (b) How can government regulate this monopolist to produce the efficient amount of products?Activity 1 A firm produces a good which is sold directly to consumers and to restaurants. The demand curve function for consumers and restaurants are, respectively, P,=20 - 0.2Q, P=15 - 0.05Q, The firm's total cost function is TC = 110 + 6Q Calculate the output and price in each market and profit of the firm when there is price discrimination.5(Chapter 11 Monopoly) The inverse demand for an app is P = PD (Q) = 30 - 0,4. Q. The inverse demand function indicated the price P, were the quantity Q will be sold. The app is sold just from the app developer. The programing of the app creats fixed costs of 420. The marginal costs are 2. a) Draw the demand curve b) Calculate the marginal revenue and the average cost function. Draw the marginal revenue and marginal cost function in the diagram of a). c) Determine the profit maximizing quantity and price. What are the average costs? What is the profit? Draw the average cost curve and the profit in the diagram. Show the consumer surplus (CS) and producer surplus (PS). d) What are the price and quantity if you a have fixed costs of 490? What is the profit? e) Consider the case that the developer of the App wants to maximize the overall welfare and not just his profit. Determine price and quantity. What is the profit? Show CS and PS. f) Draw the welfare losses of the Monopoly, which occur…
- Suppose a monopoly market has a demand function in whichquantity demanded depends not only on market price (P) butalso on the amount of advertising the firm does (A, measuredin dollars). The specific form of this function isQ =(20 - P2) (1 + 0.1A - 0.01A2).The monopolistic firm’s cost function is given byC = 10Q + 15 + A.a. Suppose there is no advertising (A = 0). What outputwill the profit-maximizing firm choose? What market price will this yield? What will be the monopoly’sprofits?b. Now let the firm also choose its optimal level of advertising expenditure. In this situation, what output levelwill be chosen? What price will this yield? What will thelevel of advertising be? What are the firm’s profits in thiscase? Hint: This can be worked out most easily by assuming the monopoly chooses the profit-maximizing pricerather than quantity.1.-Dayna’s Doorstops, INC. (DD) is a monopolist in the doorstop industry. Its total cost function C(⋅) is given by the quadratic function of output C(Q) =100 – 5Q + Q2 . The inverse demand function for doorstops P(⋅) is given by the linear function P(Q) = 55 – 2Q . Note that the marginal cost C′(Q) is not constant. (Also, it happens to be negative for 0 ≤ Q < 2.5.) (a) Write down the profit-maximizing problem for DD, and determine its optimal output, QM. (b) Find the profit-maximizing price set by DD, PM and its marginal cost at the output level QM. From these two pieces of information, can you compute the elasticity of demand at that same level of output without taking any derivative? (c) How much consumer surplus CSM and producer surplus PSM and total surplus does DD generate by its profit-maximizing plan? (d) Find the profit-maximizing output, Qc, if DD acted like a price-taker (i.e., a perfect competitor). (e) Find the profit-maximizing price set by DD, Pc, as well as its…1. A monopolist with cost function c(Q) = faces an inverse demand function given by P(Q) = (a) Find the elasticity of demand with respect to price. (b) Assuming that the monopolist uses MR = MC pricing rule, find his profit maximizing price, p", and output level, q™. (c) Find the marginal cost at q" and calculate the Lerner index. (d) Does the monopolist's market power depend on his cost curve? In particu- lar, does it depend on a? Is your answer surprising?
- 1. The inverse demand function for a monopolist's product is given by P=21-2Q. What is the maximum price per unit a monopolist can charge to be able to sell 6 units? What is marginal revenue when Q=6? Show your solution 2. Suppose the inverse demand function for a Meralco's service is given by P= 83 -2Q and the cost function is C=12 + 2Q. Required: Compute the profit-maximizing price, quantity and maximum profits.5. A monopolist with cost function c(Q)=faces an inverse demand function given by P(Q)= √Q' (a) Find the elasticity of demand with respect to price. (b) Assuming that the monopolist uses MR = MC pricing rule, find his profit maximizing price, p", and output level, q". (c) Find the marginal cost at q" and calculate the Lerner index. (d) Does the monopolist's market power depend on his cost curve? In particu- lar, does it depend on a? Is your answer surprising?a. b. If a firm's the price elasticity of demand (Eg) to be-3.5 and marginal cost (MC) is $15. Using the mark-up rule, what is the optimal price for the firm to charge? If the price elasticity of demand (En) changes to -3.0, and MC is still $15. Use the mark-up rule to find the new optimal price for the firm to charge? What is the defining feature of a Pure Selling Problem and what impact does it have one the firm's goal to maximize profit?
