Q: A monopolist faces an inverse demand of P(Q) = 210 – 4Q and constant marginal costs 1. Calculate the…
A: P= 210-4Q TR= P×Q = (210-4Q)Q MR = dTR/dQ = 210-8Q
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A: Given : Demand function : Qm = 34 - 1*Pm or Pm = 34 - 1*Qm Cost function : TC = 20 + 2*Qm + .5*Qm2…
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A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…
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- 8. A monopolist with cost function c(q) = q faces two consumers whose demand functions are given below. Q₁ = 100-P 50-P Q₂ (a) Suppose the monopolist is a uniform pricing firm (i.e.the monopolist can- not engage in any price discrimination). Find the firm's optimal pricing strategy. Calculate the firm's Lerner index. (b) What is the deadweight loss associated with this pricing strategy, if any? (c) Now, assume that price discrimination is possible. Find the monopolist's optimal second degree price-discrimination strategy. (d) Find the monopolist's optimal third degree price-discrimination strategy.1. A monopolist with zero cost, that is c(q) = 0, faces two consumers whose demand functions are given below. Q1 = 10-P Q2 (a) Suppose the monopolist cannot engage in any price discrimination. Find the firm's optimal pricing strategy. (b) Now, assume that price discrimination is possible. Find the monopolist's optimal first degree price-discrimination strategy. (c) Find the monopolist's optimal second degree price-discrimination strategy.4. Consider a monopolist with cost funetion c(q) = 20g, who is facing two con- sumers. The consumers' demand functions are given by 91 = 100 - p 92 = 300 – 3p. (a) Suppose the monopolist does not price discriminate. Find the monopolist's optimal pricing strategy, the resulting profit, and Lerner Index. (b) Suppose the monopolist can engage in third degree price discrimination. Find the monopolist's optimal pricing strategy and the resulting profit. Compare the profit with that found in part (a), and give an intuitive ex- planation. (c) Now, suppose the monopolist can produce the good at zero cost. That is clq) = 0. Find the monopolist's optimal second degree price discrimination strategy.
- 2. A market analysis employed by the "Sad Student Company" reveals that the number of lots of the game named "Handsome Killer: Revenge of the Teacher" ordered by the wholesalers when the game is offered at a price of dollars per lot is given by the formula: p=1500 – 2.5q a) Find the company's total, marginal and average revenues b) Find the price and quantity maximizing the total revenue by first expressing the revenue as a function of price rather than of quantity9. A monopolist produces a good at a constant marginal cost of 4. Suppose the monopolist is able to practice first-degree price discrimination (FDPD). The (in- verse) market demand function for the good is given by P-10-bQ where P is price, Q is quantity and b>0 is a constant. Let DL(Q) denote the deadweight loss at quantity Q, and let CS(Q) denote the consumer surplus at (a) Under FDPD, the marginal revenue function of the monopolist is the same as the market demand function. Is this true or false? Explain carefully. (b) Let Q be the monopolist's optimal quantity under FDPD. Calculate the value of CS(Q) - DL(Q). (c) Suppose a regulator imposes a per-unit tax of t on the monopolist and re- distributes tax revenue to consumers, so that tax revenue becomes part of consumer surplus. Let Q; be the monopolist's optimal quantity under FDPD given a per-unit tax of t. Calculate the value of t that maximises CS(Q)-DL(Q).2. Acme Pharmaceutical Company discovers a vaccine that prevents the common cold and has a patent that grants it a monopoly on this drug. Acme has plants in both the North America and Europe and can manufacture the drug on either continent at a marginal cost of $10. Assume there are no fixed costs. In Europe, the demand for the drug is QE = 70 - PE, where QE is the quantity demanded when the price in Europe is PE. In North America the demand for the drug is QN 110 PN, where QN is the quantity demanded when the price in North America is PN =
- 10) Many restaurants offer "early-bird specials" to dinner customers. These specials consist of a significant price reduction on selected menu items purchased before some pre-determined time, e.g., 6 p.m. Is such a practice a form of price discrimination? If so, what type?9. A monopolist produces a good at a constant marginal cost of 4. Suppose the monopolist is able to practice first-degree price discrimination (FDPD). The (in- verse) market demand function for the good is given by P=10-bQ where P is price, Q is quantity and b> 0 is a constant. Let DL(Q) denote the deadweight loss at quantity Q, and let CS(Q) denote the consumer surplus at Q. (a) Under FDPD, the marginal revenue function of the monopolist is the same as the market demand function. Is this true or false? Explain carefully.Exercise A.6 A monopolist facing the demand curve Q = 42 – 0.6P operates with constant average and marginal costs equal to 20. a) Calculate the quantity, price and profit obtained by the monopolist. Represent graphically. (b) What quantity, what price and what benefit will you get if you can apply first-degree price discrimination? Calculate the consumer surplus and represent graphically. c) The monopolist warns that he can separate consumers into two distinct groups with demands Q1 = 12 - 0.1P1 and Q2 = 30 - 0.5P2. Calculate the quantities, the prices you will set in each market, and the profit you will make. Represent graphically.
- 3. Consider a monopolist who faces the following demand: Demand: P= 100 – 10Q MC= 50+20 a) Find the price quantity combination that maximizes profit for the monopolist. b) Is the firm making positive, negative or zero profits? (100,100) Kareem chooses (60, 105) (500, 400) Saleem chooses Kareem chooses (50,420) 4. Calculate the SPNE/SPNES for the game stated above.7. A monopolist with zero cost, that is c(q) = 0, faces two consumers whose demand functions are given below. 6-P 12-2P (a) Suppose the monopolist cannot engage in any price discrimination. Find the firm's optimal pricing strategy. Calculate the firm's Lerner index. (b) Now, assume that price discrimination is possible. Find the monopolist's optimal first degree price-discrimination strategy. (c) Find the monopolist's optimal second degree price-discrimination strategy.2. Consider a pharmaceutical company considering research and development of a new drug. They estimate that demand for this new, innovative product (the only of its kind) is given by p = 200-q, and the firm knows that once the drug is developed it can produce as much as it would like at a constant marginal cost of $10 (this implies a cost function of c(q) = 10q). (a) What is the monopolist's profit-maximizing price and quantity produced, pm and qm if they develop the drug? Be sure to include a well-labeled diagram! (b) If the firm expects that the R&D will cost $10,000, should the firm pursue this product innovation? (c) What is the most the firm should be willing and able to spend on this innovation? (d) What is the socially optimal quantity of output, q*? (e) What is the value of the innovation to society if it was competitively/efficiently supplied? (f) Calculate the deadweight welfare loss we should expect if the firm produces the new drug as a monopoly.