"Vitamin Strong" has the monopoly on the production of vitamin C. It faces geographically separated markets, denoted A and B. The demand on these two markets are respectively QA = 1-PA and QB = 0.5-PB. The transport and production costs are zero for simplicity. Suppose that the firm chooses to set a local prices for each of the two markets. In this case the optimal prices are PA and QB= (All numeric 11111' = _____ and PB- and would supply A-- PB... ----- answers rounded to two decimals) Blank # 1 N Blank # 2 Blank # 3 Blank # 4 N
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- Inverse elasticity rule Use the first-order condition (Equation 15.2 ) for a Cournot firm to show that the usual inverse elasticity rule from Chapter 11 holds under Cournot competition (where the elasticity is associated with an individual firm's residual demand, the demand left after all rivals sell their output on the market). Manipulate Equation 15.2 in a different way to obtain an equivalent version of the inverse elasticity rule: pMCp=sieQ,p , where si=qi/Q is firm i's market share and eQp is the elasticity of market demand. Compare this version of the inverse elasticity rule with that for a monopolist from the previous chapter.A nightclub manager realizes that demand for drinks is more elastic among students, and is trying to determine the optimal pricing schedule. Specififically, he estimates the following average demands: • Under 25: qr= 18 − 5p • Over 25: q = 10 − 2p The two age groups visit the nightclub in equal numbers on average. Assume that drinks cost the nightclub $2 each. (a) If the market cannot be segmented, what is the uniform monopoly price? (b) If the nightclub can charge according to whether or not the customer is a student but is limited to linear pricing, what price (per drink) should be set for each group? (c) If the nightclub can set a separate cover charge and price per drink for each group, what two-part pricing schemes should it choose? (d) Now suppose that it is impossible to distinguish between types. If the nightclub lowered drink prices to $2 and still wanted to attract both types of consumers, what cover charge would it set? (e) Suppose that the nightclub again restricts itself…A manager of a nightclub realizes that demand for drinks is more elastic among students and is trying to determine the optimal pricing schedule. Specifically, he estimates the following average demand for his customer types: Under 25: qr=18-5p Over 25: q=10-2p The two age groups visit the nightclub in equal numbers on average. Assume that drinks cost the club $2 to make. If the manager cannot identify to which group his customers belong, what is the uniform monopoly price? If the manager can identify to which group his customers belong, what price will he charge each group. Assume the manager can only charge a single price to each group. If the manager can charge a separate entry fee and a price per drink for each group, what two-part price will the manager set for reach group. Now suppose that once again it is impossible to identify which group the customers belong. Suppose the manager lowers the price of drinks to equal to marginal cost and still wanted to attract both…
- Suppose that demand for cruise ship vacations is given by P =1200 − 5Q, whereQ is the total number of passengers when the market price is P.a) The market initially consists of only three sellers, Alpha Travel, Beta Worldwide, and ChiCruiseline. Each seller has the same marginal cost of $300 per passenger. Find the symmetricCournot equilibrium price and output for each seller.Suppose that the market demand for mountain spring water is given as follows: P = 1200 - Q Mountain spring water can be produced at no cost. Determine the level of output produced and price charged by each firm in a Cournot duopoly. A monopolist faces a demand with constant elasticity of -2.0.It has a constant marginal cost of R20 per unit and sets a price to maximise its profit. If marginal cost should increase by 25 percent, would the price charged also rise by 25 percent? Provide a brief explanation.Recently, the major firms in the United States cigarette industry joined with the government in a settlement of liability claims. Under the tentative agreement, the industry would curb advertising and pay the equivalent of about $15 billion per year (for smoking-related state Medicaid expenses) in exchange for protection against smoker lawsuits.a) Before the settlement, a leading cigarette manufacturer estimated its marginal cost at $1.00 per pack and its elasticity of demand at -2. What is its optimal price? The firm’s share of the industry payment (based on its historic market share) will raise its average total cost per pack by $.60. What effect will this have on its optimal price?b) A marketing manager suggests that the firm should offer price discounts to the company’s long-term, older, most-loyal (addicted?) customers. Do you agree? Explain carefully.c) In the past, anti-smoking information campaigns have had some limited success in reducing smoking. What price reaction (if any)…
- A nightclub manager realizes that demand for drinks is more elastic among students, and is trying to determine the optimal pricing schedule. Specifically, he estimates the following average demands: • Under 25: qr = 18 − 5p • Over 25: q = 10 − 2p The two age groups visit the nightclub in equal numbers on average. Assume that drinks cost the nightclub $2 each. (a) If the market cannot be segmented, what is the uniform monopoly price?Suppose that the monopolist from Question 4 is now forced to charge the same price in both markets. Using thedemand functions and cost function from Question 4, what is the total inverse demand in this case? What is theprofit-maximizing price? What is the monopolist’s profit? (Question 4 = A monopolist is operating in two separate markets. The inverse demand functions for the two markets are P1 = 35 – 2.5Q_1 and P2 = 30 – 2Q_2. The monopolist’s total cost function is TC(Q) = 8 + 5(Q_1 + Q_2). Q_1 means Q subscript 1A monopolist can produce at a constant average and marginal cost of ATC = MC = $5. It faces a market demand curve given by Q = 53 - P. Suppose there are N firms in the industry, all with the same constant MC = $5. Find the Cournot equilibrium. How much will each firm produce, what will be the market price, and how much profit will each firm earn? Also show that as N becomes large, the market price approaches the price that would prevail under perfect competition. (Hint: your answers will be functions of N)(BONUS)
- Market demand is given by p= 12-Q. There are two firms; the incumbent firm (1) and the entrant firm (E). Incumbent moves first by choosing quantity q, from the interval [0.1]. The entrant observes q and decides whether or not to enter and how much to produce if he enters (qe). There is no fixed cost of entry. If the entrant decides to stay out, his profit is zero and the incumbent enjoys a monopoly position. Suppose that both incumbent and entrant have identical marginal costs equal to c= 8 a) What is the subgame perfect equilibrium of this game? What are the quantities produced by the incumbent and entrant? What are their profits? b) What is the minimum quantity that must be produced by the incumbent to deter entry (to make entry unprofitable)? In this game, will the incumbent ever try to deter entry by increasing quantity?Consider any market that has a demand curve given by: Qd = 240 - 2P. Where Qd is the total quantity demanded in the market, given in millions of units and P is the market price, calculated in monetary units. Imagine that there are 2 Cournot oligopolists operating in this market with Cmg = CVme = 15 and fixed monthly costs equal to 1,400. About this market, ask yourself: a) What is the profit of each of the oligopolists? b) Imagine that one of the companies managed to implement a process innovation capable of halving its Cmg and CVme, so that they would go from 15 to 7.5. This investment implies an additional monthly expense of $1,800. Discuss the statement: "If this situation occurs, the innovative company will not implement variable cost reduction, as the quantity supplied in the market will increase very little; prices will remain very close to what they are today and its profits will not increase"Suppose that a firm is an imperfect competitor in the product market and a perfect competitor in the input markets and uses two variable inputs: Derive mathematically the first order condition showing how much of each input the firm should use se to maximize total profits Give a graphical interpretation of your answer to part (a). What characteristic of your figure indicates that the second order condition for maximization is satisfied? Indicate on your figure the level of "monopolistic exploitation".