Assume a monopoly firm is considering the production of two brands, 1 and 2. Marginal cost is constant at 20 for both products -- assume no fixed costs. The inverse demand for brand i is Pi = 140 - qidq;, where i ‡ j and d is a constant. Part a) Find the firm's quantities Part b) Find the firm's prices Part c) Find the firm's profit
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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.Assume a monopoly firm is considering the production of two brands, 1 and 2. Marginal cost is constant at 20 for both products -- assume no fixed costs. The inverse demand for brand i is pi=140−qi−dqj , where i≠j and d is a constant. Part A) Find the firm's QUANTITIESConsider a monopoly with a constant marginal cost of 10 that faces the following inverse demand function from senior citizens: PS = 50 − 2QS The monopoly also faces the following inverse demand function for all other customers: PO = 35 −Q0 a) List and explain the three conditions that must be satisfied for a firm to be able to price discriminate. b) Solve for the monopoly’s profit maximizing price and output levels assuming that they can price discriminate. c) In this example, who benefits and who loses from price discrimination? Be sure to explain/justify your answer.
- Consider a monopolist local movie theater which has two distinct client groups, adults and seniors. The inverse demands for the two group are given by:p(qA) = a − b · qAp(qB) = a/3-b/3.qB(a) Describe the demand function in the two markets graphically and then compute the demand elasticity in each market.(b) Compute the demand function qP under the assumption that the movie theather canonly offer a single price to both segments of the market. (Hint: at a given price addthe demand of the adults and senior market. You need to go from the inverse demand function to the demand function.) Illustrate the aggregate demand function in contrast to the demand functions in each segment. Now compute the optimal price of the movie theater when it can only offer a single and common price to the market segments. Who goes to the movies and who does not?(c) Next allow the movie theater to offer different prices in each segment and customerscannot mispresent their identity. What is the optimal price in…(Figure: Short-Run Monopoly) Look at the figure Short-Run Monopoly. If the firm is trying to maximize its profit, the per-unit profit is: The difference between O and where ATC at output R. The difference between N and where ATC at output R. The difference between N and where AVC at output R. N-PA monopolist faces the inverse demand function P(x) = a - bx and produces with constant marginal cost c. a. Determine the effect on equilibrium price of the introduction of a specific tax of value t.Is the tax over shifted? b. Calculate the effect on profitof the tax. Show that 5% =x, where x is the equillorium output level. Explain this result, . Now replace the specific tax with an ad valorem tax at rate t. Find a pair of taxes that lead to the same level of tax revenue. Which gives a lower price?
- Suppose a monopoly's price elasticity of demand equals-5 and the marginal cost of production equals $500.00. The profit-maximizing price is $ 625 (Enter a numeric response using a real number rounded to two decimal places.) What will be the firm's markup? When maximizing profit, the monopoly's markup is______percent. (Round your response to the nearest percent.)Assume the following equations describe the conditions for a monopoly: Qd = 2,000 - 100P TC = 3,500 + 5q + .005q2 Where Qd is the quantity demanded, P is the commodity's price in dollars, TC is the firm's total cost in dollars and q is the quantity of output produced. Based upon these equations, answer the following questions: a. What is the firm's equation for total revenue expressed as a function of quantity? b. What is the firm's equation for marginal revenue expressed as a function of quantity? What is the firm's equation for marginal cost expressed as a function of quantity? c. What is the firm's profit maximizing quantity of output? d. What price will the firm charge for the commodity? e. What would be the socially optimal quantity of output? f. What price would regulators have to establish in order to have the firm produce the socially optimal quantity of output?Explain Monopoly profit maximization and price determination using a detailed graphicalapproach. Be sure to label all relevant curves and axis. Make sure to explain monopolyprofits and the relationship between the demand and average cost curves. Part B. Using a graph, explain how a monopolist may price discriminate if identical units ofoutput are sold at different prices.
- Can you help with parts d,e, and f please? Assume the following equations describe the conditions for a monopoly: Qd = 2,000 - 100P TC = 3,500 + 5q + .005q2 Where Qd is the quantity demanded, P is the commodity's price in dollars, TC is the firm's total cost in dollars and q is the quantity of output produced. Based upon these equations, answer the following questions:a. What is the firm's equation for total revenue expressed as a function of quantity? b. What is the firm's equation for marginal revenue expressed as a function of quantity? What is the firm's equation for marginal cost expressed as a function of quantity? c. What is the firm's profit maximizing quantity of output? d. What price will the firm charge for the commodity? e. What would be the socially optimal quantity of output? f. What price would regulators have to establish in order to have the firm produce the socially optimal quantity of output?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…Consider a monopoly that faces the demand curve P = 20 − Q, and has the marginal cost curve MC = 2. a) Use the demand curve to find the equation of the marginal revenue curve. b) Find the profit-maximizing price and quantity for this monopoly if the monopoly uses uniform pricing. What is the producer surplus? c) Now, suppose the monopoly wants to increase profits using block pricing. The total cost the monopoly incurs is T C = 2Q. Find the optimal quantities, Q1 and Q2, and their corresponding optimal prices, P1 and P2 that maximize profits using a two-block pricing scheme. What is the new producer surplus? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
