please solve question 4- Prove that total revenue is maximized for a linear demand function, P = a - bQ point where Q = a / 2 * b . - Minimize the following cost function: TC = 1/3 * Q ^ 3 - 8.5Q ^ 2 + 60Q + 27
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please solve question 4- Prove that total revenue is maximized for a linear demand function, P = a - bQ point where Q = a / 2 * b .
- Minimize the following cost function:
TC = 1/3 * Q ^ 3 - 8.5Q ^ 2 + 60Q + 27
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- Ticket Price, Cost ($) 10 8 00 D₁ = Dx+DA MC = ATC MRT 20 28 38 10 0 Adult Tickets DK 6 4 MC = ATC MRK Children's Tickets 20 20 1. The Figure above describes demand and cost conditions facing the Salinas Cinema-Plex. Note that marginal costs are constant ($). The demand for Cinema-Plex movie tickets by adult patrons is given by DA and by child patrons Dk. a) Calculate total revenue from ticket sales IF the Cinema-Plex did NOT practice 3rd degree price discrimination, but rather charged a single price to adult and child patrons. b) Calculate the total number of tickets sold if the Cinema-Plex DID practice 3rd degree price discrimination. c) Calculate the change in consumer surplus (CS) received by adult patrons if the Cinema-Plex shifted from a single price to a 3rd degree price discrimination regime. d) How much (economic) profit does the Cinema-Plex stand to gain by engaging in 3rd degree price discrimination?Suppose a monopoly market faces a demand curve given by Q = (20 – P)(1 + 0.1A – 0.01A²) %3D - - and the cost function is given by C = 10Q + 15 + A %3D What output level will be chosen if the firm chooses its optimal level of advertising expenditures (A)? (a) Qm = 3 (b) Qm = 6.05 (c) Qm = 90.75 %3D %3D1. A company can sell its product in two separate market defined by the following inverse demand functions, P1=10-Q1 , P2=20-1.5Q2 the cost associated with production is given by ?? = 4 + 2Q a) What prices and quantities should the firm charge and produce in each market. b) What profit will the firm make if it practice price discrimination c) If the firm is charging uniform price in all market what price will it charge and what output will maximize profit d) What is the maximum profit for charging same price? e) Calculate the elasticity of demand in each market and comment on your result
- 3. A monopolist with zero cost, that is c(q) = 0, faces two consumers whose demand functions are given below. Q1 = 10 -P Q2 4--P (a) Suppose the monopolist cannot engage in any price discrimination. Find the firm's optimal pricing strategy. 1 (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-diserimination strategy.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…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 quantity
- You are the manager of a monopoly, and your analysts have estimated your demand and cost functionsas P = 300 − 3Q and C(Q) = 2, 000 + 2Q2, respectively.(a) What price-quantity combination maximizes your firm’s profits?(b) Calculate the maximum profits.(c) Is demand elastic, inelastic, or unit elastic at the profit maximizing price-quantity combination?(d) What price-quantity combination maximizes revenue?(e) Calculate the maximum revenues.(f) Is demand elastic, inelastic, or unit elastic at the revenue maximizing price-quantity combination?Restaurant Pricing. Suppose there is a single restaurant in a small town facing the demand function P=13-0.10×Q. Further, suppose the marginal cost of providing a meal is constant at $3. 15- 14 13- Given the above information: 12-1 11- 1) Use the line drawing tool to draw the demand line. Properly label this line. 10- 2) Use the line drawing tool to draw the corresponding marginal revenue line. Properly label this line. 3) Use the line drawing tool to draw the marginal cost. Properly label this line. my 4) Use the point drawing tool to identify the profit-maximizing price and quantity. Label this point 'a, 4. 3. Note: if you aren't prompted for labels, then you are using the wrong tool The profit-maximizing quantity is | Tand the profit-maximizing price is (Enter your responses as integers) e 00 Number of meals served Price permeal9. 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.
- Q. Total consumers can be divided into Group A and Group B, and it is assumed that a monopoly company makes third-degree price discrimination. The demand function of each group and the cost function of the company are as follows. QA = 10-PA, QB = 12-2 PB, C(Q) = Q2 (1) Find the third-order price discrimination price that maximizes the profit of the company. (2) Assume that price discrimination between groups is prohibited by law. Find the maximum profit price.A monopolist's inverse demand function is P=150-3Q. the company produces output at two facilities; the marginal cost of producing at facility 1 is MC1(Q1)=6Q1, and the marginal cost of producing at facility 2 is MC2(Q2)=2Q2 A). Provide the equation for the monopolist's marginal revenue function. MR(Q)= ___ -___Q1-____Q2 B). Determine the profit-maximizing level of output for each facility. Output for facility 1: Output for facility 2: C). Determine the profit-maximizing price.Suppose a certain city has a monopoly cable-television company. This company has total costs TC = 0.25Q2 + 30Q + 70. (Hint: using calculus, this means MC = 0.5Q+ 30since MC is the derivative of TC with respect to output.) The demand in the community is approximated by the equationQd = 60- P/2(alternatively, you can write the demand equation as Qd = 60–0.5P). Graphically depict the demand curve as well as the marginal cost (MC) curve. If the cable company is free to choose its own pricePm and quantityQm, graphically depictthe monopoly equilibrium price and quantity. Add any other curve(s) to your diagram that may be required to obtain this outcome. Compute and state the exact monopolist equilibrium pricePm and quantityQm that you depicted graphically.