1) Suppose you are operating a discount movie theater and want to increase profits by charging adults and kids different prices. Assume there are no variable costs, just fixed costs to show the movie. You estimate the inverse demand function for kids to be: p1(y1) = 4 - 0.05y1 You estimate the inverse demand function for adults to be: p2(y2) = 9.6 - 0.08y2 a) How many kids will watch a movie? What price will you charge kids? b) How many adults will watch a movie? What price will you charge adults? -
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- As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 400,000 −400Q and P = 900,000 −250Q, respectively. Your cost function is C(Q) = 125,000 + 430,000Q. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes Profits you can expect: $As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 300,000 – 400Q and P = 500,000 – 275Q, respectively. Your cost function is C(Q) = 140,000 + 240,000Q. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes Profits you can expect: $As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 40 percent chance of low demand and a 60 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 400,000 −450Q and P = 600,000 −250Q, respectively. Your cost function is C(Q) = 170,000 + 256,000Q. How many new homes should you build, and what profits can you expect? a. Number of homes you should build: _____ homes b. Profits you can expect: $
- As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 80 percent chance of low demand and a 20 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 300,000 −300Q and P = 800,000 −200Q, respectively. Your cost function is C(Q) = 180,000 + 260,000Q. How many new homes should you build, and what profits can you expect? Give typing answer with explanation and conclusionYou are a medical group manager. Some market research has suggested that the price elasticity of demand for the services of your physicians is −4.1. The marginal cost for the average unit of physician service in your group is approximately $536. A. Using the economic pricing model formula, calculate your profit-maximizing price for each unit of physician services. B. Suppose that your medical group is considering new contracts with two particular businesses to provide physician services to their employees. If the marginal cost for each service unit is the same as with the rest of your customers, but the price elasticity of demand from the first new business customers is −0.9, and the second group of business customers is −4.4, how would that change your profit-maximizing price for each of the new groups? Would you recommend that your medical group obtain contracts with both new groups, just one of them or none? Explain your reasoning. C. In order to maximize your profits, what specific…Suppose the demand function for a product is given by the function: D ( q ) = − 0.02 q + 80 D ( q ) = - 0.02 q + 80 Use integration (or other appropriate methods) to find the following: (Do no rounding of results until the very end of your calculations. At that point, round to the nearest tenth, if necessary. It may help you to sketch the demand curve, which crosses the horizontal at q = 4 , 000 q = 4 , 000 .) A) The total actual revenue for q = 3 , 350 q = 3 , 350 units: Answer 1: B) The total possible revenue (for all quantities and prices): Answer 2: C) The Consumer's surplus corresponding to q = 3 , 350 q = 3 , 350 units: Answer 3: D) The "Not Sold" value corresponding to q = 3 , 350 q = 3 , 350 units: Answer 4
- Assume you are the Director of Marketing for Majjus Enterprise, a firm that produces a new product called African Solar. Your company sells to two distinct geographical markets-East Legon and Nima. Majjus Enterprise is described as a monopolist and has the possibility of discriminating between its East Legon and Nima Markets. In order to derive the maximum profit from the production process, you engaged the services of an Econometrician, who estimated the demand functions for both East Legon and Nima markets to be: Q1 = 24 – 0.2P1 East Legon Market Q2 = 10 – 0.05P2 Nima Market Where Q1 and Q2 are the respective quantities of African Solar demanded in the East Legon and Nima markets and P1 and P2 are their respective prices (in GH¢). If the Total Cost (TC) of Majjus Enterprise for producing African Solar for these two markets is given as TC = 35 + 40Q, where Q = Q1 + Q2. What profit will Majjus Enterprise make with and without price discrimination? What…– A certain cleaning company cleans professional offices and believes its staff can clean up to 300 office units a week at a labor and supply cost of $58 per unit. Preliminary pricing surveys indicate that if that if the company charges $100 per unit, it will have clients for 300 units. For every $5 price increase it can expect a demand of 10 fewer units. Assume the demand, s, is a linear function of price p. Find an equation for demand as a function of price. Find the Revenue and Cost functions, both of which are dependent on price p. Write the Profit function. Using Desmos, graph the Revenue, Cost, and Profit functions on the same coordinate plane. Label the axes and the functions and use an appropriate scale. Find the break-even points graphically and confirm algebraically. Label the regions of profit and loss on the graph. Algebraically find the price that results in a maximum profit. Conclusion: A price of $_________ results in a quantity of _____________ units…Exercise 4.6 An econometrician hired to analyse a local golf course has determined that there are two types of golfers, the regular and the occasional. The annual demand for games from regular players is given by QH = 24 – 0.3P, where P is the price of a round of golf. On the other hand, the annual demand for occasional items is given by QO = 10 – 0.1P. The marginal cost and the average total cost per item are equal to €20. a) If you could distinguish between regular and casual players, what price would be set for each type? How many games would each type of player play? How much profit could the golf course generate? Represent graphically. b) As an alternative to the discrimination of third degree prices, those in charge consider a double tranche rate according to which the members can play as many games as they wish at a price of € 20 per game. How much profit will the golf course generate if it charges all players the same annual fee for becoming a member of the club? What if you…
- Question: As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 300,000 − 400Q and P = 500,000 − 275Q, respectively. Your cost function is C(Q) = 140,000 + 240,000Q. How many new homes should you build, and what profits can you expect?James mainly sells confectionery items, newspapers, magazines and cigarettes in his convenience store. Noting his small business is not thriving, he thought of selling hot pies and rolls too. Suppose the total cost function for rolls and pies is, TC = 900 + 50Q, Q = Q1 + Q2 Where Q1 and Q2denote the quantities of rolls and pies respectfully. If P1 and P2 denote the corresponding prices, the inverse demand equations are. Q1 = 70 - P1 and 0.5Q2 = 100 - P2 a)If James decides to make a total of 48 rolls and pies per day and charges different prices as above (that is, P1 ≠ P2 ), how many of rolls and pies each should he make in order to maximize the profit of a particular day? Estimate and interpret the Lagrange Multiplier λ [note: assume second-order conditions are satisfied]. b)Using your knowledge of input-output tables, explain which components of the economy will be affected if all convenience stores, including James’, closed down for three months due to the COVID-19. What would…You have been appointed the new manager for Ghana Airways Company Limited, an internationalairline company that flies from the Kotoka International Airport in Accra to Heathrow Airport inLondon every day. The airline is described as a monopolist and has the possibility of discriminatingbetween its Business and Economy Travelers. To help you determine the prices your servicesappropriately to maximise profit, you engaged an economist who estimated the demand function forboth Economy and Business Travelers as:Q1 = 24 – 0.2P1 Economy TravelersQ2 = 10 – 0.05P2 Business TravelersWhere Q1 and Q2 are the respective numbers of Economy and Business Travelers and P1 and P2 aretheir respective fares (in GH¢). If the Total Cost (TC) of this airline company for flying these twocategories of travelers is given as TC = 35 + 40Q, where Q = Q1 + Q2.What can you say about the fares, number of travelers and profit of Ghana Airways CompanyLimited, with and without price discrimination?