Please complete the following two applied problems:Problem 1: Robert’s New Way Vacuum Cleaner Company is anewly started small business that produces vacuum cleaners and belongsto a monopolistically competitive market. Its demand curve for theproduct is expressed as Q = 5000 – 25P where Q is the number of vacuumcleaners per year and P is in dollars. Cost estimation processes havedetermined that the firm’s cost function is represented by TC = 1500 +20Q + 0.02Q2. Show all of your calculations and processes.Describe your answer for each question in complete sentences, wheneverit is necessary.What are the profit-maximizing price andoutput levels? Explain them and calculate algebraically for equilibriumP (price) and Q (output). Then, plot the MC (marginal cost), D(demand), and MR (marginal revenue) curves graphically and illustratethe equilibrium point. How much economic profit do you expect that Robert’s company will make in the first year? Do you expect this economic profit level to continue in subsequent years? Why or why not? Problem 2: Greener Grass Company (GGC) competes with itsmain rival, Better Lawns and Gardens (BLG), in the supply andinstallation of in-ground lawn watering systems in the wealthy westernsuburbs of a major east-coast city. Last year, GGC’s price for thetypical lawn system was $1,900 compared with BLG’s price of $2,100. GGCinstalled 9,960 systems, or about 60% of total sales and BLG installedthe rest. (No doubt many additional systems were installed bydo-it-yourself homeowners because the parts are readily available athardware stores.) GGC has substantial excess capacity–it couldeasily install 25,000 systems annually, as it has all the necessaryequipment and can easily hire and train installers. Accordingly, GGC isconsidering expansion into the eastern suburbs, where the homeowners areless wealthy. In past years, both GGC and BLG have installed severalhundred systems in the eastern suburbs but generally their sales effortsare met with the response that the systems are too expensive. GGC hashired you to recommend a pricing strategy for both the western andeastern suburb markets for this coming season. You have estimated twodistinct demand functions, as follows: Qw =2100 – 6.25Pgw + 3Pbw + 2100Ag – 1500Ab + 0.2Yw for the western market and Qe = 36620 – 25Pge + 7Pbe + 1180Ag – 950Ab + 0.085Ye for the eastern market, where Q refers to thenumber of units sold; P refers to price level; A refers to advertisingbudgets of the firms (in millions); Y refers to average disposableincome levels of the potential customers; the subscripts w and e referto the western and eastern markets, respectively; and the subscripts gand b refer to GGC and BLG, respectively. GGC expects to spend $1.5million (use Ag = 1.5) on advertising this coming year and expects BLGto spend $1.2 million (use Ab = 1.2) on advertising. The averagehousehold disposable income is $60,000 in the western suburbs and$30,000 in the eastern suburbs. GGC does not expect BLG to change itsprice from last year because it has already distributed its glossybrochures (with the $2,100 price stated) in both suburbs, and its TVcommercial has already been produced. GGC’s cost structure has beenestimated as TVC = 750Q + 0.005Q2, where Q represents single lawnwatering systems. Show all of your calculations and processes.Describe your answer for each item below in complete sentences, wheneverit is necessary.Derive the demand curves for GGC’s product in each market. Derive GGC’s marginal revenue (MR) andmarginal cost (MC) curves in each market. Show graphically GGC’s demand,MR, and MC curves for each market. Derive algebraically the quantities that should be produced and sold, and the prices that should be charged, in each market. Calculate the price elasticities ofdemand in each market and discuss these in relation to the prices to becharged in each market.Add a short note to GGC managementoutlining any reservations and qualifications you may have concerningyour price recommendations.
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