A small business which produces plastic vacuum-suction covers for round household

Please, complete the following 2 applied problems in a Word or Excel document. Show all yourcalculations and explain your results. Submit your assignment in the drop box by using theAssignment Submission button.1. A small business which produces plastic vacuum-suction covers for round householddishes has a monopoly that is protected by a utility patent. The market demand curve forthis product is estimated to be: Q = 6009 25P where Q is the number of plate coversper year and P is in dollars. Cost estimation processes have determined that the firmscost function is represented by TC = 120 + 2500Q -0.25*Q2.(i)What is the profit-maximizing price and outputlevel? Solve this algebraically for equilibrium P and Q andalso plot the MC, D and MR curves and illustrate theequilibrium point.(ii)What profit do you expect that the firm will make in the firstyear?(iii)Do you expect this profit level to continue in subsequentyears? Why or why not?2. Greener Grass Company (GGC) competes with its main rival, Better Lawns and Gardens(BLG), in the supply and installation of in-ground lawn watering systems in the wealthywestern suburbs of a major east-coast city. Last year, GGCs price for the typical lawnsystem was $1,995 compared with BLGs price of $2,100. GGC installed 9,130 systems,or about 55% of total sales and BLG installed the rest. (No doubt many additionalsystems were installed by do-it-yourself homeowners since the parts are readily availableat hardware stores.) GGC has substantial excess capacityit could easily install 25,000systems annually, as it has all the necessary equipment and can easily hire and traininstallers. Accordingly, GGC is considering expansion into the eastern suburbs, where thehomeowners are less wealthy. In past years, both GGC and BLG have installed severalhundred systems in the eastern suburbs but generally their sales efforts are met with theresponse that the systems are too expensive. GGC has hired you to recommend a pricingstrategy for both the western and eastern suburb markets for this coming season. Youhave estimated two distinct demand functions, as follows:Qw = 1,035.548 – 6.07164Pgw + 2.83Pbw + 2,100Ag – 1,500Ab + 0.2348Ywfor the western market andQe = 49,714.29 – 30.7692Pge + 6.984Pbe + 1,180Ag – 950Ab + 0.0825Yefor the eastern market, where Q refers to the number of units sold; P refers to price level;A refers to advertising budgets of the firms (in millions); Y refers to average disposableincome levels of the potential customers; the subscripts w and e refer to the western andeastern markets, respectively; and the subscripts g and b refer to GGC and BLG,respectively. GGC expects to spend $1.5 million on advertising this coming year andexpects BLG to spend $1.2 million on advertising. The average household disposableincome is $55,000 in the western suburbs and $25,000 in the eastern suburbs. GGC doesnot expect BLG to change its price from last year, since it has already distributed itsglossy brochures (with the $2,100 price stated) in both suburbs, and its TV commercialhas already been produced. GGCs cost structure has been estimated as TVC 5 755.363Q1 0.005Q2 where Q represents single lawn watering systems.a. Derive the demand curves for GGCs product in each market.b. Plot graphically the demand and MR curves for each market, and also showGGCs combined marginal revenue curve (MR) and its MC curve. Showgraphically the quantities that should be produced and sold, and the prices thatshould be charged, in each market.c. Confirm your quantity and price results algebraically.d. Calculate the price elasticities of demand in each market and discuss these inrelation to the prices to be charged in each market.e. Add a short note to GGC management outlining any reservations andqualifications you may have concerning your price recommendations.