Please, complete the following 2 applied problems in a Word or Excel document. Show all your calculations and explain your results. Submit your assignment in the drop box by using the Assignment Submission button. (A solved example is attached after the question)

1. A small business which produces plastic vacuum-suction covers for round household dishes has a monopoly that is protected by a utility patent. The market demand curve for this product is estimated to be: Q = 6009 – 25P where Q is the number of plate covers per year and P is in dollars. Cost estimation processes have determined that the firm’s cost function is represented by TC = 120 + 2500Q -0.25*Q2.

(i) What is the profit-maximizing price and output level? Solve this algebraically for equilibrium P and Q and also plot the MC, D and MR curves and illustrate the equilibrium point.

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 wealthy western suburbs of a major east-coast city. Last year, GGC’s price for the typical lawn system was $1,995 compared with BLG’s price of $2,100. GGC installed 9,130 systems, or about 55% of total sales and BLG installed the rest. (No doubt many additional systems were installed by do-it-yourself homeowners since the parts are readily available at hardware stores.) GGC has substantial excess capacity—it could easily install 25,000 systems annually, as it has all the necessary equipment and can easily hire and train installers. Accordingly, GGC is considering expansion into the eastern suburbs, where the homeowners are less wealthy. In past years, both GGC and BLG have installed several hundred systems in the eastern suburbs but generally their sales efforts are met with the response that the systems are too expensive. GGC has hired you to recommend a pricing strategy for both the western and eastern suburb markets for this coming season. You have estimated two distinct demand functions, as follows:

Qw = 1,035.548 – 6.07164Pgw + 2.83Pbw + 2,100Ag – 1,500Ab + 0.2348Yw

for the western market and

Qe = 49,714.29 – 30.7692Pge + 6.984Pbe + 1,180Ag – 950Ab + 0.0825Ye

for 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 disposable income levels of the potential customers; the subscripts w and e refer to the western and eastern 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 and expects BLG to spend $1.2 million on advertising. The average household disposable income is $55,000 in the western suburbs and $25,000 in the eastern suburbs. GGC does not expect BLG to change its price from last year, since it has already distributed its glossy brochures (with the $2,100 price stated) in both suburbs, and its TV commercial has already been produced. GGC’s cost structure has been estimated as TVC 5 755.363Q 1 0.005Q2 where Q represents single lawn watering systems.

a.    Derive the demand curves for GGC’s product in each market.

b.    Plot graphically the demand and MR curves for each market, and also show GGC’s combined marginal revenue curve (MR) and its MC curve. Show graphically the quantities that should be produced and sold, and the prices that should be charged, in each market.

We create some values for Q and derive the respective values for MC, and for P and MR in each market. Then we plot the functions for each market:

Q Pgw MRw MC Pge MRe
0 3498.725 3498.725 755.363 2179.875 2179.875
3000 3004.625 2510.524 785.363 2082.375 1984.874
6000 2510.524 1522.323 815.363 1984.874 1789.874
9000 2016.424 534.1226 845.363 1887.374 1594.874
12000 1522.323 -454.078 875.363 1789.874 1399.874
15000 1028.223 -1442.28 905.363 1692.374 1204.874
18000 534.1226 -2430.48 935.363 1594.874 1009.874
21000 40.02214 -3418.68 965.363 1497.374 814.8733

Western Market

c.    Confirm your quantity and price results algebraically.

d.    Calculate the price elasticities of demand in each market and discuss these in relation to the prices to be charged in each market.

e.    Add a short note to GGC management outlining any reservations and qualifications you may have concerning your price recommendations.

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