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Given that,<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

(1) Qw = 1,035.548 – 6.07164Pgw + 2.83Pbw + 2,100Ag – 1,500Ab + 0.2348Yw for the western market, and

(2) Qe = 49,714.29 – 30.7692Pge + 6.984Pbe + 1,180Ag – 950Ab + 0.0825Ye for the eastern market,

We have,

<?xml:namespace prefix = v ns = "urn:schemas-microsoft-com:vml" /> = $1.5 million

= $1.2 million

= $0.055 million

= $0.025 million

= = $2,100

And also,

TVC = 5755.363Q – 10.005

TC = 1.5 + 5755.363Q – 10.005

How do I solve alegebracially for Quantity and Price?

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Mahe Alam
Mahe AlamLv10
28 Sep 2019

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Related questions

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 east ¬ern 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 = 755.363Q + 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 (î“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.

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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