# Economics: Elasticity Theory – #29504

Question:

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 $1,900 compared with BLG’s price of$2,100. GGC installed 9,960 systems, or about 60% of total sales and BLG installed the rest. (No doubt many additional systems were installed by do-it-yourself homeowners because 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:

$Qw\text{ }=2100\text{ }\text{ }6.25Pgw\text{ }+\text{ }3Pbw\text{ }+\text{ }2100Ag\text{ }-\text{ }1500Ab\text{ }+\text{ }0.2Yw$

for the western market and

$Qe\text{ }=\text{ }36620\text{ }-\text{ }25Pge\text{ }+\text{ }7Pbe\text{ }+\text{ }1180Ag\text{ }-\text{ }950Ab\text{ }+\text{ }0.085Ye$

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 (use Ag = 1.5) on advertising this coming year and expects BLG to spend$1.2 million (use Ab = 1.2) on advertising. The average household disposable income is $60,000 in the western suburbs and$30,000 in the eastern suburbs. GGC does not expect BLG to change its price from last year because 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 = 750Q + 0.005Q2, where Q represents single lawn watering systems.

Show all of your calculations and processes. Describe your answer for each item below in complete sentences, whenever it is necessary.

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

b. Derive GGC’s marginal revenue (MR) and marginal cost (MC) curves in each market. Show graphically GGC’s demand, MR, and MC curves for each market.

c. Derive algebraically the quantities that should be produced and sold, and the prices that should be charged, in each market.

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.

Guidance: First, review the "grading rubric", second, use the following hints as a guide through the above questions….; (a) To derive the demand curve for the western suburbs, substitute the values for advertising, incoMeand prices and derive a function/equation for the price…..in the same manner, derive a function/equation for the eastern suburbs; (b) Similar to what you did for the first problem, derive the MR, to do this you must first calculate TR….recall that TR = P * Q., next marginal cost (MC) can be derived from the total cost (TC) function; (c) calculate P & Q by setting MR = MC (profit maximization condition) and solving for Q and then using that Q to find P form the demand curve…do this for both markets. (d) calculate price elasticity of demand for each market (percentage change in quantity demanded/percentage change in price) recall that we use the absolute value; (e) note that there are price strategies related with elastic/inelastic demand….does it make sense for price to be reduced/increased so as to increase sales/total revenue?