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 5 755.363Q 1 0.005Q2 where Q represents single lawn watering systems.

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

Answer:

We are given

Ag = $1.5 million, Ab = $1.2 million, Yw = $55000, Ye = $25000, Pb = $2100

To derive the demand curves, we substitute these values in the demand functions;

Qw = 1,035.548 – 6.07164Pgw + 2.83*2100 + 2,100*1.5 – 1,500*1.2 + 0.2348*55000 or

6.07164Pgw = 21242.548 – Qw or

Pgw = 3498.6508 – 0.1647Qw   ……… this is derived demand for western markets.

Similarly for Eastern markets;

Qe = 49,714.29 – 30.7692Pge + 6.984*2100+1,180*1.5 – 950*1.2 + 0.0825*25000 or

Pge=67073/ 30.7692 -Qe/ 30.7692 or

Pge= 2,179.88 – 0.0325Qe . ……… this is derived demand for Eastern markets.

  • 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.

Answer:

Let us start with the Western market:

TRw= (3498.6508 – 0.1647Qw) *Qw or

(3,498.65 – 0.1647Qw)Qw

=3498.65Qw – 0.1647Qw2


MRw = 3498.65 – 0.3294Qw (see the note on calculus)

For the Eastern market, we have:

Pge=67073/ 30.7692 -Qe/ 30.7692

Pge = 2,179.88 – 0.0325Qe

TRe = (2,179.88 – 0.0325Qe)*Qe

TRe = 2179.88Q – 0.0325Qe2

MRe= 2,179.88 – 0.065Qe

The cost information is the same for both markets:
TVC=755.363Q+0.005Q2


MC=dTVC/dQ = 755.363+2*0.005Q

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

The optimal allocation occurs at a point where MR and MC intersect. We can note from the graph that this happens when quantity is between 6000 and 9000 units.And price is between

Eastern Market

For the Eastern states, optimal quantity (as identified by the intersection of MR with MC) is just under 20000

  • Confirm your quantity and price results algebraically.

Answer:

For western market;

MRw = 3498.65 – 0.3294Qw and MC=755.363+2*0.005Q

At optimum, MRw = MC i.e.

3498.65 – 0.3294Qw = 755.363+ 0.01Qw i.e.

0.3394Qw = 2734.287, implies profit maximizing quantity in western market Qw* = 8083

And profit maximizing price in western market Pgw* = 3498.6508 – 0.1647*8083 = $2167

For eastern market;

MRe= 2,179.88 – 0.065Qe and MC=755.363+2*0.005Q

At optimum, MRe = MC i.e.

2,179.88 – 0.065Qe = 755.363+0.010Qe or

0.075Qe = 1424.517, implies profit maximizing quantity in eastern market Qe* = 18994

And profit maximizing price in eastern market Pge* = 2,179.88 – 0.0325*18994 = $1563

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

Answer:

Elasticity (Western) = (dQw/dPw)*(Pw/Qw)

Using demand function (Pgw = 3498.6508 – 0.1647Qw)  for Western market, we derive (dQw/dPw) as;

(dQw/dPw) = -1/0.1647 = -6.07164

So, Elasticity (Western) = (dQw/dPw)*(Pw/Qw) = (-6.07164)*2167/8083= -1.63, which is elastic

Elasticity (Eastern) = (dQe/dPe)*(Pe/Qe)

Using demand function (Pge= 2,179.88 – 0.0325Qe) for eastern market, we derive (dQe/dPe) as;

(dQe/dPe) = 1/0.0325 = 30.769

So, Elasticity (Eastern) = (dQe/dPe)*(Pe/Qe) = (-30,7692)*(1563/18994)= -2.53, which is more elastic

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

Answer:

Since the competitor i.e. BLG charges same price (=$2100) in both the market, GGC’s pricing strategy in the eastern market looks appropriate and allows GGC to optimize its sales. On the other hand, GGC’s pricing in the western market is very similar to BLG’s pricing i.e. they are operating symmetrically.

e) As the competitor is charging $2100 in both markets, it appears that GGC’s pricing strategy is appropriate in the Eastern markets as it will optimize its sales and allow it to more than double its sales there. The pricing in the Western markets is very similar to its competitor’s pricing

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