Demand Curve

a. To derive the demand curve for the western suburbs, substitute the values for advertising, income and prices and derive a function/equation for the price. Qw = 2100 - 6.25Pgw + 3Pbw + 2100Ag - 1500Ab + 0.2Yw = 2100 - 6.25Pgw + 3*2100 + 2100*1.5 - 1500*1.2 + 0.2*60000 = 2100 - 6.25Pgw + 6300 + 3150 - 1800 + 12,000 Pgw = 21750/6.25 - Qw/6.25 = 3480 - 0.16Qw is the derived demand curve. In the same manner, derive a function/equation for the eastern suburbs: Qe = 36620 - 25Pge + 7Pbe + 1180Ag - 950Ab + 0.085Ye = 36620 - 25Pge + 7*2100 + 1180*1.5 - 950*1.2 + 0.085*30000 = 36620 - 25Pge + 14700 + 1770 - 1140 + 2550 Pge = 54500/25 - Qe/25 = 2180 - 0.04Qe is the derived demand curve.

b. Let us start with the western market: TRw = Pgw∙Qw = (3480 - 0.16Qw)∙Qw = 3480Qw - 0.16Qw2 MRw = dTRw/dQw = 3480 - 0.32Qw For the eastern market, we have: TRe = Pge∙Qe = (2180 - 0.04Qe)Qe = 2180Qe - 0.04Qe2 MRe = dTRe/dQe = 2180 - 0.08Qe The cost information is the same for both markets: TVC = 750Q + 0.005∙Q2 MC = dTVC/dQ = 750 + 2*0.005∙Q = 750 + 0.01Q Western Market Price 3480 MC = 750 + 0.01Q 750 10875 21750 Qty MRw = 3480 - 0.32Qw D = Pgw = 3480 - 0.16Qw Eastern Market Price 2180 MC = 750 + 0.01Q 750 27250 54500 Qty MRe = 2180 - 0.08Qe D = Pge = 2180 - 0.04Qe

c. We can calculate by setting MR = MC (profit maximization condition) and solving for Q and then using that Q to find P form the demand curve: For the Western market: MRw=MC: 3480 - 0.32Qw = 750 + 0.01Qw Qw* = 8273 Pgw = 3480 - 0.16Qw Pgw* = $2156 For the Eastern market: MRe= MC: 2180 - 0.08Qe = 750 + 0.01Q Qe* = 15889 Pge = 2180 - 0.04Qe Pge* = $1544

d. The price elasticity of demand in the western market is: Elasticity (Western) = (dQw/dPw)*(Pw/Qw) = (-6.25)*2156/8273= -1.63, which is elastic. The price elasticity of demand in the eastern market is: Elasticity (Eastern) = (dQe/dPe)*(Pe/Qe) = (-25)*1544/15889= -2.43, which is more elastic. With elastic demand, it makes sense for price to be reduced so as to increase sales/total revenue. This indicates that the GGC strategy to lower its price for the eastern suburbs seems to work fine there.

e. As the competitor, Better Lawns and Gardens (BLG), is charging $2,100 in both markets, it appears that GGC's pricing strategy of charging a lower price ($1,544) is appropriate in the eastern market as the maximizes its profit. Although the profit maximizing price in the western market is $2156, GGC may lower its price to around $2,100 to be more competitive in the western market.