Question

 

The XYZ Company is a producer of dishwashers. The company’s marketing department has estimated the following demand curve for the company’s best-selling model in one of its regions.

Q=2000-4P+6A+5I+5Pc-4Ac

Where Q = Number of dishwashers demanded

P = $600; Price of dishwashers

A = $150; Advertising expenditures (thousands)

I = $50; GDP per capita (thousands)

PC = $500; Competitor’s price

AC = $200; Competitor’s advertising expenditures (thousands)

d. What would be the effect on the sales of dishwashers if the competitor reduces price by $50? What should be the change in P to offset the decrease in PC ?

e. In response to competitor’s strategy of reducing PC , what else can the company do to keep sales at the same level if it does not want to change P ? (Base your answer on the information given above.)

f. If the government increases the sales tax by 1 percent, what will be the sale price of dishwashers after the tax (assume that the elasticity of demand is equal to the elasticity of supply in absolute value).

Answer 1

Demand equation is Q=2000-4P+6A+5I+5Pc-4Ac

For the given values, we have

• Advertising elasticity of demand = Advertising coefficient x Advertising / Quantity = 6 x 150 /2450 = 0.3673
• Cross price elasticity of demand = Competitor's Price coefficient x  Competitor's Price/Quantity = 5 x 500/2450 = 1.0204
• Own price elasticity = -4 x 600/2450 = -0.9795

d. What would be the effect on the sales of dishwashers if the competitor reduces price by $50?

CPE = 1.0204

% change in sales / % change in Competitor's Price = 1.0204

% change in sales / (-50*100/500) = 1.0204

% change in sales = -10.204%

Hence sales are reduced by -10.204% to reach 2200.

What should be the change in P to offset the decrease in PC?

Own price elasticity = -0.9795. We want our sales to rise by 10.204% so that the final effect can be negated./cancelled out

% change in sales / % change in own price = -0.9795

10.204%/% change in own price = -0.9795

% change in own price = 10.4175%

Hence own price should be reduced by 10.4175% to reach 537.50

e. In response to competitor’s strategy of reducing PC , what else can the company do to keep sales at the same level if it does not want to change P ?

We want our sales to rise by 10.204% so that the final effect can be negated./cancelled out. This can be done by increasing advertising

Advertising elasticity of demand = % change in sales / % change in advertising

10.204% / % change in advertising = 0.3673

% change in advertising = 27.78%

If advertising is increased by 27.78% to reach a level of 191.67 (thousand) the demand is increased to reach its original value.

f. If the government increases the sales tax by 1 percent, what will be the sale price of dishwashers after the tax

Given that ed = es, we have a tax burden that is shared equally so the price paid by buyers (P = 600) rises by 0.5% to become 603.