John Smith, C.E.O. of A.B.Co. is attempting to estimate the quantity of his prod

Question

John Smith, C.E.O. of A.B.Co. is attempting to estimate the quantity of his product that will be demanded during April. At the current price of $20.00, A.B. Co. is selling 100,000 units per month. Mr. Smith has been informed that on April 1st, Delta Co., a producer of a substitute good, will be decreasing the price of its product by 10%. Given a cross elasticity of 2 and the following information answer the following questions. For this problem you may use the definition of elasticity to forecast quantity even. MC = $4 Current Advertising Budget $200,000

A) How many units can Smith expect to sell during April and by how much will his profits be affected?

B) If Mr. Smith wants to maintain his current sales of 100,000 units, to what level should he change his price? (Assume Ep = -4)

C) At this new price for his product profits will change by how much from part A? D) An alternative strategy to lowering his price to restore his sales volume to 100,000 units would be to increase advertising expenditures. Given and Advertising elasticity of.5 how much should advertising expenditures be changed to restore his sales to 100,000 units?

E) Given your answer to D, what will be the change in his level of profits from part A?

F) Which alternative would you favor if profit is the most important variable to Mr. Smith?

Explanation / Answer

A) Cross price elasticity is defined as the change in quantity demanded of good x due to change in price of good y

Cross price elasticity = %change in QX / %change in PY

%change in QX = Cross price elasticity * %change in PY

%change in Price of subsitute = -10%

Hence %change in demand of A.B.C's product = 2 * -10 = -20%

Hence demand will decrease by 20%

Demand for April = (1-0.2)*100,000 = 80,000

Foregone Revenue = 20*20,000 = 400,000

Foregone Cost = 4*20,000 = 80,000

Foregone Profit = 320,000

B) Now EP = -4

Ep = %change in QX / %change in PX

Now change in QX required = 20,000

%change in QX = 20,000 / 80,000 = 25%

%change in PX =  %change in QX / EP = 25% / -4 = -6.25%

Hence he should decrease price by 6.25%

New price = (1 - 0.0625)*20 = $18.75

C) Profit foregone from original = (18.75 - 20)*100,000 = -$125,000

Change in Profit from A = -125000 - (-320000) = $195,000

If he decides to increase advertising

Advertising elasticity = %change in quantity demanded / %change in Ad. expenditure

%change in quantity = 25%

%change in Ad. expenditure = 25% / 0.5 = 50%

Hence he will have to increase advertising expenditure by 50%

New advertising expenditure = (1+0.5)*200,000 = $100,000

Profit foregone from original = -$100,000

D) Change in profit from A = -100000 - (-320000) = $220,000

F) Increasing advertising is the best alternative alternative as the profit foregone is minimum at $100,000.

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