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Homework answers / question archive / You are the marketing manager for XYZ Corp
You are the marketing manager for XYZ Corp. You have this regression result for your product:
Q=2000-3.5P+1.2I Right now your price is 10 and the average income of your customers is $30,000.
a. Compute income elasticity
b. Is your good a normal good or an inferior good?
c. You expect recession. You estimate that your customers average income will fall 5% due to this recession. Estimate the impact on your sales.
a.
Step one: Find the value of Q
The demand equation is given as:
Q=2000 - 3.5P + 1.2I
But
P = 10
I = $30,000
Hence, Q=2000 - 3.5(10) + 1.2(30,000) = 37,965 units
Step: Use the Q to work out the income elasticity
Income Elasticity (IE) = (change in quantity/change in income) * (income / quantity)
Where;
(Change in quantity/change in income) = 1.2: found by differentiating Quantity demanded (Q) with respect to income (I).
Income = $30,000
Quantity = 37,965 units
Hence, IE = 1.2 * (30,000 / 37,965) = 0.95
b.
Normal good because income elasticity of demand is greater than zero (0.95 > 0)
c.
Income elasticity of demand (YED) = %change in demand / %change in income
But
YED = 0.95
%change in income = 5%
0.95 = %change in demand / 5%
%change in demand = 0.95 * 5% = 4.75%.
When the average income of customers falls by 5%, the demand will decline by 4.75%.
Impact of revenue
Q = 37,965
4.75/100 * (37,965) = 1803.34 units
37,965 - 1803.34 = 36161.66 units
Revenue = P * Q
(37,965 * 10) - (36161.66 * 10) = $1803.34
Revenue will fall by $1803.34.
