You are the marketing manager for XYZ Corp

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.