The demand for voice mail is Q = 1,000 - 150P + 25I. Assume that per capita disposable income I is $900. At a price P of $50, the income elasticity of demand is

Question

Quizplus · Accepted Answer

Using the formula for income elasticity of demand:

Income elasticity of demand = (% change in quantity demanded / % change in income)

We can rearrange the demand equation to solve for quantity demanded at a price of $50:

Q = 1,000 - 150(50) + 25(900)
Q = 11,500

Now, we can calculate the quantity demanded at a higher income level of $1,000 per capita:

Q1 = 1,000 - 150(50) + 25(1000)
Q1 = 13,000

The % change in quantity demanded is:

% change in quantity demanded = (Q1 - Q) / Q
% change in quantity demanded = (13000 - 11500) / 11500
% change in quantity demanded = 0.1304

The % change in income is:

% change in income = (1000 - 900) / 900
% change in income = 0.1111

Plugging these values into the formula for income elasticity of demand:

Income elasticity of demand = 0.1304 / 0.1111
Income elasticity of demand = 1.41

Therefore, the income elasticity of demand at a price of $50 is 1.41. This means that for a 1% increase in per capita income, the quantity demanded of voice mail increases by 1.41%.

The Demand for Voice Mail Is Q = 1,000 -