Question

A recent study of the effects of income on demand for health care evaluated the effects of job changes, including job loss, unemployment compensation, and salary increases on the demand for healthcare. The study found that when income dropped by 2%, the demand for health services dropped 0.5%. Another recent study analyzed these effects by comparing the demand for health care across families at different income levels in the United States. The second study found that among families with annual incomes of $60,000, the demand for health care was approximately 0.75 times the demand among families with annual incomes of $80,000.

a. What is the formula for calculating income elasticity of demand? (Show the formula and describe each term in the formula.)

b. What is the income elasticity of demand implied by the first study? (Show your calculations.)

c. What is the income elasticity of demand implied by the second study? (Show your calculations.)

d. If these estimates are different, how would you explain these differences? (2-4 sentences.)

Answer 1

(a)

Income elasticity of demand = % Change in demand for a good (service) / % Change in consumer income

In this case Income elasticity is measured as the ratio of percentage change in demand for healthcare across families to the percentage change in income of consumers (demanders of healthcare).

(b)

Income elasticity (first study) = (-0.5%) / (-2%) = 0.25

(c)

As per second study, let

M1: Income of lower-income group = $60,000

M2: Income of higher-income group = $80,000

D1: Demand by lower-income group

D2: Demand by higher-income group

Given, D1 = 0.75 x D2

Using mid-point method,

% Change in demand = (D2 - D1) / [(D2 + D1)/2] = (D2 - 0.75D2) / [(D2 + 0.75D2)/2] = (1 - 0.75) / [(1 + 0.75)/2]

= (0.25 x 2) / 1.75 = 0.29

% Change in income = (M2 - M1) / [(M2 + M1)/2] = (80,000 - 60,000) / [(80,000 + 60,000)/2] = 20,000 / (140,000/2)

= 0.29

Income elasticity (second study) = 0.29/0.29 = 1

(d)

The difference lies in the calculation method. The first method uses the Point elasticity method (when we know which value is treated as initial value and which value is treated as new value), and the second method uses the Arc elasticity method (when we do not know which value is treated as initial value and which value is treated as new value).