The government subsidizes daycare for low-income families (especially important now that welfare ends after 2 years). For

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Question:

The government subsidizes daycare for low-income families (especially important now that welfare ends after 2 years). For simplicity, consider a single mother who wants to enroll in school. If possible, she would enroll in school full time and buy 40 hours of daycare. Assume all commodities are normal, indifference curves are smooth and convex, ignore any effects on the price of daycare, and ignore changes in her future income, etc. It is your job to evaluate the following three proposed government programs.

Plan A: Daycare subsidies where the subsidized price is set so that exactly 40 hours of daycare are purchased.

Plan B: Direct cash payments which can be used for any purchase (welfare payments are continued while the family is in school). The family receives an exact quantity of additional income which leads to 40 hours of daycare purchased.

Plan C: The government provides 40 hours of daycare free of charge to low-income families. (Cost to government is current market price.)

There are two families: the Smith family and the Jones family. Let’s see how the policies from question 3 (Plans A-C) would affect them. Daycare costs $10 per hour (Px = 10). Both have an initial income of $100 (m = 100). With Plan C, the government provides free childcare for 40 hours, and since daycare is $10 an hour, Plan C will cost the government $400.

(a) The Smith family has a demand function for daycare given by

x = 10mP _x ^–2

where x is the number of hours of daycare and P _x is the price of x.

i. What is their income elasticity of demand?

ii. Is day care a normal good or an inferior good?

iii. What is their price elasticity of demand?

iv. Is demand elastic or inelastic?

v. How many hours of daycare do they buy before the government intervention?

vi. Under Plan A the government offers a price subsidy for child care. What would the subsidy have to be to induce the Smith family to buy 40 hours of daycare?

vii. How much would that cost the government? (Take the subsidy and multiply it by 40)

viii. Under Plan B, the government gives the Smith family enough income to induce them to purchase 40 hours of childcare. How much income would they need to voluntarily buy 40 hours of child care?

(b) The Jones family has a demand function given by

x = 10 m ^1/2 P _x ^-1

i. What is their income elasticity of demand?

ii. What is their price elasticity of demand?

iii. Which family’s demand is more responsive to changes in the price? To changes in income?