A consumer has the utility function: U (q1,q2) = q11/4q23/4 where q1 is the amount spent on childcare and and q2 is a composite good (each therefore have prices of 1 per unit). The consumer has an income of Y = 60 (a) Find the quantities of childcare and composite good the consumer purchases. (b) The government is testing a new policy of providing this family with 40 units of free childcare. Childcare is not transferable (cannot be sold for cash). Derive the consumer’s optimal consumption quantity of childcare and composite good. (c) Suppose instead that the government simply gave the family 40 of additional income to spend as the family wants. Find the optimal consumption bundle. Which policy is better for the family (or are they the same)?
A consumer has the utility function: U (q1,q2) = q11/4q23/4 where q1 is the amount spent on childcare and and q2 is a composite good (each therefore have prices of 1 per unit). The consumer has an income of Y = 60 (a) Find the quantities of childcare and composite good the consumer purchases. (b) The government is testing a new policy of providing this family with 40 units of free childcare. Childcare is not transferable (cannot be sold for cash). Derive the consumer’s optimal consumption quantity of childcare and composite good. (c) Suppose instead that the government simply gave the family 40 of additional income to spend as the family wants. Find the optimal consumption bundle. Which policy is better for the family (or are they the same)?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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A consumer has the utility function:
U (q1,q2) = q11/4q23/4
where q1 is the amount spent on childcare and and q2 is a composite good (each therefore have prices of 1 per unit). The consumer has an income of Y = 60
(a) Find the quantities of childcare and composite good the consumer purchases.
(b) The government is testing a new policy of providing this family with 40 units of free childcare. Childcare is not transferable (cannot be sold for cash). Derive the consumer’s optimal consumption quantity of childcare and composite good.
(c) Suppose instead that the government simply gave the family 40 of additional income to spend as the family wants. Find the optimal consumption bundle. Which policy is better for the family (or are they the same)?
Answer all three.
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