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)?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter5: Income And Substitution Effects

Section: Chapter Questions

Problem 5.4P

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Concept explainers

Form Utility

The term utility in general refers to the satisfaction earned from usage of a particular product or service. Utility always plays an important role because it influences various important elements like demand & thereby the price of the good or service as well. Though utility is not easy to measure, various types of economic models can be used indirectly. There can be various types of utilities like economic utility, marginal utility, cardinal utility, form utility.

Question

A consumer has the utility function:

U (q₁,q₂) = q₁^1/4q₂^3/4

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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