### Utility Maximization Problem#### Problem Statement:**Given:**- Amy derives utility from housing ($ h $), and a consumer good ($ z $), with the following utility function:\[ U = h^{1/3} z^{2/3} \]- Her Mashallian demand equations are:\[ h = \frac{M}{3p_h} \quad \text{and} \quad z = \frac{2M}{3p_z} \]- Amy lives in a city where everyone works downtown. While her income is $160 per month, her commute cost (bus pass) costs her $40 per month, so she only has $120 to spend on $ h $ and $ z $ (we assume no time cost of the commute). The consumer good $ z $ has a price of $1 and the price of her housing $ h $ is $2 per unit.**Questions:****a.** What is her quantity demanded of $ h $ and $ z $ and what level of utility is she currently enjoying?**b.** She is considering moving to a location further from work to a house where her commuting cost would be $60 per month (so she will have $100 to spend on $ z $ and $ h $). The market adjusts $ p_h $ and housing sizes across the city so that utility is the same at every location around the city. What is the equation for the appropriate demand function for housing in this city?**c.** What is the price of housing at the new location and what will be her quantity demanded of $ h $ and $ z $ at that location?---### Solution Approach:**a. Current Quantity Demanded and Utility Level**1. **Determine the budget available for housing and consumer good:** - Income: $160/month - Commute cost: $40/month - Amount available for $ h $ and $ z $: $120/month2. **Given prices:** - Price of $ z $ ($ p_z $): $1 - Price of $ h $ ($ p_h $): $23. **Use Mashallian demand equations to find $ h $ and $ z $:**\[ h = \frac{M}{3p_h} = \frac{120}{3 \times

Utility function : U = h1/3 z2/3 h* = M/3ph , z* = 2M/ 3pz Income = 160 Commute Cost = 40 Pz = 1…

1. Let Amy derive utility each from housing, h, and a consumer good, z, with the following utility function: 1/ 2/ U=h¾/³₂¾3 M 2M Her Mashallian demand equations are the following: h=; and z: 3ph 3p₂ Amy lives in a city where everyone works downtown. While her income is $160 per month, her commute cost (bus pass) costs her $40 per month, so she only has $120 to spend on h and z. (we assume no time cost of the commute) The consumer good, z, has a price of $1 and the price of her housing, h, is $2 per unit. a. What is her quantity demanded of h and z and what level of utility is she

1. Let Amy derive utility each from housing, h, and a consumer good, z, with the following utility function: 1/ 2/ U=h¾/³₂¾3 M 2M Her Mashallian demand equations are the following: h=; and z: 3ph 3p₂ Amy lives in a city where everyone works downtown. While her income is $160 per month, her commute cost (bus pass) costs her $40 per month, so she only has $120 to spend on h and z. (we assume no time cost of the commute) The consumer good, z, has a price of $1 and the price of her housing, h, is $2 per unit. a. What is her quantity demanded of h and z and what level of utility is she

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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QUESTION 12 The relationship between the marginal utility that George gets from eating a bag of cookies and the number of bags he eats per month is as follows: Bags of Cookies Marginal Utility 1 2 3 4 5 6 20 16 12 8 4 0 George receives 2 units of utility from the last dollar spent on each of the other goods he consumes. If cookies cost $4 per bag, how many bags of cookies will he consume per month if he maximizes utility?
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4.
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