Morgan has the following utility function: u(x, y) = 5 ln(x) + 3y. Her income is given by I = 15 and the prices originally are pa = 2 and py = 3. (a) What are Morgan's Marshallian demands? (b) How much of each good is Morgan currently consuming? (c) What is the utility level that Morgan can achieve? (d) Assume the price of x increases to p' = 4, find Morgan's new levels of consumption. (e) Find the total, substitution and income effects for good x caused by the price change. Consider this price change a "large" price change (APx = P - Px = 4 - 2 = 2).

Morgan has the following utility function: u(x, y) = 5 ln(x) + 3y. Her income is given by I = 15 and the prices originally are pa = 2 and py = 3. (a) What are Morgan's Marshallian demands? (b) How much of each good is Morgan currently consuming? (c) What is the utility level that Morgan can achieve? (d) Assume the price of x increases to p' = 4, find Morgan's new levels of consumption. (e) Find the total, substitution and income effects for good x caused by the price change. Consider this price change a "large" price change (APx = P - Px = 4 - 2 = 2).

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter6: Consumer Choice And Demand

Section: Chapter Questions

Problem 8QFR

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Question

Morgan has the following utility function: $ u(x, y) = 5 \ln(x) + 3y $. Her income is given by $ I = 15 $ and the prices originally are $ p_x = 2 $ and $ p_y = 3 $.

(a) What are Morgan’s Marshallian demands?

(b) How much of each good is Morgan currently consuming?

(c) What is the utility level that Morgan can achieve?

(d) Assume the price of $ x $ increases to $ p_x' = 4 $, find Morgan’s new levels of consumption.

(e) Find the total, substitution, and income effects for good $ x $ caused by the price change. Consider this price change a “large” price change ($ \Delta p_x = p_x' - p_x = 4 - 2 = 2 $).

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