A 2015 report by the music industry estimated the revenue lost to the industry every year from illegal downloading. In this problem we will derive some of the estimates that may have gone into their calculation (approximately). First, start with the individual consumer’s problem. Suppose a typical consumer has a yearly entertainment budget of I that they can allocate between music downloads (D) and other forms of entertainment (E). Consumer preferences are characterized by a utility function U(D, E). a.) Write an expression for the consumer’s budget constraint as a function of their entertainment budget and the prices of music downloads (Pd ) and other entertainment (Pe). (b) Write the consumer’s constrained optimization problem in Lagrangian form. (Note: You do not need to solve it or derive first order conditions.)

A 2015 report by the music industry estimated the revenue lost to the industry every year from illegal downloading. In this problem we will derive some of the estimates that may have gone into their calculation (approximately). First, start with the individual consumer’s problem. Suppose a typical consumer has a yearly entertainment budget of I that they can allocate between music downloads (D) and other forms of entertainment (E). Consumer preferences are characterized by a utility function U(D, E). a.) Write an expression for the consumer’s budget constraint as a function of their entertainment budget and the prices of music downloads (Pd ) and other entertainment (Pe). (b) Write the consumer’s constrained optimization problem in Lagrangian form. (Note: You do not need to solve it or derive first order conditions.)

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter10: Consumer Choice Theory

Section: Chapter Questions

Problem 9P

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Alexi has a budget of $21 to spend on toaster and breads. He does not directly gain any utility from owining a toaster but for every slice of toasted bread he consumes he gain 2 units of utility, that is if he owns a toaster. Without the toaster, he gain 0 units of utility from consuming plain bread. Suppose the toaster has inferior quality and will break after toasting only 10 slices, then Alexi needs to buy a new one. The current market price for cheap toaster is $5 and the price for a single slice of bread is $1. Assume that Alexi aims to maximize consumer surplus. In a graph, draw total utility as a function of number of toasted slices, assuming that Alexi buys 1 toaster.
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How can one's choice of purchases/consumption be infuenced by utility or marginal utility?
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