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.)
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