Question

For this question, think of the world as having two goods—movies and “all other goods,” i.e. a composite good. Your good friend Jane really likes to go to the movies and she goes quite often. You think movies are alright, but you aren’t as enamored/obsessed with them as Jane is and hence you go far less than she does. Show explain that despite these differences, at the margin, you and Jane value an addition movie at the same rate relative to the composite good. 2 pts)

Answer 1

Consider the given problem here there are 2 goods “Movie” and “Other goods” and consumers “Jane” and “Consumer A”. So, let’s assume that the “Pm=Price of movie” and “Po=Price of other goods”. Now the consumer equilibrium condition is given by, “MUm/MUo=Pm/Po”.

So, the above condition implied that the ratio of “MU” must be equal to the price ratio, which is also a tangency condition between the “indifference curve” and the budget line, => the absolute slope of the IC and the budget line must be equal.

So, here if “MUmj” be the marginal utility derived from movie and “MUoj” be the marginal utility derived from other good for “Jane”. So, the equilibrium condition for “Jane” is given by “MUmj/MUoj=Pm/Po”. Now, if “MUma” be the marginal utility derived from movie and “MUoa” be the marginal utility derived from other good for “consumer A”. So, the equilibrium condition for “consumer A” is given by “MUma/MUoa=Pm/Po”.

So, we can combine the above two condition into a single one which is given by, “MUma/MUoa = Pm/Po = MUmj/MUoj”. So, we can say that even if the “MU’s” are different for consumers but at the margine both consumer will value an additional movie same relative to other goods. In other words at the margin “MUma/MUoa = Pm/Po = MUmj/MUoj” condition will hold.