Ulrich likes video games and sausages. In fact, his preferences can be represented by u(x, y) = ln(x + 1) + y where x is the number of video games he plays and y is the number of dollars that he spends on sausages. Let px be the price of a video game and m be his income.
(a) Write an expression that says that Ulrich’s marginal rate of substitution equals the price ratio.
(b) Since Ulrich has ________ preferences, you can solve this equation alone to get his demand function for video games, which is ________. His demand function for the dollars to spend on sausages is ________.
(c) Video games cost $.25 and Ulrich’s income is $10. Then Ulrich demands ________ video games and ________dollars’ worth of sausages. His utility from this bundle is ________. (Round off to two decimal places.)
(d) If we took away all of Ulrich’s video games, how much money would he need to have to spend on sausages to be just as well-off as before?
(e) Now an amusement tax of $.25 is put on video games and is passed on in full to consumers. With the tax in place, Ulrich demands ________video game and ________dollars’ worth of sausages. His utility from this bundle is ________. (Round off to two decimal places.)
(f) Now if we took away all of Ulrich’s video games, how much money would he have to have to spend on sausages to be just as well-off as with the bundle he purchased after the tax was in place?
(g) What is the change in Ulrich’s consumer surplus due to the tax? ________How much money did the government collect from Ulrich by means of the tax? ________.