Image transcription text 1. Constrained Consumer Choice: Josef receives a monthly royalty check of $150 for his bestselling book “My Greatest Insights" He spends this

Image transcription text 1. Constrained Consumer Choice: Josef receives a monthly royalty check of $150 for his
bestselling book “My Greatest Insights" He spends this income on Russian Tea and Albanian
Wine. The price of tea (PT) is $2 per cup and his favorite Albanian Wine is selling for $15 per
bottle (PW = $15]. His preferences can be described by the “quasi-linear” utility function:
U(T,W) = 4ln(1′) + W. a. Set up Josef’s consumer maximization problem. Be sure to identify what he is
maximizing and what is his constraint. b. Given the budget constraint, write the number of bottles of wine Josef consumes in
terms of the cups of tea he purchases. Using this result, write Josef’s utility as a
function of the number of cups of tea he chooses to consume. (Hint! You might want to
do parts b and c symbolically and then plug in for price and income so that you can use
your resuits for the same calculation for part id). c. Using your setiup from part (b), find the quantity of tea Josef will choose to purchase.
Then, given 7", use the first part of your answer in part b to find W’. Be sure to show
your work for full credit! d. Now imagine that Josef shares his insights on several reality TV shows. And, following
these appearances many more people buy iosef’s book and so his royalty payments
increase to $300 per month. What happens to his consumption of Tea and Wine? In
general terms, what does this result tell us about iosef’s income-Elasticity of Demand
for these two goods ii.e. interpret the elasticity’s sign and magnitude]? e. Finally, use calculus to derive a formula for the income elasticity of demand for Wine
(£59). interpret your results, paying particular attention to what happens as income
gets big. Note, in answering the second part of this question, It will if you simplify
your expression for {an