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), nd the quantity of tea Josef will choose to purchase. Then, given 7", use the first part of your answer in part b to nd 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 help if you simplify your expression for {an