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Page Question 2: Utility and Individual Demand Alastor Moody is a wealthy man who likes to keep bats as pets; he has a very large cave where he keeps them, so he never runs out of room. He buys bats at the local pet store for price pb. Alastor also likes to consume sandwiches, purchased from the local sandwich shop for price 17,. He has a monthly budget for bats and sandwiches of Y. Alastor's preferences can be represented by U = b + ln(s). a. Sketch a few of Alastor's indifference curves, with bats on the x-axis. While they do not have to be exact, it may help to calculate some examples to better identify the shape. b. Find Alastor's (Marshallian) demand functions for bats and sandwiches. You can use any method you like to nd the demands, as long as you show your work. What is interesting about his demand for sandwiches? c. Alastor's partner complains that whenever Alastor gets an extra dollar, he always spends it on batsi Is he right? How can you show this using his demand functions (assume y > 171,). (1. Suppose the price of sandwiches is 2 and the price of bats is 1. On a graph, draw Alastor's Engel curve for sandwiches and his Engel curve for bats (hint: rst draw the Engel curve for incomes greater than 1, then draw them for incomes less than 1). e. Suppose Alastor allocates $100 to sandwiches and bats. What is his optimal bundle of sandwiches and bats using the prices in part (d) (assume one could purchase partial bats and sandwiches)? What utility would Alastor have at this bundle'.7 fl Suppose ination causes an increase in prices: the price of sandwiches is now 3, and the price of bats is now 2' What does Alastor's new sandwich and bat budget need to be to keep the same bundle? Is this the utility-maximizing bundle at these prices and this new budget? If not, nd the new utility-maximizing bundle and the new utilityi gr By how much would Alastor have to increase his budget with the price changes in part (f) if he wants to maintain the same utility as in part 22) (allowing the allocations to change)? What allocation would be optimal with that budget? ZOOM +