Question

Sterling is out to purchase bottles of vodka (q1) and black turtlenecks (q2). The price of vodka is p1 = 4 and the price of turtlenecks is p2 = 1. However, the store also offers a bulk discount on vodka: after purchasing the first 5 bottles, any additional bottles purchased are 50% off (for example, 8 bottles of vodka and 8 turtlenecks would cost 4 × 5 + 2 × 3 + 2 × 8 = 42). Assume Sterling starts with Y = 40 dollars in income. (a) What is the maximum number of turtlenecks he can afford? What is the maximum number of bottles of vodka? If he bought exactly 5 bottles of vodka, how many turtlenecks could he afford? (b) Sketch Sterling’s budget constraint. Label all slopes, intercepts, and other key points. (Your answer to part (a) should be helpful here.) (c) Sterling enjoys vodka and turtlenecks equally, and cares only about the total number of bottles of vodka and turtlenecks that he has. Write down a utility function that describes these preferences. Re-draw the budget constraint from part (a) and add indifference curves corresponding to these preferences. How many bottles of vodka and how many turtlenecks will he buy? (d) Next, consider Lana, who prefers vodka to turtlenecks, and also has Y = 40 dollars. In particular, she is always willing to trade 3 turtlenecks for 1 bottle of vodka. Write down a utility function that describes her preferences. Re-draw the budget constraint from part (a) and add indifference curves corresponding to her preferences. How many bottles of vodka and how many turtlenecks will she buy? (e) Ray, on the other hand, thinks vodka and turtlenecks are perfect complements, and always wants exactly twice as many turtlenecks as bottles of vodka. He also has Y = 40 dollars. Write down a utility function that describes his preferences. Re-draw the budget constraint from part (a) and add indifference curves corresponding to his preferences. How many bottles of vodka and how many turtlenecks will he buy? (f) Last, consider Mallory. We do not know Mallory’s specific utility function, but we do know that her preferences are monotonic and strictly convex (i.e., they have a strictly diminishing MRS). Is it possible that Mallory will buy exactly 5 bottles of vodka? Justify your answer with a sketch.

Answer 1

As turtleneck has no discount the maximum bottle he can afford of it is 40/1= 40

B) 5*4=20 being the standard price. Out of remaining 20 rs he could normally buy 20/4=5 bottles but due to discount he can buy 10 bottles. So he can buy a total of 30 bottles of vodka.

C) if he enjoys both vodka and turtleneck equally then he will consider only about the quantity of bottles.

As first 20$ will remain same for both vodka and turtleneck, he will be indifferent between both of them. for remaining $ 20 he will go for turtleneck instead of vodka as even after 50% discount 50% discount the bottle of vodka will cost 2 Whereas turtleneck will still cost him 1.

D) as she prefer vodka 3 times she prefer turtleneck so shw would buy all vodkas from her total income of 40.

E) as he perefer twice the turtleneck over vodka he would prefer all turtlenecks as its cost is 4 times low then the vodka even before discount and even after discount it is 2 times low.