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?

(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

Please note that the price of turtlenecks is not correct. Initially it says p2 = 1, but in the below line, it uses p2=1.

I have considered p2 = 2 for the answer.