Question

Judd has one hour of time. His objective is to eat bowls of fresh coleslaw and drink fruit smoothies. He has to make both from scratch. It takes 6 minutes for him to make a fruit smoothie and 30 minutes to make a proper fresh coleslaw. So if he spend half of his time making smoothies and half of his time making coleslaw, he can have 5 fruit smoothies and 1 bowl of coleslaw Judd is friends with Sarah. While they both like coleslaw and fruit smoothies, they have different skills. It takes Sarah 20 minutes to make a bowl of coleslaw and 15 minutes to make a fruit smoothie (a) If Judd and Sarah are prevented from trading with one another, and they each spend half of their hour making and consuming each product, how much of each will they consume? (b) If Judd only makes smoothies, how many can he make? If Sarah only makes coleslaw, how many bowls can she make in one hour? (c) Suppose that Judd and Sarah each like smoothies and coleslaw the same amount If they are allowed to trade, what is the maximum amount that each will consume if each only spends one hour of time? (d) How much better off is Sarah in (c) as compared to (a)? How much better off is Judd in (c) than (a)?

Answer 1

a) If both spend half of their time in making each product,

Judd will consume 5 fruit smoothies and 1 coleslaw

Sarah will consume 1.5 bowls of coleslaw and 2 fruit smoothies.

b) If Judd only make smoothies, he will be able to make 10 smoothies.

If Sarah makes only coleslaw, she will be able to make 3 bowls of coleslaw.

c) We know that both are now allowed to trade and both the goods in same amount. Sarah can make 3 bowls of coleslaw and she initially used to have only 1.5 bowls of coleslaw. So she can give 1.5 bowls of coleslaw to Judd.

Judd can make 10 smoothies and he used to have 5 initially , so he can now afford to give 5 extra smoothies to Sarah.

d) After trade Sarah will have 3 extra smoothies and Judd will have extra 0.5 bowls of coleslaw to consume.