One day a king left his castle with a bag of silver coins to wander his kingdom. to the first peasant he met, he gave half his coins plus two more. a little later, he met another peasant to whom he also gave half his coins plus two more. walking on, he met a third peasant and again gave half his coins plus two more. finally, the king went home with two coins left in his bag.

(a) how many coins did he have to begin with?

(b) what if he was left with "n" amount of coins?

(c) what if he gave away any unit fraction (1/a) each time?

(d) what if he gave away any unit fraction (1/a) each time and was left with any amount of coins (d)?

1. an economy consists of three workers: larry, moe, and curly. each works 10 hours a day and can produce two services: mowing lawns and washing cars. in an hour, larry can either mow one lawn or wash one car; moe can either mow one lawn or wash two cars; and curly can either mow two lawns or wash one car. a. calculate how much of each service is produced under the following circumstances: a. all three spend all their time mowing lawns. b. all three spend all their time washing cars. c. all three spend half their time on each activity d. larry spends half of his time on each activity, while moe only washes cars and curly only mows lawns b. using your answers to part a, draw a production possibilities frontier and label points a, b, c, and d on your graph. explain why the production possibilities frontier has the shape it does. c. are any of the allocations calculated in part a inefficient? explain.