Question

3. Problems and Applications Q3 Lucia and Sharon are roommates. They spend most of their time studying (of course), but they leave some time for their favorite activities: making pizza and brewing root beer. Lucia takes 3 hours to brew a gallon of root beer and 2 hours to make a pizza. Sharon takes 7 hours to brew a gallon of root beer and 5 hours to make a pizza. Lucia's opportunity cost of making a pizza is5/7 gallon of root beer, and Sharon's opportunity cost of making a pizza is 2/3 gallon of root beer. Lucia has an absolute advantage in making pizza, and Sharon or Lucia  has a comparative advantage in making pizza. If Lucia and Sharon trade foods with each other,Sharon will trade away pizza in exchange for root beer. The price of pizza can be expressed in terms of gallons of root beer. The highest price at which pizza can be traded that would make both roommates better off is1 1/2 gallons of root beer, and the lowest price that makes both roommates better off is1 1/2 gallons of root beer per pizza.

Answer 1

Output table for number of the goods produced in 1 hour is as follows.

	Root beer	Pizza
Lucia	1/3 = 0.33	1/2 = 0.5
Sharon	1/7 = 0.14	1/5 = 0.2

(a) Lucia's opportunity cost of making a pizza is [(1/3)/(1/2)] = 2/3 gallon of root beer. Sharon's opportunity cost of making a pizza is [(1/7)/(1/5)] = 5/7 gallon of root beer.

(b) Lucia has an absolute advantage in making pizza (since Lucia can make more pizza than Sharon can in 1 hour: 0.5 > 0.2), and Lucia has a comparative advantage in making pizza (since Lucia can make pizza at lower opportunity cost than Sharon can: (2/3) < (5/7)].

(c) If Lucia and Sharon trade, Lucia will trade pizza in exchange for root beer (since Lucia has comparative advantage in pizza, she will specialize in pizza and will trade away pizza for beer).

(d) The highest price at which pizza can be traded that would make both roommates better off is 5/7 gallons of root beer, and the lowest price that makes both roommates better off is 2/3 gallons of root beer per pizza (since trade is mutually beneficial when terms of trade lies between opportunity costs of both trading parties).