Go back to the numerical example with no factor substitution that leads to the production possibility frontier in Figure 5-1. In this example, we are given the following resource constraints: ake =2,8,c =2, age =3, 3, = 1 L =2,000; K = 3,000 Each unit of cloth is produced with 2 units of capital and 2 units of labor. Each unit of food is produced with 3 units of capital and 1 unit of labor. Furthermore, the economy is endowed with 2,000 units of labor and 3,000 units of capital. a. What is the range for the relative price of cloth such that the economy produces both cloth and food? Which good is produced if the relative price is outside of this range? As long as the relative price of cloth lies between 2/3and 2 units of food, the economy will produce both goods. If the price of cloth falls below 2/3 | then the economy should completely specialize in food production. If the price of cloth rises above 2 |, complete specialization in cloth will occur. For parts (b) through (f), assume that the price range is such that both goods are produced. b. Write down the unit cost of producing one yard of cloth and one calorie of food as a function of the price of one machine-hour, r, and one work-hour, w. Ina competitive market, those costs will be equal to the prices of cloth, P, and food, P. Solve for the factor prices rand w. The unit cost of producing one yard of cloth and one calorie of food as a function of the price of one machine-hour, r, is r= :| The unit cost of producing one yard of cloth and one calorie of food as a function of the price of one work-hour, w, is w= D Quantity of food, OF 2,000 Labor constraint slope =-2 Production possibility frontier: slope = opportunity cost of cloth in terms of food Capital constraint slope=-2/3 750 1,000 1,500 Quantity of cloth, @