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: age =28, =2 ag =3,a,=1L=2000;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 units of food, the economy will produce both goods. If the price of cloth falls below | |, then the economy should completely specialize in | production. If the price of cloth rises above | , complete specialization in | will oceur. Quantity of food, Q. 2,000 Labor constraint slope=-2 Production possibility frontier: slope = opportunity cost of cloth in terms of food 1,000 Capital constraint slope =-2/3 750 1,000 1,500 Quantity of cloth, Q As long as the relative price of cloth lies between 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.To find the range for the relative price of cloth such that the economy produces both cloth and food, we need to determine the opportunity costs of producing cloth and food in terms of each other, given the resource constraints. Let's denote: * P = Price of Cloth * Pr = Price of Food Given that each unit of cloth requires 2 units of capital and 2 units of labor, and each unit of food requires 3 units of capital and 1 unit of labor, we can set up the following equations for the production possibilities: For Cloth: 2ac +2a50 =2 x2+2x2=8 For Food: 3agr +largp =3 x3+1x1=10 Given the total available capital and labor: L = 2,000 K = 3,000 Now, we can set up the production possibility frontier: 2a50C + 2a1cC = K 3GKFF - 1aLFF =L 2xC+2xC=3,000 3x F1+1xF=2000 4C = 3,000 4F = 2,000 Cc =200 =750 F =20 _ 500 Now, the relative price of cloth PC/PF is the slope of the production possibilities frontier. In this case, it's % = % = 1.5. Given the constraint, the range for the relative price of cloth such that the economy produces both cloth and food would be between the opportunity cost of producing cloth and food: S