Please look at The economy of Opryland produces two goods - cloth and food. Production of one yard of cloth requires a combination of two work-hours and two machine-hours. The production of food is more automated; as a result, production of one calorie of food requires only one work-hour along with three machine-hours. Thus, all the unit input requirements are fixed at akc = 2, alc = 2, akf = 3, alf = 1 and there is no possibility of substituting labor for capital or vice versa. Assume that an economy is endowed with 6,000 units of machine-hours along with 4,000 units of work-hours.

a. Write down the labor and capital constraints. Plot the production possibilities frontier for the economy (label appropriately to receive full points). Note: For parts (b) through (f), assume the price range is such that both goods are produced.

b. 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?

c. 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. In a competitive market, those costs will be equal to the prices of cloth and food. Solve for the factor prices r and w.

d. What happens to those factor prices when the price of cloth rises? Who gains and who loses from this change in the price of cloth? Why? Do those changes conform to the changes described for the case with factor substitution? e. Now assume the economy's supply of work-hours decreases from 4,000 to 3,000 units. Derive the new production possibility frontier.

[25 points] The economy of Opryland produces two goods cloth and food Production of one yard of cloth requires a combination of two work-hours and two machine-hours. The production of food is more automated; as a result, production of one calorie of food requires only one work-hour along with three machine-hours. Thus, all the unit input requirements are xed at at\" = 2, am = 2, ox}: = 3, a\": = 1 and there is no possibility of substituting labor for capital or vice versa. Assume that an economy is endowed with 6,000 units of machine-hours along with 4,000 units of work-hours. a. Write down the labor and capital constraints. Plot the production possibilities frontier for the economy (label appropriately to receive lll points). Note: For parts (b) through (I), assume the price range is such that both goods are produced. b. 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? c. 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. In a competitive market, those costs will be equal to the prices of cloth and food. Solve for the factor prices r and w. d. What happens to those factor prices when the price of cloth rises? Who gains and who loses from this change in the price of cloth? Why? Do those changes conform to the changes described for the case with factor substitution? e. Now assume the economy's supply of work-hours decreases from 4,000 to 3,000 units. Derive the new production possibility frontier. f. How much cloth and food will the ecOnomy produce after the decrease in work-hours from 4000 to 3000 units