An economy produces cloth and food by using capital and labor

An economy produces cloth and food by using capital and labor. The unit input requirements to produce cloth are aKCaKC= 10 and aLCaLC= 4, whereas the unit input requirements to produce food are aKFaKF= 5 and aLFaLF= 10.

Assume the economy is endowed with 12,000 units of machine-hours (K) along with 6,000 units of work-hours or hours of labor (L).

a. Draw the corresponding production possibilities frontier (PPF) by plotting the quantity of cloth along the x axis.

b. What is the range for the relative price of cloth such that the economy produces both cloth and food? (Hint: Calculate the opportunity cost of cloth in terms of food)

c. How many yards of cloth and calories of food the economy should produce to maximize the value of output? (Calculate the optimal production point by solving the system of equations. Show all your calculations in your solution.)

d. Now assume that the economy’s supply of labor (labor force) increases from 6,000 to 9,000. Derive the new production possibilities frontier.

e. How much cloth and food will the economy produce after this increase in its labor force? (Calculate the optimal production point by solving the new system of equations. Show all your calculations)

f. Explain concisely why this biased expansion of production possibilities (after the increase in the economy’s labor supply) is consistent with the Rybczynski theorem or effect.