Go back to the numerical example with no factor substitution that leads to the production possibility frontier in Figure 5-1.

1. Go back to the numerical example with no factor substitution that leads to the productionpossibility frontier in Figure 5-1.a. What is the range for the relative price of cloth such that the economy producesboth cloth and food? Which good is produced if the relative price is outside of thisrange?For parts (b) through (f), assume that the price range is such that both goods areproduced.b. Write down the unit cost of producing one yard of cloth and one calorie of food asa function of the price of one machine-hour, r, and one work-hour, w. In a competitivemarket, those costs will be equal to the prices of cloth and food. Solve for thefactor prices r and w.c. What happens to those factor prices when the price of cloth rises? Who gains andwho loses from this change in the price of cloth? Why? Do those changes conformto the changes described for the case with factor substitution?d. Now assume that the economy's supply of machine-hours increases from 3,000 to4,000. Derive the new production possibility frontier.e. How much cloth and food will the economy produce after this increase in itscapital supply?f. Describe how the allocation of machine-hours and work-hours between the clothand food sectors changes. Do those changes conform with the changes describedfor the case with factor substitution?