2. Agricultural Household Model

a. Assume there is a farming household which has to make a decision about how much food to produce. The marginal cost of producing an extra unit of food, where Q is the total quantity of food produced, is MC = 0.5*Q. If the price of food, PFood, = $10, how muchwill the farm produce? What is the farm's profit?

1. The price of other stuff is POther= $5. Assume the household has consumption preferences such that the household utility = minimum of (XFood, XOther), where XFoodis the amount of food consumed and XOtheris the amount of other stuff consumed. That is if XFood= 5 and XOther= 10, the household's utility is 5. If XFood= 5 and XOther= 100, the household'sutility is still 5. (These are called Leontief Preferences.)
2. First, draw the budget curve for the household, assuming that all of its profits from part (a) are exactly equal to its income. Put the amount consumed of other stuff on the Y-axis and food on the X-axis. Second, determine the amount of food (XFood) and other stuff (XOther) that the household consumes given the household'sutility function. (The household can buy fractions of the goods, e.g. if it has $2, it can buy 1/5 of a unit of food.) Hint: It may help to draw some indifference curves and trace out the path they take.
3. Assume the price of food increase to PFood= $12. What is the new amount of food that the farm household produces andwhat is the farm'sprofit?
4. Assume the price of other goods is unchanged. Draw the new budget constraint for the household and find the new consumption level of the household for food and other goods. Does the amount of food consumed go up or down? Comparing the situation where PFood= $10 vs PFood= $12, how much net food is produced for the market, that is, what is total amount of food produced minus amount of food consumed in each case? Why might it be difficult to use food price increases to get farm households like this one to increase food production for non-farm households to purchase?