Suppose you are a farmer whose land produces 50 units of food this year and is expected to produce another 50 units of food next year. (Assume that there is no one else in the world to trade with.)
A: On a graph with “food consumption this year” on the horizontal axis and “food consumption next year” on the vertical, indicate your choice set assuming there is no way for you to store food that you harvest this year for future consumption.
(a) Now suppose that you have a barn in which you can store food. However, over the course of a year, half the food that you store spoils. How does this change your choice set?
(b) Now suppose that, in addition to the food units you harvest off your land, you also own a cow.
You could slaughter the cow this year and eat it for 50 units of food. Or you could let it graze for another year and let it grow fatter — then slaughter it next year for 75 units of food. But you don’t have any means of refrigeration and so you cannot store meat over time. How does this alter your budget constraint (assuming you still have the barn from part (a)?)
B: How would you write the choice set you derived in A(b) above mathematically, with c1 indicating this year’s food consumption and c2 next year’s food consumption?