Final answer:
Budget constraints are diagrammed and explained for Barry, first under a simple scenario with equal prices for food and other things, then with the addition of food stamps, and finally considering a black market trade scenario, each time adjusting the intercepts and the slopes accordingly.
Step-by-step explanation:
The student has been asked to draw and label three budget constraints with 'food' on the horizontal axis and 'other things' on the vertical axis.
Part a: For Barry, who earns $1,000 each month, if the price of food (Pf) is $1 and the price of other things (Py) is also $1, Barry can purchase up to 1,000 units of food if he spends all his money on it, and similarly, he can also purchase 1,000 units of other things. The intercepts are therefore, at (1000, 0) for food and (0, 1000) for other things. The slope of the budget constraint is -1, representing an equal trade-off between the two goods.
Part b: Now, with $200 in food stamps, Barry's purchasing power for food increases while his purchasing power for other goods remains unchanged. The new budget constraint for food would extend to 1,200 units (his original $1,000 plus $200 in food stamps), maintaining the other things intercept at (0, 1000).
Part c: With the ability to trade food stamps on the black market at a rate of 2 food stamps for $1, Barry could potentially convert his $200 in food stamps into $100 additional dollars for other goods. The intercepts of this new budget constraint are then (1200, 0) for food and (0, 1100) for other things, with a kink at the point where food stamps are exchanged on the black market affecting the budget line's shape.
It is important to note that the slope of the budget constraint in part a and b is -1, indicating that one unit of 'other things' is given up for one more unit of food until food stamps run out. However, in part c, there is a kink in the budget line where he starts trading his food stamps due to the different exchange rate on the black market.