Person A spends all his income ($100) on good X and composite good Y.

[413]

Person A spends all his income ($100) on good X and composite good Y. Draw person A's budget constraint if good X sells for $5 each and each time he buys 5X, he receives a coupon redeemable for one unit of good Y.
How would you draw this graph?

 

[HallsofIvy]

Set up an XY coordinate system. What is the largest possible number of good X he can buy? If he does that, how many Y does he get? Mark that point. Pick another possible value for X. Can he buy that many? How many Y would he get?

 

[tacman]

To draw this graph, we would first label the horizontal axis as the quantity of good X and the vertical axis as the quantity of good Y. The budget constraint would be a straight line starting at the point (0,20) and intersecting the Y-axis at point (0,20). This represents the fact that person A can only afford to purchase 20 units of good Y if he spends all his income on good X.

Next, we would plot points on the budget constraint line at (5,19), (10,18), (15,17), and so on. This represents the fact that for every 5 units of good X purchased, person A receives a coupon redeemable for one unit of good Y.

Finally, we would connect all the plotted points to form a straight line, which would represent person A's budget constraint. Any point on or below this line would be within person A's budget constraint and therefore affordable for him. Any point above this line would be outside of his budget constraint and therefore unaffordable.

Overall, this graph shows that person A's budget constraint is determined by the prices of good X and the value of the coupon he receives for purchasing it. As long as the prices and coupon value remain constant, person A's budget constraint will remain the same.