Sherry is on vacation and wants to bring souvenirs home to family and friends. Her souvenir budget is $100, and she can choose between T-shirts, which cost $20 each, and key chains, which cost $5 each. a) Draw a graph of Sherry’s budget line (key chains are measured on the vertical axis). b) What is the slope of Sherry’s budget line? How does that slope represent an opportunity cost? Suppose that Sherry now finds a store where T shirts are on sale for $10 each. (Key chains still cost $5 each). c) Draw the new budget line in the figure. d) What is the slope of the new budget line? How has the opportunity cost changed?
Question
Sherry is on vacation and wants to bring souvenirs home to family and friends. Her souvenir budget is 20 each, and key chains, which cost 10 each. (Key chains still cost $5 each). c) Draw the new budget line in the figure. d) What is the slope of the new budget line? How has the opportunity cost changed?
Solution
a) To draw the budget line, we need to find out how many of each item Sherry can buy with her budget. If she spends all her money on T-shirts, she can buy 5 (100/20). If she spends all her money on key chains, she can buy 20 (100/5). So, the budget line will start at point (0,20) on the vertical axis (if she buys only key chains) and end at point (5,0) on the horizontal axis (if she buys only T-shirts).
b) The slope of the budget line is the ratio of the prices of the two goods, which is -20/5 = -4. This slope represents the opportunity cost of buying a T-shirt in terms of key chains. In other words, for every T-shirt that Sherry buys, she gives up the opportunity to buy 4 key chains.
c) If T-shirts are now $10 each, Sherry can buy 10 T-shirts if she spends all her money on T-shirts. The new budget line will start at point (0,20) on the vertical axis (if she buys only key chains) and end at point (10,0) on the horizontal axis (if she buys only T-shirts).
d) The slope of the new budget line is -10/5 = -2. This means that the opportunity cost of buying a T-shirt has decreased. Now, for every T-shirt that Sherry buys, she gives up the opportunity to buy 2 key chains, instead of 4.
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