1.Sarah consumes apples and oranges (these are the only fruits she eats). She has decidedthat her monthly budget for fruit will be $50. Suppose that one apple costs $0.25, while one orange costs $0.50.

a) What is the expression for Sarah's budget constraint?

b) Draw a graph of Sarah's budget line.

c) Show graphically how Sarah's budget line changes if the price of apples increases to $0.50.

d) Show graphically how Sarah's budget line changes if the price of oranges decreases to $0.25.

e) Suppose Sarah decides to cut her monthly budget for fruit in half. Coincidentally, the next time she goes to the grocery store, she learns that oranges and apples are on sale for half price, and will remain so for the next month; that is, the price of apples falls from $0.25 per apple to to

$0.125 per apple, and the price of oranges falls from $0.50 per orange to $0.25 per orange. What happens to the graph of Sarah's budget line?

2.Julie has preferences for food F and clothing C de- scribed by a utility function U(F, C ) = FC. Suppose that food costs N$1 a unit and that clothing costs N$2 a unit. Julie has N$12 to spend on food and clothing.

a) On a graph draw indifference curves corresponding to u = 12, u = 18, and u = 24. Using the graph (and no algebra), find the optimal (utility-maximizing) choice of food and clothing. Let the amount of food be on the horizontal axis and the amount of clothing be on the vertical axis.

b) Using algebra (the tangency condition and the budget line), find the optimal choice of food and clothing.

c) What is the marginal rate of substitution of food for clothing at her optimal basket? Show this graphically and algebraically.

d) Suppose Julie decides to buy 4 units of food and 4 units of clothing with her $12 budget (instead of the op- timal basket). Would her marginal utility per dollar spent on food be greater than or less than her marginal utility per dollar spent on clothing? What does this tell you about how she should substitute food for clothing if she wanted to increase her utility without spending any more money?