4. Jennifer buys both turkey (x) and cheese (y) for her sandwiches. Her preferences over these two goods can be represented by the utility function U(x,y) = min[x, 2.5y] where x represents the number of slices of turkey and y represents the number of slices of cheese.

a) Given her preferences find her demand functions for turkey (x) and cheese(y).

b) Suppose that the price of a slice of turkey is $1 and that Jennifer has $36 to spend on turkey and cheese. Write Jennifer's demand curve for cheese. Illustrate her demand curve

c) Suppose that the price of a slice of cheese is $.50 (the price of turkey and income remain $1 and $36, resp.). Use your demand functions to find her best bundle. Illustrate her best bundle at these prices. For the remainder of the question assume that the price of turkey falls to $.60 and that the price of cheese and income are unchanged at Py=$.50 and I = $36.

d) Use your demand functions to find her new best bundle. Illustrate the new budget line and the new best bundle that you found above in your diagram for part (c). What is the cross price elasticity of turkey for these preferences?

5. Phyllis drinks both coffee (x) and milk (y). Her preferences over these two goods can be represented by the utility function U(x,y) = x + 3y^1/2 where x represents the number of pounds of coffee and y represents the number of quarts of milk.

a) Given her preferences find her demand functions for coffee (x) and milk(y).

b) Suppose that the price of a pound of coffee is $4 and that she has $56 to spend on coffee and milk. Write her demand curve for milk. Illustrate her demand curve.

c) Suppose that the price of a quart of milk is $1 (the price of coffee and income remain $4 and $56, resp.). Use your demand functions to find her best bundle. In an indifference curve diagram illustrate her best bundle at these prices. For the remainder of the question assume that her income rises to $60 and that the prices of coffee and milk are unchanged at Px=$4 and Py=1.

d) Use your demand functions to find her new best bundle.

e) Illustrate the new budget line and the new best bundle that you found above in your diagram for part (c). Be sure to indicate the slopes of both budget lines.

f) What is the income elasticity of milk for these preferences (as a function of prices and income)?

Bonus: Anna is indifferent between bread and rolls for her sandwiches. She believes that 2 slices of bread is always just as good as 1 roll. Let bread be the x-good measured in slices and rolls be the y-good measured in number of rolls. Suppose Anna has $1 to spend on bread and rolls.

a) Given our assumptions on preferences and the information above, Illustrate indifference curves that represent Anna's preferences. What is her MRS?

b) If the price of a slice of bread is $.10 and the price of a roll is $.25 then what bundle will she choose? Show that her MRS is not equal to the price ratio at that bundle. Illustrate your answer in your diagram for part (a).

c) If the price of a slice of bread rises to $.20 then what bundle will she choose? Show that her MRS is not equal the price ratio at that bundle. In a new diagram illustrate her best bundle.

d)Briefly explain why her MRS is not equal to her best bundles in parts (b) and (c).

e)Illustrate her demand curve for bread.