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# 6. My preferences are monotonic. a. Do I prefer 3 apples to 2 bananas? Why or why not?

6. My preferences are monotonic.
a. Do I prefer 3 apples to 2 bananas? Why or why not?
b. Write down a monotonic utility function in apples and bananas.
c. Write down a utility function showing I prefer 2 apples to 3 bananas.
7. My utility function is -3x-7y, what’s my optimal consumption bundle? Name some commodities these might be.
8. I need a minimum of 7 apples/week to make one apple pie per week. I don’t like to eat apples unless they are in a pie. (They’ll just sit on the shelf and get rotten in a week if I get less than 7.) I do, however, like bananas, even if they are not in a pie. Draw my indifference curves.
9. Utility is U(x,y)= x2+y
a. Derive the formula for the indifference curve that gives me a utility of exactly 8. Draw that indifference curve.
b. Derive marginal utility functions mux(x,y) and muy(x,y). Derive MRS(x,y).
c. Does this utility function satisfy the hypothesis of diminishing MRS? (Explain.)
d. Name some commodities these might be.
10.
a. Jim’s preferences over apples and bananas exhibit diminishing MRS. Draw his indifference curves.
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b. Define Lance’s utility to be u(Xf, Xw) where Xf are bicycle frames and Xw bicycle wheels. Assume Lance derives utility from bicycles, but not from their parts alone. What do his indifference curves look like?
11. What is the MRS for the utility function ? 11)8.6(),(532121xxxxU
12. My utility function is 1/21212(,)Uxxxx
a. Holding my consumption level of x1 constant, would a rise in my consumption level of x2 raise or lower my marginal utility of x1?
13. My utility function U(x1, x2) depends on the two commodities x1, x2. If my preferences are monotonic and satisfy the Hypothesis of Strictly Diminishing Marginal Rate of Substitution, and if MRS(5,5) = -2, what can you say about how I would rank commodity bundles (4,6) and (6,5)? Draw a graph to illustrate. (Hint: How would each of these bundles compare with the bundle (5,5)?)
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