4. Consider an economy consisting of two individuals, Ann and Bob, and two goods, scotch and wine. Ann has 5 bottles of scotch and 2 bottles of wine as her endowment, while Bob has 3 bottles of each. Suppose their preferences are described by the following utility functions uA (s, w) - sw and un(s, w) su. Assume also that the prices of goods scotch and wine are represented by P. 1 (scotch is the numeraire), and P >0. a. Sketch the Edgeworth box of the economy with Ann at the lower left corner and Bob at the upper right corner; scotch on the horizontal axis, and wine on the vertical axis. Indicate the endowment point e in the box. b. Write the budget lines for Ann and Bob. e. Solve Ann's utility maximization problem. Express Ann's optimal consumption bundle in terms of P d. Solve Bob's utility maximization problem. Express Bob's optimal consumption bundle in terms of P e. Define competitive equilibrium. Compute and plot the CE for this problem.
4. Consider an economy consisting of two individuals, Ann and Bob, and two goods, scotch and wine. Ann has 5 bottles of scotch and 2 bottles of wine as her endowment, while Bob has 3 bottles of each. Suppose their preferences are described by the following utility functions uA (s, w) - sw and un(s, w) su. Assume also that the prices of goods scotch and wine are represented by P. 1 (scotch is the numeraire), and P >0. a. Sketch the Edgeworth box of the economy with Ann at the lower left corner and Bob at the upper right corner; scotch on the horizontal axis, and wine on the vertical axis. Indicate the endowment point e in the box. b. Write the budget lines for Ann and Bob. e. Solve Ann's utility maximization problem. Express Ann's optimal consumption bundle in terms of P d. Solve Bob's utility maximization problem. Express Bob's optimal consumption bundle in terms of P e. Define competitive equilibrium. Compute and plot the CE for this problem.
Chapter3: Preferences And Utility
Section: Chapter Questions
Problem 3.15P
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Transcribed Image Text:Please answer every part.
4. Consider an economy consisting of two individuals, Ann and Bob, and two goods, scotch and wine.
Aun has 5 bottles of scoteh and 2 bottles of wine as her endowment, while Bob has 3 bottles of
each. Suppose their preferences are described by the following utility functions uA(s, w) = sw and
up(s, w) = s'u. Assume also that the prices of goods scotch and wine are represented by P,= 1
(scotch is the mumeraire), and P>0.
a. Sketch the Edgeworth box of the economy with Ann at the lower left corner and Bob at the
upper right corner; scotch on the horizontal axis, and wine on the vertical axis. Indicate the
endowment point e in the box.
b. Write the budget lines for Ann and Bob.
e. Solve Ann's utility maximization problem. Expross Ann's optimal consumption bundle in
terms of P.
d. Solve Bob's utility maximization problem. Express Bob's optimal consumption bundle in
terms of P.
e. Define competitive equilibrium. Compute and plot the CE for this problem.
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VIEWStep 5: d. Solve for utility maximization problem for Bob
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