Question

Question 2.

Consider the following 8 bundles of goods x and y: A = (8,4) B = (5,6) C = (5,9) D = (10,3) E =(1,4) F =(6,5) G=(2,8) H =(7,8)

(a) Come up with an example of a utility function that will produce the following order of preference for the bundles, where H is most preferred, A and G are equally preferred, and E is least preferred. H , C , B , F , A = G , D , E. Prove that your utility function gets the correct utility ranking of bundles. (Hint: Try utility functions of Cobb-Douglas form) (8 points)

(b) Come up with a new bundle, called bundle I, that has the same utility level as bundle E but has different quantities of good x and good y AND has more of good x than it does of good y. Explain clearly how your bundle I satisfies these requirements. (2 points)

(c) Graph and label bundles A-I on the following grid. Graph the indifference curves that go through each point and specify the utility level of each indifference curve. Make sure to label the bundle, the utility level, the axis, and to number the axis. (10 points)

(d) Give an example of another utility function that represents the same preferences that you came up with in part a. Explain how two functions can represent the same preferences (2 points)

(e) Are these preferences rational? Continuous? Strongly or weakly monotone? Strictly convex? Define each property and then explain/prove your answer for each property. (4 points)

Answer 1

Ansuse coer; Siven date The 8 bundles good x and y ,D(to,3) Utu function 엄 Cobb-Dougla, or The Cobb- Douglas echnolo la chnology

UlE) b, 12-21s

니3 2

the otGity funcion epreerds The tso too function eprejerts saume peronte increasin ng monotonic oformotion in nodue