Question

24. Consider a consumer with a utility function of u(x,y)=xy. (10 total) a) Draw to scale the consumer's indifference curves for u(x,y)=100 and u(xy)=400. (2) b) Verify the both x and y are "goods" rather than "bads." (3) c) Verify that the law of diminishing marginal rate of substitution holds. (3) d) Suppose that the utility numbers assigned to bundles are determined by the formula (xy) Vxy, instead of u(x,y)= xy. How does the change in the formula change the indifference curve mapping? Explain in terms of utility as on ordinal measure. (2) 8. Felicity is studying economics and political science. She can read 40 pages of political science per hour but only 6 pages of economics per hour. This week, she has a 50-page assignment in economics and a 150-page assignment in political science. She's determined that she cannot devote more than 10 hours to studying these subjects this week and she realizes she cannot complete all of her assignments but is determined to complete at least 30 pages of her economics reading. (8 total) a) Draw a graph with pages of economics on the horizontal axis and pages of political science on the vertical axis. On this graph, show the possibilities that are consistent with the constraints that Felicity has imposed on herself. (She is allowed to read ahead in either subject.) Label key points on your graph with their numerical values. (4 pts) b) Explain the tradeoff Felicity faces. (4)

Answer 1

Due to presence of HOMEWORKLIB POLICY, I am answering first question.

3.

We have:

U(x,y) = xy

a.

IC for xy = 100: Red line

IC for xy = 400: Blue line

b.

We have:

Since utility is increasing in both x and y, both are goods, neither is bad.

c.

We can see that as x rises, MRS falls. This implies diminishing MRS.

d.

With u(x, y) = xy,

IC are:

With

,

IC are:

where,

c, d are utility levels.

Since both ICs are identical, we can see that sqrt{} is just a monotonic transformation and relative properties (preferences) remain intact.

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