# Microeconomics Contract Curve Assignment

Microeconomics Contract Curve Assignment
Consider the setting of the exchange economy is as follows:

• There are only two goods.

• There are only two individuals (economic agents).

• No production: only exchange between these two people is possible; goods are consumed.

• The first agent has the utility function u(q1, q2)

• The second agent has the utility function v(z1, z2)

• The total endowments of these goods are W1 and W2.

Assume that utility functions are Cobb-Douglas form, that is:

u(q1, q2)=(q1^a)(q2^(1-a))

v(z1, z2)=(z1^b)(z2^(1-b))

To make the analysis easier, assume that W1 = W2 = 1

(1) Find the contract curve as a function of q1 vs q2 and graph it on the q1 − q2 plane when a= b = 1/2.

(2) Similarly, find the contract curve and graph it when a = 2/3 and b= 1/2.

Hint: Recall that on the contract curve, marginal rates of substitution (MRSs) must be equalized: MRS1=MRS2

Also, recall that MRS=marginal utility for good 1/marginal utility for good 2.

Use the relations: z1 = W1 − q1, z2 = W2 − q2.

Your professor may use a slightly different rubric, but the standard rubric at AUR will assess your writing according to the following standards:

 A (4) B (3) C (2) D/F (1/0) Focus: Purpose Purpose is clear Shows awareness of purpose Shows limited awareness of purpose No awareness Main idea Clearly presents a There is a main idea Vague sense of a No main idea main idea and supported throughout main idea, weakly supports it most of the paper. supported throughout the throughout the paper. paper. Organization: Well-planned and Good overall There is a sense of No sense of Overall well-thought out. organization, includes organization, organization Includes title, the main although some of the introduction, organizational tools. organizational tools statement of main are used weakly or idea, transitions and missing conclusion. Organization: All paragraphs have Most paragraphs have Some paragraphs Para. lack clear ideas Paragraphs clear ideas, are clear ideas, are have clear ideas, supported with supported with some support from examples and have examples and have examples may be smooth transitions. transitions. missing and transitions are weak. Content Exceptionally well- Well-presented and Content is sound and Content is not sound presented and argued; ideas are solid; ideas are argued; ideas are detailed, developed present but not detailed, well- and supported with particularly developed, evidence and details, developed or supported with mostly specific. supported; some specific evidence & evidence, but facts, as well as usually of a examples and generalized nature. specific details. Research (if Sources are Sources are well Sources support The paper does not assignment exceptionally well- integrated and some claims made in use adequate includes a integrated and they support the paper’s the paper, but might research or if it does, research support claims claims. There may be not be integrated the sources are not component) argued in the paper occasional errors, but well within the integrated well. very effectively. the sources and paper’s argument. They are not cited Quotations and Works Cited conform There may be a few correctly according Works Cited to MLA style sheet. errors in MLA to MLA style, nor conform to MLA style.. listed correctly on style sheet. the Works Cited page. Style: Sentence Sentences are clear Sentences are clear Sentences are Sentences aren’t structure and varied in but may lack generally clear but clear pattern, from simple variation; a few may may have awkward to complex, with be awkward and there structure or unclear excellent use of may be a few content; there may punctuation. punctuation errors. be patterns of

Microeconomics Contract Curve Assignment

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