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.

Grading Rubric for Writing Assignment

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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