ECO 3152 Lecture Notes - Lecture 4: Budget Constraint, Barter, Lump Sum

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16 Nov 2018

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Act as a stand in for all of the consumers in the economy. Preferences: two goods that they desire, physical good, aggregation of all consumer goods in the economy or measured aggregate consumption. Indifference curve: downward slope, convex and bowed in towards the origin, slope is the marginal rate of substitution, rate which a consumer is willing to substitute leisure for consumption good. Leisure time (l), and work or labor supply (n: time constraint for consumer: l + n = h. Lump sum tax (t) is a tax that doesn"t depe(cid:374)d o(cid:374) a(cid:374)y actio(cid:374)s of the eco(cid:374)o(cid:373)ic age(cid:374)t. Budget constraint: one period economy, meaning no reason to save, all disposable income is consumed. C = wn + (pie) - t or c= w(h-l) + (pie) - t. Adding wl to both sides --> c + wl = wh + pie - t. Left side is implicit expenditure: right side is implicit quantity of real disposable income.

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utility function

1.	_____	The satisfaction or benefit that consumers receive from consuming goods or services.
2.	________________ _	A particular combination of specific quantities of goods or services
3.	________________ _	Consumers can rank all conceivable bundles of goods or services
4.	_____	If A is preferred to B, and B is preferred to C, then A is always preferred to C.
5.	_____	Equation showing a consumerâs perception of the total utility forthcoming from consuming each bundle of goods and services.
6.	_____	A set of consumption bundles each and every one of which provides a consumer with exactly the same level of total utility.
7.	_____	The number of units of Y that must be given up for total utility to remain the same when one more unit of X is consumed.
8.	_____	The addition to total utility attributable to consuming one more unit of a good, holding the consumption of all other goods constant.
9.	_____	The line showing all bundles of goods that can be purchased at given prices if the entire income is spent.
10.	_____	The change in the consumption of a good that would result if the consumer remained on the original indifference curve after the price of the good changes.
11.	_____	The change in consumption of goods results strictly from the change in purchasing power after the price of a good changes.
12.	________________ _	The sum of the substitution and income effects.
13.	_____	A good for which quantity demanded varies directly with price, causing an upward sloping demand curve.
14.	_____	A list of prices and the corresponding quantity consumers are willing and able to purchase at each price.

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Are the following statements true or false? A simple yes-no answer will not suffice. Explain, with the use of diagrams where necessary.

1. The utility function u(a, b) = aâ0.2 b0.8 violates the non-satiation assumption.

2. If a consumer is a net borrower, an increase in the interest rate must reduce his borrowing, if consumption in each date is a normal good.

3. If a good has income elasticity less than one, it is inferior.

4. If the demand curve for good A is everywhere flatter than that of good B, then good A has a higher price elasticity of demand.

5. If a given set of consumer preferences are transitive, then there must be an infinite number of indifference curves describing those preferences.

6. If there are two goods, A and B, and A is Giffen, then B must be a price-substitute for A.

Please answer all 6 true/false questions and explain your asnwer. Use diagrams when necessary to explain your answer.

Willy the Worker has unavoidable personal commitments taking 8 hours per day. He can choose to work or to play (i.e., take leisure, a normal good) in the remaining hours. Being a graduate in Economics, he can charge $100 per hour for his consulting services when he chooses to work. The government's income tax system has a 0% tax rate for daily incomes from $0 to $ $600 per day; above $600 per day, the tax rate is 20%. Willy has a certain Utility Function U(L, I) where L = leisure play time and I = Income. His Marginal Rate of Substitution is known to be derived from this equation: MRSLI = 21/L . [Note that the "price" of Income is $1.] 1.1 (4) Willy thinks he pays enough taxes via the excise taxes on things he buys. So he decides to work the maximum number of hours he can without paying any income taxes. According to our Indifference Theory model, is Willy maximizing his satisfaction with his "no tax" choice, or should he work fewer hours? Explain your answer. [No diagram; use "the logic" of the model only.] At equilibrium, MRSLA = price ratio =PL/P1 = 100/1 = slope of BL = wage rate = 100 At "no tax” point, L = 10 and I = $600, hence MRS = 1200/10 = 120 Since MRS > P ratio, he must reduce MRS by taking more Leisure and working less He should (be at the "no tax" point / work fewer hours than the "no tax" point*)

ECO 3152 Lecture Notes - Lecture 4: Budget Constraint, Barter, Lump Sum

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