ECON 2GG3 Lecture Notes - Lecture 1: Utility

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purplewolf914

2 Dec 2017

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A preference relation that is complete, reflexive, transitive and continuous can be represented by a continuous utility function. Continuity means that small changes to a consumption bundle cause only small changes to the preference level. There is no unique utility function representation of a preference relation. All bundles in an ic have the same utility level. The collection of all ic for a given preference is an indifference map. An indifference map is equivalent to a utility function; each is the other. A good is a commodity unit which increases utility (gives a more preferred bundle) A bad is a commodity unit which decreases utility (gives a less preferred bundle)

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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.

blushwildebeest943

1. Suppose the price of x₁ is $20 and the price of x₂ is $4. If good x₁ is on the horizontal axis, what is the slope of the consumer's budget constraint?

a. -0.20

b. -0.25

c. -5.0

d. -0.2

e. -4.0

f. -20.0

2. Suppose the price of x1 is $5 and the price of x2 is $1 and Toni's income is $20. Suppose Toni gets a $5 gift card that can only be used for the purchase of x1 and there is no resale value of the gift card. With the gift card, the commodity bundle (1,20) is on Toni's budget constraint.

True

False

3. Tiffany's utility function is given by the formula U(x1, x2) = min{20x1, 10x2}. If x1 = x2, which commodity will have a greater marginal utility?

A. Both x1 and x2 have the same marginal utility

B. It is not possible to determine which commodity has higher marginal utility

C. x2

D. x1

4. For U(x₁,x₂) = 6x₁^1/3 + x₂, preferences are

a. consistent with diminishing marginal rate of substitution.

b. consistent with constant marginal rate of substitution.

c. consistent with increasing marginal rate of substitution.

d. not consistent with a utility function.

5. For a utility function of the form U(x₁,x₂)=min{5x₁,10x_2}, the individual will have excess x₂ for commodity bundles where

a. x2>2x1 b. x2>5x₁

c. x₂>0.5x₁ d. x2>10x₁

6. Matt enjoys Fuji and Gala apples and finds 1 Fuji apple to be just as good as 4 Gala apples.

a. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=0.25F+G

b. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=F+4G

c. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=4F+.25G

d. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=4F+G

e. Both A and B

f. Both C and D

amaranthelk637

Let us have an economy that lives only for 2 periods. The representative household has a utility function that values consumption goods for any period as follows

u(c) = ln(c).

The valuation throughout both periods can be represented as a total utility function that discounts future utility with a Î² discount parameter as follows,

U(c1, c2) = u(c1) + Î²u(c2) = ln(c1) + Î² ln(c2),

where ct represent consumption good in period t for every period t = 1, 2. The budget constraint for this person in every period is expressed as

(1+Ïtc)ct + xt =(1âÏtI)(wtnt +rtkt), t=1,2.

where xt represent investment in period t, wt the wages earned by hours worked, rt the return of capital in period t, nt the hours worked supplied by the household in every period t, kt the stock of capital that the household has in period t, Ïtc the tax rate imposed by the government in consumption goods in every period t, and ÏtI the tax rate imposed by the government to total household income in every period t. In every period, the total amount of hours that the representative household is of H Ì = 1. Investment in every period can be defined by the following law of motion of capital

kt+1 = xt +(1âÎ´)kt, t=1,2.

Acknowledge that k3 = 0 because there is no period 3 in this economy. The household starts with a given amount of capital k Ì1 > 0. The representative firm produces good by the following production function in every period t,

Y_t =z_tK_tÎ±N_t1âÎ±, t=1,2.

There is a government that covers government expenditures in period 1 and period 2 by taxing capital rent and labor. Hence, their budget can be expressed as

Ïtcct +ÏtI(wtnt +rtkt)=gt, t=1,2.

a) Before writing any competitive equilibrium definition or the Social Planner Problem, can we modify the budget constraint in â¨order to get rid a variable in every period? Explain.

b) Define the Social Planner Problem.

c) Solve the Social Planner Problem. This is, find the Euler equation in terms of exogenous variables and the only endogenous variable k2.

d) Define the tax distorted competitive equilibrium of this economy.

e) Solve the representative household problem.

f) Solve the representative firm problem in period 1 and 2.

g) Find the optimal Euler equation in terms of exogenous variables and the only endogenous variable k2.

h) Imagine that the government can only implement income taxes. This is Ïtc = 0 for every period t = 1, 2. Can the government implement a tax plan that achieves the Pareto allocation reached by the Social Planner Problem?

i) Imagine that the government can only implement consumption taxes. This is ÏtI = 0 for every period t = 1,2. Can the government implement a tax plan that achieves the Pareto allocation reached by the Social Planner Problem? â¨

ECON 2GG3 Lecture Notes - Lecture 1: Utility

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