CAS EC 201 Lecture Notes - Lecture 10: Utility, Inferior Good, Normal Good

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21 Feb 2017

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Effects of changes in income and prices on optimum consumer choices: demandfunctionsforgoodsforan individual consumer! , p y x and i, we can calculate x given individual"s utility function. , the optimal quantity of x demanded, for a. Individualdemandfunctionsarehomogeneousof degree zero in all prices and i. That is, if all prices and income double, x if i = p y, then 2i = 2p x+2p x+p x y x y will not be affected. On the graph of the budget constraint. I and p p will xy not change if both numerator and denominator are multiplied by 2 or any other constant (t). Preferences do not change, ie. , indifference curves do not change with changes in prices or income. So if all prices and income move together, no change in y and y x. Changes in income ceteris paribus prices and preferences (utility function) Changes in income shift the budget constraint parallel because prices are assumed not to change.

Related Questions

True or False. If False explain why it's false.

1. If all prices are doubled an money income is the left the same, the budget set does not change because the relative prices do not change.

2. A decrease in income pivots the budget line around the bundle initially consumed.

3. If preferences are well-behaved, then for any commodity bundle (x1,x2), the set of commodity bundles that are worse than (x1,x2) is a convex set.

4. The marginal rate of substitution measures the distance betwee one indifference curve and the next one.

5. If someone has the utility function U= 2min(x, y), then x and y are perfect complements for that person.

6. At the boundary optimum, a consumers indifference curve must be tangent to her budget line.

7. If two goods are substitutes, then an increase in the price of one of them will increase the demand for the other.

8. An Engel curve is a demand curve with the vertical and horizontal axes reversed.

9. An inferior good is less durable than a normal good.

10. When other variables are held fixed, the demand for a Giffen good rises when income increase.

PROBLEM 1 (This one is designed to give you lots of math practice!)

Consider the following individual utility functions:

Adam Smith: U(x,y) = xy

Jeremy Bentham: U(x,y) = x^ay^b (Cobb-Douglas utility function)

Alfred Marshall: U(x,y) = ln x + ln y

John M. Keynes: U(x,y) = x + y^b (Quasi-linear utility function)

Joan Robinson: U(x,y) = aX + bY (linear; perfect substitutes)

a. Solve for the MRS(XY) for each of the gentlemen (i.e., all but Joan Robinson). Show that Mr. Smith, Mr. Bentham, and Mr. Marshall all have diminishing MRS(XY), but that if a=b=2, their preferences exhibit constant, increasing, and decreasing marginal utility respectively. (Fortunately, diminishing MRS is the condition that guarantees convex indifference curves, so we can solve for their optimal consumption!)

b. What is the general formula for Mrs. Robinsons (constant) MRS?

c. Find demand functions for x and y for Smith, Bentham, Marshall, and Keynes. Assume that each man has income I and that the prices of x and y are p_x and p_y respectively.

d. Now assume that a=1/2, b = 1/4, I = 600, p_x = 10 and p_y = 20. Use these values to find the utility-maximizing quantities of x and y consumed by each man.

e. Find an expression for the share of income Mr. Bentham and Mr. Marshall each devote to the consumption of good x, where this share, s_x, is defined as

(p_x x)/I.

f. Find expressions for the income elasticity of demand for good x for Mr. Bentham and Mr. Marshall. Find expressions for the (own) price elasticity of demand for good y for these two men.

aquamarinescorpion997

budget line

marginal utility

complete property of preferences

market demand

consumption bundle

substitution effect

Giffen good

total effect

income effect

transitive property of preferences

indifference curves

utility

the marginal rate of substitution

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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CAS EC 201 Lecture Notes - Lecture 10: Utility, Inferior Good, Normal Good

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