ECON2209 Lecture Notes - Lecture 5: January 30, Budget Constraint, Indifference Curve

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8 Jun 2018

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January 30th

(1.) Consumer Theory Budget Constraint

● Marginal ability to trade (MAT)... slope

● Relative price of X in terms of Y

● Opportunity cost (marginal cost)

● Change in income:

○ Pushes the budget constraint outward or inward

● Changes in prices

○ One price:

■ Rotation of the budget constraint, the price that doesn't change is the

anchor that it pivots from

○ Both prices

■ 2 intercepts change

■ Slope MAY change

● Except when both prices change at same rate…. Parallel shift

● 2. Indifference Curve

○ What a consumer wants

○ Tastes in preferences as well as utility

○ Shows the combinations of 2 goods that provide same level of utility

● Most indifference curves are Y axis and X axis with concave

● They do not cross, as they are

○ Downward sloping

○ Higher Indifference curves are preferred

○ Convex

○ DO NOT CROSS

● Perfect substitutes are straight lines like a budget constraint

● Perfect compliments: right angle lines

● MRS:

○ Marginal Rate of Substitution

○ MRS = Slope of the indifference curve…. changey/changex

○ Should equal: -MUX/MUY

○ Say we are on the indifference curve….

■ U(x,Y) = U1

● Always U1 anywhere on this curve

■ Differentiate DU/DX*Dx+DU/DY*DY= 0

■ dy/dx = -MUX/MUY

○ Graphically

■ MRS at point A… slope of the graph at point A

■ Draw a tangent line….

■ The MRS at point A is the slope of the tangent line to the indifference

curve!

■ As we move down the curve, the MRS gets smaller and smaller

○ Interpretation of the slope (MRS)

■ 1. Marginal Willingness to Trade (MWT)

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Document Summary

Relative price of x in terms of y. Pushes the budget constraint outward or inward. Rotation of the budget constraint, the price that doesn"t change is the anchor that it pivots from. Except when both prices change at same rate . Tastes in preferences as well as utility. Shows the combinations of 2 goods that provide same level of utility. Most indifference curves are y axis and x axis with concave. They do not cross, as they are. Perfect substitutes are straight lines like a budget constraint. Mrs = slope of the indifference curve . changey/changex. Say we are on the indifference curve . Mrs at point a slope of the graph at point a. The mrs at point a is the slope of the tangent line to the indifference curve! As we move down the curve, the mrs gets smaller and smaller. The rate at which consumer is willing to trade x for y, without a change in utility.

Related Questions

Suppose all consumers are maximizing utility with convex indifference curves. All face the same prices, and are perfectly rational. According to microeconomic models, at the maximization bundle they should

A. All have the same marginal rate of substitution

B. All buy more of the least expensive good

C. All end up with the same bundle of goods

D. All have the same level of satisfaction

Consider an indifference map with food on the vertical axis and shelter on the horizontal axis.

If a consumer is willing to give up 3 units of food in exchange for 1 unit of shelter and food is priced at $5 per unit and shelter at $10 per unit, then the consumer is:

A. Purchasing too much food for utility maximization

B. Purchasing too much shelter for utility maximization

C. Purchasing just the right amount of each good for utility maximization

D. Purchasing less than the budget would allow

If a consumer with convex indifference curves moves along her budget line, closer and closer to the horizontal axis, as she is moving:

		A. The marginal utility she gets from good Y declines.
		B. The marginal utility she gets from good X declines.
		C. The marginal utility she gets from good X increases.
		D. The price ratio of the two goods changes.

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.

1.The Phillie Phanatic always eats his ballpark frank in a special way; he uses a foot-long hot dog together with precisely half a bun, 1 ounce of mustard, and 2 ounces of pickle relish. He only gains utility/satisfaction from these 4 items, any extra of a single item without the others is worthless.

What can we say about the relationship among these goods for the Phillie Phanatic and the shape of his indifference curve with respect to these goods?

2. Consider a person with convex indifference curves. When she optimally chooses a consumption bundle of a particular amount of fruit on the Y-axis, and vegetables on the X-axis, her marginal rate of substitution equals:

A. 1

B. PV_/PF (The price of vegetables divided by the price of fruit)

C. P_F/P_V (The price of fruit divided by the price of vegetables)

D. 0

3. A consumer has a budget for food (F) and shelter (S). With income M, and prices PF and PS, the budget constraint for this consumer may be represented as:

A. PSS + PFF = M

B. F = M/PF - (PS/PF)S

C. S = M/PS - (PF/PS)F

D. All of the above

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ECON2209 Lecture Notes - Lecture 5: January 30, Budget Constraint, Indifference Curve

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