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Consumer Theory

What is Consumer Theory?
Study of how people use their limited means to make purposeful choices. Assumes that consumers understand their choices (possibilities) and the prices (opportunity costs) associated with each choice. Assumes that consumers consider the alternatives and choose the one they like best.

Consumer Theory - Why? Two important reasons:
to understand the foundations of market demand (bake the demand curve from scratch) to address several interesting consumer theory issues that are best understood using this model rather than the aggregate demand model

Two Components of Consumer Demand
Opportunities: What can the consumer afford? What are the consumption possibilities? Summarized by the budget constraint Preferences: What does the consumer like? How much does a consumer like a good? Summarized by the utility function

What is a Budget Constraint?
A budget constraint shows the consumer’s purchase opportunities as every combination of two goods that can be bought at given prices using a given amount of income. The budget constraint measures the combinations of purchases that a person can afford to make with a given amount of monetary income.

Li’s Demand for Wheat and Rice
Illustration of consumer theory Li’s demand for wheat and rice depends upon the prices for these goods, her income, and her preferences. Suppose we look first at her budget constraint: Wheat costs \$4/lb. Rice costs \$2/lb. Li has \$40 of income.

Li’s Budget Constraint
The mathematical expression for Li’s budget constraint is: I = PW W + PR R R = I/PR - (PW / PR)W I like to refer to the |slope| of the budget line as the ERS=Economic Rate of Substitution In this case it is PW / PR For Li: PW=\$4 PR=\$2 I=\$40 ERS=2

Graph of Li’s Budget Constraint
The graph to the right shows a picture of Li’s budget constraint. Each blue diamond is a point from the table. The slope is equal to -2, as shown on the last slide.

Budget Line gymnastics
An increase in income only. An increase in the price of wheat only. A decrease in the price of rice only. Income doubles as do the prices of wheat and rice. Note: Changes in the price of wheat relative to the price of rice will change the ERS.

Preferences Let R = “at least as good as” Let IN = “indifferent to”
B0 R B1 means: B0 is at least as good as B1 Let IN = “indifferent to” B0 R B1 and B1 R B0 implies B0 IN B1 Let P = “strictly preferred to” B0 R B1 and not B1 R B0 implies B0 P B1

Preferences Basic assumptions about an individual’s preferences (R) over bundles (B) more is better: If B0 has more in it than B1 then B0 R B1 transitivity: If B0 R B1 and B1 R B2 then B0 R B2 average bundles are at least as good as extreme bundles: If B0 IN B1 and B2 is an “average” of B0 and B1, then B2 R B0 and B1

Utility and Preferences
Utility is the way economists represent preferences. Among two bundles, the one with the higher utility is the preferred bundle. If two bundles have the same utility, we say that the consumer is indifferent.

Indifference Curves Preferences that satisfy the conditions I have noted above can be represented by indifference curves. The set of all indifference curves that describe an individual’s preferences are referred to as an indifference curve map. An indifference curve connects all of the bundles that a consumer likes equally. We will assume only two goods when using indifference curve analysis.

Indifference Curve Map - Properties
An indifference curve should not slope up. Indifference curves can not cross one another. Better bundles are to the northeast. Indifference curves will not be “bowed out.”

Li’s Preferences in Indifference Curves
An indifference curve connects all the bundles that have the same utility. Higher indifference curves indicate more utility (IC2 is preferred to IC1). Lower indifference curves indicate less utility (IC1 is preferred to IC0). The indifference curve map is FULL of indifference curves.

The Marginal Rate of Substitution
The Marginal Rate of Substitution(MRS) tells us how much of one good Li would willingly trade for an incremental unit of the other good and remain indifferent. The MRS=|slope| of the indifference curve at a bundle. Common to assume the MRS declines as we move down an indifference curve.

How Much Wheat and Rice Li’s optimal amount of wheat and rice to consume is the amount that maximizes Li’s utility subject to her budget constraint. In the graph... Get to the highest indifference curve possible Stay on the budget constraint (b/c more is better)

How to Find Li’s Best Combination
The black bundle is best. The pink bundle is not the best. Li has spent all her income but is not on the highest indifference curve possible. Bundles n/e of IC0 are better and some are affordable. At (W*, R*) she is doing the best she can subject to her budget constraint. Wheat Rice 20 10 IC0 IC1 IC2 W* R*

How to Find the Best Combination
Utility is maximized when: the indifference curve is just tangent to the budget line. you are on the budget line and the slope of the indifference curve equals the slope of the budget line Income=PRR + PWW MRS=ERS

The “bang per buck” story
Let MUW = Li’s marginal utility of wheat it measures the change in utility as we change wheat consumption by an incremental unit while holding rice constant Let MUR = Li’s marginal utility of rice it measures the change in utility as we change rice consumption by an incremental unit while holding wheat constant Common to assume that marginal utilities decline as we increase consumption - the law of diminishing marginal utility

The “bang per buck” story
The MRS = MUW / MUR The ERS = PW / PR At an optimal bundle: MRS=ERS Rewritten we have: MUW / MUR = PW / PR MUW/PW = MUR/PR bang/buck in wheat = bang/buck in rice Get same optimal bundle either way

Handling a change in PW Li wants to achieve the highest indifference curve that the budget constraints permit. The points A, B, and C represents the best that Li can do at prices of \$4, \$2, and \$1 for wheat. The equation MRS=ERS is satisfied at each of the points.

Li’s Demand for Wheat The table shows the amount of wheat that Li demands at each price. These are the points of tangency from the previous slide.

Graph of Li’s Demand for Wheat
When we connect the points from the table in the previous slide we get Li’s demand for wheat. The points A, B, and C correspond to the tangencies of the budget constraint and the indifference curves.

Li’s Best Choice Reconsidered
Consider the choice at PW=\$2/lb. The point B is optimal. The point A is feasible but inferior to all points on the red budget line between E and F. The point C is preferred to B but cannot be purchased with Li’s \$40 income at the given prices; it is above the red budget line. The point E is feasible but Li prefers more wheat and less rice (B). The point F is feasible but Li prefers less wheat and more rice (B, again). There is no combination that Li prefers to B that she is able to buy.

Handling a change in PW Li wants to achieve the highest indifference curve that the budget constraints permit. The points A, B, and C represents the best that Li can do at prices of \$4, \$2, and \$1 for wheat. The equation MRS=ERS is satisfied at each of the points.

Li’s Demand for Wheat The table shows the amount of wheat that Li demands at each price. These are the points of tangency from the previous slide.

Graph of Li’s Demand for Wheat
When we connect the points from the table in the previous slide we get Li’s demand for wheat. The points A, B, and C correspond to the tangencies of the budget constraint and the indifference curves.

From IC Map to Li’s Demand for Wheat

Income and Substitution Effects
Economists decompose the effect of a change in price on the quantity demanded into an income and a substitution effect. Income effect: due to the increase in real income associated with a fall in prices (you can buy more with the same nominal income) or the loss of real income associated with a rise in prices (you cannot buy as much as you once did with the same nominal income). Substitution effect: due to the change in the relative price of the good, cheaper goods are substituted for more expensive ones.

Income and Substitution Effects: Price Decline, “X” normal
When the price of a good falls, the quantity demanded rises for two reasons. The income effect: real income is higher because the same money income buys more at the lower prices. For normal goods, then, the income effect of a price fall is positive. The substitution effect: consumers substitute the now cheaper good for ones whose price has not fallen, real income held constant. This increase in demand is called the substitution effect of a price decline.

Li’s Income and Substitution Effects: Price Fall, Rice normal
Graph shows the income and substitution effects of the fall in the price of wheat from \$4/lb. (A) to \$1/lb. (C). The movement from point A to point D is the substitution effect: Li buys less rice and more wheat, and would do so even if she had an income of only \$20 (as the black budget line shows). The movement from point D to point C is the income effect, the price decline is like giving Li an additional \$20 of real income.

Li’s Substitution Effect
The substitution effect is the amount by which Li's wheat consumption increased holding real income constant. Substitution effect is the difference between Li's consumption of wheat at the new and old prices holding her real income constant, that is, staying on the same indifference curve (compare points A and D).

Li’s Income Effect When the price falls from \$4/lb. of wheat to \$1/lb. per wheat, Li is able to buy both more wheat and more rice. The income effect is the difference between what she would have bought on the old indifference curve at the lower wheat price (point D) and what she actually did buy with her nominal income (\$40) at the lower price (point C). Li increases her consumption of wheat and rice because of the increase in her real income from the price decline.

General effect of a price fall
PX falls Substitution Effect X now looks relatively cheaper Income effect - you feel richer “X” normal “X” inferior Quantity demanded increases Quantity demanded decreases Quantity demanded increases Total effect is the substitution effect AND the income effect working at the same time.

From Individual to Market Demand
Market demand is the sum of all individual demands in the economy. In the following example there are two consumers of wheat: Li and Juanita. The market demand, then, is the sum of the quantities demand by Li and Juanita.

Juanita’s Demand for Wheat
Juanita’s income is also \$40. Juanita faces the same price for rice as Li: \$2/lb. Her preferences are different from Li’s. Her demand for wheat is derived in the figure at the left.

Graph of Juanita’s Demand for Wheat
The points A, B and C correspond to Juanita’s best choices given her income and the three prices of wheat illustrated. This is her demand curve for wheat.

Market Demand The market demand (green) is the sum of Li’s (blue) and Juanita’s (red) demand for wheat at each price. At PW=4, Li demands 6 lbs., Juanita demands 5 lbs. and the market demand is 11 lbs. At PW=2, Li and Juanita demand 10 lbs. and the market demand is 20 lbs. At PW=1, Li demands 16 lbs., Juanita demands 18 lbs. and the market demand is 34 lbs.

Application: Effect of a Tax & Transfer Program
Suppose I have the preferences illustrated at the right. Question A: If Income = \$16 If Price of food = \$1 If Price of shelter = \$1 Food = ? Shelter = ? Indifference curve = ?

Answer A Point A: If Income = \$16 If Price of food = \$1 If Price of shelter = \$1 Food = 7 Shelter = 9 Indifference curve = I4

Effect of a Tax and Transfer Program: Addition of Tax
Question B: If Income = \$16 If Price of food = \$1 If Price of shelter = \$1 and Tax on shelter = 100% Tax-inclusive price of shelter = ? Food = ? Shelter = ? Indifference curve = ?

Answer B Point B If Income = \$16 If Price of food = \$1 If Price of shelter = \$1 and Tax on shelter = 100% Tax-inclusive price of shelter = 2 Food = 9 Shelter = 3.5 Indifference curve = I2

Effect of a Tax and Transfer Program: Tax & Transfer
Question C: If Income = \$16 If Price of food = \$1 If Price of shelter = \$1 and Tax on shelter = 100% and Transfer payment = \$8 Food = ? Shelter = ? Indifference curve = ?

Answer C Point C If Income = \$16 If Price of food = \$1 If Price of shelter = \$1 and Tax on shelter = 100% and Transfer payment = \$8 Food = 10 Shelter = 7 Indifference curve = I4

Tax and Transfer Systems Give Pure Substitution Effects
Notice in the example that the consumer ends up on the same indifference curve after the tax and transfer program as in the initial choice (I4). In public finance (the study of tax and transfer systems) this result usually occurs when the tax and transfer system is combined with a balanced budget. In our example, tax receipts are \$7 per person (= 7 units of shelter x \$1 tax), while the transfer is \$8 per person. This is as close to “balanced” as we can get and still be able to graph the consumer’s choice legibly. Knowledge of the substitution effect of the price change induced by the shelter tax is sufficient to predict the effect of the complete tax and transfer system.

Food Stamps vs. \$\$\$\$\$ Suppose the following for the Parker family:
u(F, \$aog) where \$aog=\$all other goods I=\$200 PF = \$2/unit Paog = \$1 Consider three alternative government policies no support \$200 in food stamps \$200 in cash

Food Stamps vs. \$\$\$\$\$ Notes:
the budget line under the food stamp program is the thick black segment and the purple segment The budget line with cash is the red and purple segments the Parkers are indifferent between food stamps and cash \$aog 200 IC1 IC0 BL0 100 200 Food

Food Stamps vs. \$\$\$\$\$ Notes:
the budget line under the food stamp program is the thick black segment and the purple segment The budget line with cash is the red and purple segments if this is the case then the Parkers prefer cash to food stamps \$aog IC\$\$ ICFS IC0 BL0 Food

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