Individual Demand Curves

Individual Demand Curves

• The consumer's optimal basket was determined in Chapter 4.
• It can determined how much a consumer will demand of X for a given price of X, for a given income and prices of other goods.
• This is a point on the consumer's demand curve.
• More points on the demand curve for X can be found by changing the price of X and determining how much of X the consumer will demand, while holding prices of other goods and income constant.

The Price Consumption Curve of Good X

• It is the set of optimal baskets for every possible price of good x, holding all other prices and income constant.
• The price consumption curve for good x can be written as the quantity consumed of good x for any price of x.
• This is the individual's demand curve for good x.

Individual Demand Curve: Key Points

• The consumer is maximizing utility at every point along the demand curve.
• The marginal rate of substitution (MRS) falls along the demand curve as the price of x falls; if there was an interior solution.
• As the price of x falls, it causes the consumer to move down and to the right along the demand curve as utility increases in that direction.
• The demand curve is also the "willingness to pay" curve.
• Willingness to pay for an additional unit of X falls as more X is consumed.

Demand Curve for "X"

• Algebraically, the individual's demand can be solved using the following equations: pxx + pyy = I, MUx/Px = MUy/Py - at a tangency
• If this never holds, a corner point may be substituted where x = 0 or y = 0.

Demand Curve with an Interior Solution

• Suppose that: U(x,y) = xy, MUx = y and MUy = x.
• The prices of x and y are px and py, respectively, and income = I
• Have: pxx + pyy = I x/py = y/px
• Substituting the second condition into the budget constraint: pxx + py(px/py)x = I or...x = I/2px

Example

• U(x,y)=xayb, a, b>0
• pxx + pyy = I
• MUx/px = MUy/py - at a tangency
• You can find X and then Y using this information

Engel Curves

• The income consumption curve for good x is the quantity consumed of good x for any income level (I).
• It is also the same as the individual's Engel curve for good x.
• When the income consumption curve is positively sloped, the slope of the Engel curve is positive.
• When the income consumption curve is negatively sloped (inferior good), the slope of the Engel curve is negative.

Definitions of Goods

• If the income consumption curve shows that the consumer purchases more of good x as her income rises, good x is a normal good.
• If the slope of the Engel curve is positive, the good is a normal good.
• If the income consumption curve shows that the consumer purchases less of good x as her income rises, good x is an inferior good.
• If the slope of the Engel curve is negative, the good is an inferior good.

Impact of Change in the Price of a Good

• Substitution effect: relative change in price affects the amount of good that is bought as consumer tries to achieve the same level of utility.
• Income effect: consumer's purchasing power changes and affects the consumer in a way similar to the effect of a change in income.
• As the price of x falls, all else constant, purchasing power rises.
• As the price of x rises, all else constant, purchasing power falls; this is called the income effect of a change in price.
• The income effect may be positive (normal good) or negative (inferior good):
  • A consumer substitutes into the good to achieve the same level of utility if a good's price falls.
  • Purchasing power increases because the consumer can buy the same amount and still have money left.

The Substitution Effect

• As the price of x falls, all else constant, good x becomes cheaper relative to good y.
• This change in relative prices alone causes the consumer to adjust his/her consumption basket.
• This effect is called the substitution effect.
• Usually, a move along a demand curve will be composed of both effects.

Income and Substitution Effects

• Process:
  • Find the initial basket - XA
  • Find the final basket - XC
  • Find an intermediate decomposition basket that will enable identification of the portion of the change in quantity due to the substitution effect. - XB
    • Income effect XC - XB
    • Substitution effect XB - XA
    • Price Effect = SE+IE = (XB - XA) + (XC - XB) = (XC-XA)

Other situations

• Where the income effect is 0, PE = SE+IE = SE
• For quasi-linear utility functions, income effect is zero.
• Income effect is negative and offsets the substitution effect
  • PE= SE+IE =SE +(-IE)

Giffen Goods

• If a good is so inferior that the net effect of a price decrease of good x is a decrease in consumption of good x, all else constant, then good x is a Giffen good.
• For Giffen goods, demand does not slope down.
• When an income effect might be large enough to offset the substitution effect, the good would have to represent a very large proportion of the budget.

Consumer Surplus

• The individual demand curve can be seen as the individual's willingness to pay curve.
• The individual must only actually pay the market price for all units they consumed.
• Consumer surplus: difference between what the consumer is willing to pay and what the consumer actually pays.
• The net economic benefit to the consumer due to a purchase is called consumer surplus.
• The willingness to pay of the consumer net of the actual expenditure on the good.
• The area under an ordinary demand curve and above the market price provides a measure of consumer surplus.

Compensating Variation

• Helps to estimate the monetary value that a consumer would assign to a change in the price of a good.
  • Determine how much income the consumer would be willing to give up after a price reduction, or how much additional income the consumer would need after a price increase.
  • This will maintain the level of utility she had before the price change → CV
• For a price reduction, CV is positive because the price reduction makes the consumer better off.
• For a price increase, CV is negative, because the price increase makes the consumer worse off.

Equivalent Variation

• Helps to estimate the monetary value that a consumer would assign to a change in the price of a good.
  • Determine how much additional income the consumer would need before a price reduction, or how much less income the consumer would need before a price increase.
  • This will give the consumer the level of utility she would have after the price change → EV
• For a price reduction, EV is positive because the price reduction makes the consumer better off
• For a price increase, EV is negative because the price increase makes the consumer worse off
• EV > CV
• Not necessarily equal
• If it has a zero income effect, EV=CV
• Also if these have Quasi linear utility curves
• CV the change in income to maintain same original utility.
• For finding both:
  • EV the change in income to get the utility level after the price change.
  • Price change from Px1 → Px2
  • In not always equal

Market Demand

• The market demand function is the horizontal sum of the individual demands.
• Market demand is obtained by adding the quantities demanded by the individuals (or segments) at each price, and plotting this total quantity for all possible prices.

Network Externalities

• Occur if one consumer's demand for a good changes with the number of other consumers who buy the good.
• Bandwagon effect: A positive network externality refers to an increase in each consumer's demand for a good as more consumers buy the good, exhibited in any viral trends

Snob Effect

• A negative network externality refers to the decrease in each consumer's demand as more consumers buy the good.
• A snob effect may arise because consumers value being one of the few to own a particular type of good, where certain brands have become more accessible but are looked down upon by higher income groups.

The Choice of Labor and Leisure

• Divide the day into two parts: Work hours and leisure hours.
• Consumers earn income during work hours and use the income earned for activities in their leisure time. Total daily income is w(24-L), where:
  • w is the hourly wage rate.
  • L is the leisure hours.
  • 24 is the 24 hours in a day.
• An increase in wage rate reduces the amount of labor required to buy a unit of the composite good.
• This leads to both a substitution effect and income effect.

Labor Supply Curve

• The labor supply curve slopes upward over the region where the SE > IE.
• It bends backward over the region where the IE > SE.