**Chapter 3 Comparative Statics and Demand**

One of the goals of economics is to predict how people will respond to changes. We can do this using comparative statics. This is the process of comparing two equilibria. To do this, we look at the equilibrium bundle before a particular change, and compare it to the equilibrium after the change.

**3.1 Price and Income Changes**

**Own-Price Changes**

A change in the price of a commodity changes the position of the budget constraint, which changes the consumer’s opportunities. However, without information on the individual’s tastes, we cannot know for sure how the new equilibrium bundle compares with the old one.

**Derivation of the Individual’s Demand Curve**

The price consumption curve is the set of commodity bundles traced out as the price of a commodity varies. This is created by adjusting the budget constraint for different prices of unit x and finding the point where the highest difference curve is tangent to the new budget line (representing the quantities of each good that would be purchased at that point), and then connecting all of these points. These points can be translated to a graph showing quantity on the horizontal axis and price on the vertical axis – this is the individual’s demand curve for that product.

**Cross-Price Changes**

The cross-price effect is the impact of a change in the price of one good on the quantity demanded of another good.

Substitutes are two goods that satisfy similar wants. An increase in the price of one good leads to an increase in the quantity demanded of a substitute, all else equal.

Complements are two goods that tend to be used together. An increase in the price of one good leads to a decrease in the quantity demanded of a complement, all else equal.

A change in demand occurs when there is a change in the price of a substitute or a complement.

A change in quantity demanded occurs where there is a change in the item’s own price.

**Income Changes and Demand Curves**

A commodity for which consumption decreases when income decreases, or whose consumption increases when income increases is referred to as a normal good. (Example: steak, yachts) For normal goods, if income increases, the demand curve shifts to the right (demand increases).

A commodity for which consumption decreases when income increases is referred to as an inferior good. (Example: intercity rail, ramen noodles) (It is impossible to draw a diagram in which every commodity is inferior, because we assume that all income is spent – if income goes up, the consumption of something must increase.) For inferior goods, if income increases, the demand curve shifts to the left (demand decreases).

**Income Consumption Curve**

The income consumption curve is the set of equilibrium commodity bundles traced out as the consumer’s income varies, all else equal. This curve shows the quantities of the two commodities consumed at each level of income. It’s derived by increasing income (and shifting the budget constraint out), finding the point where each new budget constraint is tangent to the highest indifference curve, and then connecting these points.

**Interpreting Data on Consumer Demand**

When interpreting real-life data about changes in price and quantity demanded, it is important to understand the causes of the demand and whether they were based on a change in demand or a change in quantity demanded.

**Market Demand**

The market demand curve shows the relationship between a commodity’s price and the quantity demanded by all market participants, all else equal. This can be derived by using horizontal summation. This is the process of adding together individual demand curves to derive the market demand curve – for each price, we sum the number of units each individual would be willing to buy to get the total market demand at that price.

Even if some individual’s demand curves do not meet the assumptions made earlier (they are inconsistent), as long as most people meet the criteria, we can make good predictions about the group.

**3.2 Comparitive Statics Applied**

**In-Kind Transfers**

An in-kind transfer is a payment made to an individual in the form of a commodity or service. If this good is prohibited from reselling on the market, then we can say that from the recipient’s point of view, an in-kind transfer can be as good as cash, but it can never be better and may be worse. The in-kind transfer shifts the budget constraint out by the amount of units provided, so that the budget constraint line looks like a horizontal line the size of the transfer and then the normal diagonal budget constraint, parallel to the original. [Image page 70]

**Charitable Giving**

A contribution to charity can be considered a good as long as it provides utility. In this way, charity can be considered a good. If there is a tax deduction on charitable giving, this essentially lowers the opportunity cost of giving, pivoting the budget constraint.

**3.3 Elasticity**

**Price Elasticity of Demand**

The price elasticity of demand is the negative of the percentage change in quantity demanded divided by the percentage change in price.

ϵ=-%∆X/%∆p or

ϵ =-(∆X/X)/(∆p/p) or

ϵ=-(∆X/∆p)*(p/X)

*Del X = Xnew-Xold

As long as the demand curve slopes downward, elasticity is positive. A larger value of e means that demand is more responsive to price (more horizontal).

Arc elasticity of demand allows you to find elasticity over long distances, this is done by using the average x and average p, instead of using one of the two points. ϵ =-(∆X/Xavg)/(∆p/pavg)

**Price Elasticity and Total Expenditure**

Total expenditure is the amount of money consumers spend on a commodity, computed as the number of units purchased times the price per unit. Total expenditure = p*X

If the price elasticity is less than one, it is considered inelastic at that price. When the demand for a commodity is inelastic, quantity demanded is not very responsive to changes in price. This means that the quantity demanded does not go down very much when price increases, and consumers end up spending more money on the commodity. When the price increases, the total expenditure increases. (Demand curve is close to vertical.)

If the price elasticity of demand is greater than one, the demand curve is said to be elastic at that price. In this case, the quantity demanded is so responsive to price that total expenditure actually falls when the price rises. (Demand curve is close to horizontal.)

When demand is unit elastic, the percentage increase in price exactly equals the percentage decrease in quantity demanded. Therefore, total expenditure stays the same when price increases or decreases.

**Determinants of the Price Elasticity of Demand**

1. The presence of close substitutes for a commodity tends to make its demand more elastic. Also, in general, the demand for a more narrowly defined commodity (Reeboks) is more elastic than the demand for a more broadly defined commodity (shoes).

2. The elasticity depends on the commodity’s share in the consumer’s budget. In general, the smaller the fraction of income absorbed by a commodity, the less elastic the demand, all else equal.

3. The elasticity depends upon the time frame of the analysis. The elasticity of demand for a commodity may be greater in the long run than in the short run. (i.e. People may not stop taking the metro immediately after a fare rise, but over the long term, they may decide to invest in a vehicle.)

**Price Elasticity for Some Special Cases**

Vertical Demand Curve: A vertical demand curve is called perfectly inelastic. The price elasticity of demand equals zero; quantity demanded does not change at all when price changes.

Horizontal Demand Curve: A horizontal demand curve is called a perfectly elastic or infinitely elastic demand curve. The price elasticity of demand equals infinity. If the price increases by even a little bit, the quantity demanded falls to zero.

Unit Elastic Demand Curve: If the elasticity is equal to one everywhere on the demand curve, then the total expenditure is always the same regardless of price. This demand curve is a rectangular hyperbola (curve bowed inwards at the origin).

Linear Demand Curve: A linear demand curve has an elasticity equal to: ∈=b*pX ; At the horizontal intercept, the elasticity is 0, at the vertical intercept, the elasticity is infinity.

**Cross-Price Elasticity of Demand**

The cross elasticity of demand for good X with respect to the price of good Y, ∈xy, is the percentage change in the quantity demanded of X induced by a percentage change in the price of Y.

∈xy=%∆X/%∆py

The cross-price elasticity of demand is positive if X and Y are substitutes (when the price of Y goes up, the quantity demanded of X goes up). The cross-price elasticity of demand is negative if X and Y are complements (when the price of Y goes up, the quantity of X goes up). If two goods are unrelated, the cross-price elasticity of demand is zero.

**Income Elasticity of Demand**

The income elasticity of demand is the percentage change in quantity demanded with respect to a percentage change in income.

∈I=%(del)X%(del)I

If a commodity is normal, the income elasticity of demand is positive. If a commodity is inferior, the income elasticity of demand is negative. When the income elasticity of demand is greater than one, then the consumption of a commodity is very responsive to income. These commodities are sometimes called luxury goods.

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