Chapters 4 and 5 (Alchian & Allen)
Who pays a tax?
This will depend on the elasticity of demand and supply. The four graphs below will show the tax incidence with less elastic vs. more elastic supply, and less elastic vs. more elastic demand.
Economic Rent
Although for some goods a price may not affect the amount of a good in existence, it does affect assignment to particular persons and uses. Any price unnecessary to keeping the good in existence-- but necessary for allocation to highest-valuing users, is called economic rent: economic to emphasize that it serves an allocative function and rent to indicate that it does not affect the supply.
If the allocation of goods could be revised to make someone better off without hurting anyone else, then the market is not efficient yet. A Pareto-optimal allocation is one in which any change in allocation must result in someone worse off (i.e. it is most efficient).
Ch. 4 Summary: Market Prices as Social Coordinators
- Shortages and surpluses are eliminated almost instantly by free-market prices. A reduced supply should not be confused with a shortage, which is caused by price being too low.
- When demand for a good increases, competition among buyers raises its price. Middlemen or agents transmit the increased demands to potential sellers or suppliers of the good. The price rise, however, is not caused by the rise in costs (middlemen), but by the higher value placed on the goods by the increased public demand.
- The supply curve of a good will be upward sloping if some of the extra inputs required to increase output are more valuable elsewhere-- for if they are, they will not be put to use here unless paid at least what they could earn elsewhere. The higher proportion of inputs that have higher-valued alternative uses, the higher the costs of increasing rate of output.
- How a tax on a good affects its price depends on the slopes of the demand and supply curves. If the amount supplied is fixed regardless of price (perfectly inelastic, like land) a tax will completely be deducted from the price received by suppliers.
- Under price controls, demanders for the good will offer the fixed money price but also compete by offering more of other costly activities until the full price equals the marginal personal value. Nonprice competition is wasteful since the seller does not value the buyer's nonmonetary competitive activities as much as the direct money. Race, creed, age, sex, and personal characteristics become more important in determining how goods are allocated.
- Any payment for a good in excess of that required for the permanent existence or maintenance is a pure economic rent. A quasi-rent is the portion of revenue that does not affect the amount supplied now, but will affect the future rate of production.
The Illusion that Cost Determines Price
The money price plus the value of time is the full price. Uncertainty can also change our willingness to pay (i.e. smoke detectors and insurance). Price is not determined by the cost of inputs, rather, it is a response to quantity demanded (which is ultimately subjective valuation of individual consumers).
Private-Property Rights
A person's private-property rights are the expectation that what one decides to do with certain resources will be effectively realized. The greater the expectation that this will be upheld, the stronger the rights. To the extent that rights to goods and services are well defined, enforceable, and inexpensive to transfer, the market-exchange system, operating through prices, for controlling the use of goods is effective.
Allocation Other Than Private Property: Nonprofit Institutions
A nonprofit corporation has assets that are not owned by anyone who can distribute gains to themselves or sell as one can sell private property. Rather, all proceeds must be spent in the enterprise to further its specified purpose (i.e. Catholic schools, think tanks, charity orgs). This usually results in less efficient decisions across the board since no one is to personally gain by savings or productivity increases.
Public Goods
A public good is one which is capable of being used by many at the same time without reducing the amount available for others-- non-rival and non-excludable. It contains this dilemma: Charging a price for an existing public good is wasteful if that excludes any potential user; but without a price how can revelation of its value be induced, and who will pay? Usual solutions are taxes and informal clubs (think Ostrom's work).
Ch. 5 Summary: Information Costs of Exchange
- Information about buyers' and sellers' offerings is not free; nor is the creation and operation of the market.
- Full price is the money price plus any other costs incurred by the buyer.
- Costs of information are lowered by middlemen.
- Inventories reduce sellers' costs of maintaining a reliable supply and the buyers' costs of collecting information. Buffer inventories are not wasteful uses of goods. Transient shifts in demand are more economically met.
- The more specific, secure, and transferable are the private-property rights, the lower are marketing and exchange costs.
- IMPORTANT: the particular person by whom property rights of a resource are held does not affect how they are used if the rights are cheaply transferable by sale at a price reflecting the highest-valued uses.
- If private-property are too expensive to enforce or exchange, laws or government regulations tend to control uses of goods.
- Where property rights are weak or nonexistent, less than the full price is paid as money.
- An economic standard of the appropriate use of any resource is its value in use to the highest-valuing consumers.
- Philanthropy involves some combination of: gifts in kind (transfers at less than the market price, gifts in general purchasing power, and some waste from the recipient's point of view.
- Public goods are those of which one person may enjoy all that is available without diminishing the amount available to other people. A price could be charged as long as it would not cause any person to demand less than the amount available. They're nonexcludable and nonrival.
Chapter 5 (Hirschleifer)
The Engel Curve and Income Elasticity of Demand
The income elasticity of demand is the proportionate change in quantity purchased divided by the proportionate change in income:
\(\epsilon _x \equiv \frac{\frac{\Delta x}{x}}{\frac{\Delta I}{I}} \equiv \frac{\Delta x}{x} \cdot \frac{\Delta I}{I}\)
This ratio is the slope of the Engel curve. It is useful to distinguish between elasticity at a point or across a curve. The weighted average of an individual's income elasticities equals 1, where the weights are the proportions of the budget spent on each commodity. So if only two commodities are consumed, the proposition becomes: \(k_x \epsilon _x + k_y \epsilon _y = 1\), where \(k_x \equiv \frac{P_x x}{I}\) and same for y.
The Demand Curve and Price Elasticity of Demand
A direct measure of the consumer's response to a change in price is the ratio \(\frac{\Delta x}{\Delta P_x}\). This is the reciprocal of the slope along the demand curve. The price elasticity of demand is the proportionate change in quantity purchased divided by the proportionate change in price:
\(\eta _x \equiv \frac{\frac{\Delta x}{x}}{\frac{\Delta P_x}{P_x}} \equiv \frac{\Delta x}{\Delta P_x} \cdot \frac{P_x}{x}\)
A demand curve is elastic if \(\eta _x < -1\), and vice versa. For a given demand curve, \(x = b - aP_x\), the price elasticity of demand will be \(a \cdot \frac{P_x}{x}\) (since the changes are proportional to the slope). If consumer's demand for X is elastic, a reduction in price will leave to increased spending on commodity X, and vice versa for inelastic.
Marginal Expenditure is useful for understanding the relationship between price elasticity of demand, and total spending on good X: \(ME_x \equiv \frac{\Delta E_x}{\Delta x}\). It logically follows that: \(ME_x \equiv P_x (1 + \frac{1}{\eta _x})\).
The Cross-Elasticity of Demand
Complements in demand (bread and butter) will mean that a large change in the price ratio between the two will only bring about a small change in the ratio of consumption. Substitutes operate vice versa. The cross-elasticity of demand is defined as:
\(\eta _{xy} \equiv \frac{\frac{\Delta x}{x}}{\frac{\Delta P_y}{P_y}} \equiv \frac{\Delta x}{x} \cdot \frac{P_y}{\Delta P_y}\)
Thus complements have negative cross-elasticity of demand, as a reduction in the price in bread could increase the quantity of butter purchased. Between substitutes, it is positive.
Fitting a Demand Curve
There are two ways to approach this-- constant slope (straight line down) or constant elasticity (curved line down). Constant-slope answers: How do numerical changes of quantity respond to numerical changes of price? Constant-elasticity answers: How do proportionate changes in quantity depend upon proportionate changes in price?
For constant-slope, the general demand function is linear:
\(X = A + BP_X\) where A and B are constants, and B is usually negative in accordance with the Law of Demand.
Taking into account other variables that affect demand, such as income and prices of related goods, we can find an even more generalize demand function:
\(X = A + BP_X +CI + DP_Y + EP_Z + ...\) where C is the slope of the income expansion curve, which is positive when X is a superior good or negative when X is inferior. The sign of D is negative if X and Y are complements and positive if substitutes.
Determinants of Responsiveness of Demand to Price
- Availability of substitutes: Demand for one commodity will be more elastic the more numerous and closer the available substitutes (more competition). This creates the substitution effect of price change, in which a little change in price of one good causes a bigger change in quantity demanded.
- Luxuries versus necessities: Demand for luxuries are more elastic than demand for necessities, thus there is an income effect of a price change. A reduction in price enriches the consumer in real terms, an such an enrichment will affect purchases of more luxuries than necessities.
- High-priced versus low-priced goods: Along a linear demand curve, elasticity is higher at higher prices. At the choke price (vertical intercept), elasticity is infinite.
- The "importance" fallacy: There is a false idea that the less important a good is to your overall budget (i.e. salt) the less elastic your demand will be (you won't buy more salt just because it's cheaper). However, elasticity measures proportionate change, so the proportionate change to your budget wouldn't be that big anyway. Turns out that salt is a necessity with few substitutes, so this explains the change.
Multiple Constraints - Rationing
Historically (during WWII), increased scarcity led to coupon or point rationing. When binding, this acts as a sort of "price ceiling" on one's demand curve. The first graph shows this for one good (resulting in purchasing more of another good) but the second graph shows a ration on both.
Point rationing is a more sophisticated way of ensuring that individuals can still consume their preferences. In this system, an individual will pay the money price as well as the point price, allowing them to manifest their preferences. The point system just adds another constraint (N points) to their regular income budget constraint:
\(P_X X + P_Y Y \leq I\)
\(P_X X + P_Y Y \leq N\)
Summary:
Elasticity is a unit-free measure of how a change in one variable is associated with a change in another variable.
- The response of quantity demanded to changes in income is measured by the income elasticity of demand. It is the percent change in quantity of X purchased, divided by the percent change in income. Income elasticity is positive for superior goods and negative for inferior goods.
- The response of quantity demanded to changes in price is measured by the price elasticity of demand for good X. It is the percent change in quantity X purchased, divided by the percent change in price of good X. The Law of Demand implies that this is negative.
- The cross-elasticity of demand is the percent change in the quantity demanded of good X, divided by the percent change in the price of good Y. If the goods are complements, this will be negative; positive if substitutes.
Class Notes:
Deriving utility from a demand curve:
One way is to illustrate the indifference curves, drop down the price/quantity points, and connect for the curve. Important to remember income and substitute effects if the price of a good falls (more income to spend on more but might want to substitute that extra income for the other good).
- Hicksian Method: holds real income constant and only shows substitution effects (see graph in notes)
- Slotsky Method: holds apparent income constant so shows a little income effect as well (see graph in notes)
- Marshallian Method: includes both substitution and income effects so becomes the truest demand curve
*MIDTERM QUESTION: which demand curve is more elastic for increase in price?
Little Lesson on Love: Does John love Mary?
\(U_J= f(U_M)\)
If partial derivative of the function is > 0 then John gets happier as Mary gets happy. If < 0, then John gets sadder as Mary gets happier. If = 0 then then indifferent between happiness.
Consumer Surplus:
The difference between the maximum price you would have paid and the price you did pay. Measures the gains from exchange.
Mathematically, taking the area under the demand curve. This is done through summing, which integration accomplishes:
\(CS = \int f(Q)dQ - PQ\)
Price discrimination would soak up all of the consumer surplus by charging different prices for different amounts. Does price discrimination make the consumer worse off? No-- since you will still be on the same indifferent curve (see graph in notes).
Offer Curve and Excess Demand Curve:
Offer will show tradeoff between good X and good Y.
Excess Demand curve will show that if the price of a good is high enough, a buyer will become a seller.
Productions Possibility Curve
Priceline of P1/Px is the marginal rate of technological substitution. Find productive and consumptive optima. Exchange allows him to specialize. Exchange restrictions makes consumers worse off and producers better off (can sell goods at higher price without trade).
***Exam: Part 1 (3 questions and answer all), Part 2 (answer only 3 of 4 but select other as extra credit question for half points), and have only 15min. per question.***