Supply and Demand Models Chapter 3,4

Volatile oil prices St. Louis Fed FRED database

Prices and Production 1976-2013 BP Statistical Review of World Energy

Laws of Supply and Demand

Supply and Demand Framework A description of a market includes the quantity of goods that are sold in that market, Q, and the price, P, at which they are sold. Outcomes in the market are a function of the laws of supply and demand

Law of Demand Ceteris parabis, There is an inverse relationship between the price of a good and the quantity that consumers would like to purchase. What does Ceteris Parabis mean?

Law of Demand Two Explanations: Substitution Effect – Goods purchased to satisfy needs but other goods (substitutes) may also do so. When price rises, consumers have an incentive to switch goods. Income Effect – Consumers have a limited budget. When price of a major item goes up, less money for purchase of all items.

Mathematical representations of Law of Demand Demand Schedule (Spreadsheet) Demand Curve (Geometry) Demand Function (Algebra)

Global Daily Demand Schedule for Oil 2010 P = US$ QD = Thousand barrels daily

General Demand Curve P D P2 P1 Q Q2 Q1

Demand Functions An algebraic equation representing demand as a function of the price plus consumer income levels and other factors Example: Linear: QD = A – B × P Exponential: QD = A × P-b

Natural Logarithm z = ln(Z) Common for professional economists to deal with prices and quantities in natural logarithms z Z

p = ln(P) qD = ln(QD) Log-linear Demand qD = a - b × p Natural Logarithm: Natural Logarithm

Law of Supply: Ceteris parabis, there is a positive relationship between the price of a good and the quantity producers bring to the market.

Law of Supply Explanation Increasing Costs Producers will bring goods to market only if the price obtained from selling an extra good will exceed the cost of producing an extra good. If per unit production costs are rising in the number of goods produced, higher prices will be demanded to bring a larger quantity of goods to market.

Mathematical representation of Law of Supply Supply Schedule (Spreadsheet) Supply Curve (Geometry) Supply Function (Algebra)

Global Daily Supply Schedule for Oil 2010

Supply Curve S P P2 P1 Q Q1 Q2

Supply Functions An algebraic equation representing supply as a function of the price plus input costs and other factors Examples: Linear: QS = C + D× P Exponential: QS = C× Pd Log Linear: qS = c + d × p

Elasticity as Price Sensitivity

Price Elasticity: The % impact on quantity demanded/supplied of a 1% change in price

Midpoint Method %𝑋 ≡100× [ 𝑋 1 − 𝑋 0 ] [𝑋 1 + 𝑋 0 ] 2 If you want to calculate a % difference between two points which is the same regardless of which you designate as the reference point (denominator), you can use the average of the two points as the reference point. %𝑋 ≡100× [ 𝑋 1 − 𝑋 0 ] [𝑋 1 + 𝑋 0 ] 2

Demand Elasticity

Unit elasticity (elasticity equal to 1) is A demand curve is classified as INELASTIC if the elasticity is between 0 and 1 Unit elasticity (elasticity equal to 1) is the cutoff point A demand curve is classified as ELASTIC if the elasticity is more than 1

Prices and Revenue Revenue in a market is Revenue = P∙Q If prices change, revenue will change for two reasons: Direct Effect of the Price Change (positive) Indirect Effect of the Price Change on Quantity Demanded (negative) Rule of Thumb: The percentage change in the product of two variables is approximately the sum of the % change in each variable.

Price Elasticity of Revenue If demand is elastic, a price rise reduces revenues If demand is inelastic, a price rise increases revenues

𝑞 𝐷 1 =𝑎−𝑏× 𝑝 1 𝑞 𝐷 0 =𝑎−𝑏× 𝑝 0 (𝑞 𝐷 1 − 𝑞 𝐷 0 )=−𝑏× (𝑝 1 − 𝑝 0 ) Differences in logarithms approximate midpoint measure of % changes z1 – z0 ≡ ln(Z1) – ln(Z0) ≈ %Z/100 𝑞 𝐷 1 =𝑎−𝑏× 𝑝 1 𝑞 𝐷 0 =𝑎−𝑏× 𝑝 0 (𝑞 𝐷 1 − 𝑞 𝐷 0 )=−𝑏× (𝑝 1 − 𝑝 0 ) (𝑞 𝐷 0 − 𝑞 𝐷 1 ) (𝑝 1 − 𝑝 0 ) =𝑏≈𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦

Equilibrium

Equilibrium in the competitive market occurs when the price is set at a level (P*) such that the amount that consumers want to buy is equal to the amount that sellers want to sell (Q*). Excess Supply If P were above equilibrium, sellers would want to sell more goods than buyers would want to buy. Competition between sellers would force prices down. Excess Demand If P were below equilibrium, customers would want to buy more goods than people would want to sell. Competition between buyers would force prices up.

Competitive Market Equilibrium S D P* Q* Q

Excess Supply at P S D P* Q* Q

Excess Demand at P S D P* Q* Q

Market Equilibrium (Spreadsheet Problem) At what price and quantity (to closest $5) will the oil market clear? P QD QS 60 83,035 81,350 65 82,704 81,611 70 82,398 81,854 75 82,114 82,080 80 81,850 82,292 85 81,602 82,492 90 81,369 82,680 95 81,149 82,860 100 80,941 83,030

Algebra of Equilibrium Log Linear Functions A - B×P = QD = QS = C + D ×P A - B×P* = C+D×P* (A-C) = (B+D) ×P* 𝑃 ∗ = 𝐴−𝐶 𝐵+𝐷 QS = C+D×P* = C+D× 𝐴−𝐶 𝐵+𝐷 = = C× 𝐵 𝐵+𝐷 +A× 𝐷 𝐵+𝐷

Example

Algebra of Equilibrium Log Linear Functions a - b×p = qD = qS = c + d ×p a - b×p* = c+d×p* (a-c) = (b+d) ×p* 𝑝 ∗ = 𝑎−𝑐 𝑏+𝑑 qS = c+d×p* = c+d× 𝑎−𝑐 𝑏+𝑑 = c× 𝑏 𝑏+𝑑 +a× 𝑑 𝑏+𝑑

Algebra of Equilibrium Log Linear Functions 11.53 - .05×p = qD = qS = 11.14 + .04 ×p 11.53 - .05×p* = 11.14+.04×p* (11.53-11.14) = (.05+.04) ×p* 𝑝 ∗ = .39 .09 =4.333 qS = 11.14+.04×4.3333 = 11.316

Algebra of Equilibrium Log Linear Functions qD = 11.53 - .05×p qS = 11.14 + .04 ×p 11.53 - .05×p* = 11.14+.04×p* (.39) = .09 ×p* .39 .09 =4.333= 𝑝 ∗ 𝑞 ∗ =11.14+.04∗4.333=11.316

If you know q* and p*, then use antilog function to get Q* and P*

Market Changes: Shifts in Demand & Supply Curves

Shifting Curves/Changing Equilibrium Changes in equilibrium result from shifts in either the demand or supply schedule. We think of shifts in the curves as changes in supply or demand that are caused by factors other than changes in the price of the good. Shifts in the demand curve lead to movements along the supply curve resulting in changes in prices and quantities that move in the same direction. Shifts in the supply curve lead to movements along the demand curve resulting in changes in prices and quantities that move in different directions.

P S D′ D Q P** P* Q** Q* Shift in the demand curve A Shift in the Demand Curve: A parallel increase in the demand schedule at every price point. Price and Quantity Demanded move in same direction P S Shift in the demand curve ① P** ⓪ D′ P* Excess Demand D Q Q* Q**

A Shift in the Supply Curve is a Movement along the Demand curve- Price and Quantity Supplied Move in opposite Directions P S′ S D ① P** ⓪ P* Excess Demand Q Q* Q**

Equilibrium Effects Price system means that shifts in demand will cause accommodating changes in quantity supplied but also an attenuating change in quantity demanded. Shifts in supply will cause accommodating changes in quantity demanded but also attenuating change in quantity supplied.

P S D′ D Q P** P* Q** Q* Along demand curve Along supply curve Equilibrium Effect: Movement along the supply curve increases quantity supplied; movement along demand curve ameliorates quantity demanded. P S Along demand curve Along supply curve ① P** ⓪ D′ P* Excess Demand D Q Q* Q**

D S P S′ P** P* Q** Q* Q Along supply curve Along demand curve Equilibrium Effect: Movement along the demand curve reduces quantity demanded; movement along supply curve ameliorates quantity supplied. D S P S′ Along supply curve ① P** Along demand curve P* ⓪ Q** Q* Q

What Shifts the CurveS? Price of Related Goods Price of Inputs Income Demand Curve? What Shifts the Supply Curve? Price of Related Goods Income Consumer Preferences Expected Future Prices Expected Future Income Price of Inputs Price of Related Goods Technology/Nature Expected Future Prices Market Entry

Income Elasticity/ Cross Price Elasticity Changing Equilibrium

Income Elasticity We measure the effect of income on demand for a good as % effect on demand of a 1% increase in income: (m). Ex. For normal goods, income elasticity is positive (m > 0) . For inferior goods income elasticity is negative. (m < 0) qD = a - b×p + m × y y = ln(Income)

Luxuries vs. Necessities There are two types of normal goods. Luxuries take up an increasing share of income as your income grows. Luxuries are income elastic - the income elasticity of luxuries is greater than 1 (m > 1). Necessities take up a declining share of income as your income grows. Necessities are income inelastic – the income elasticity of necessities is less than 1 (0 < m < 1). China’s Emerging Middle Class Download

Range of Income Elasticities Inferior Goods Range of Income Elasticities Normal Goods 1 Income Elastic (Luxury Goods) Income Inelastic (Necessities)

Changes in Prices of Other Goods For any good there are two types of other goods which are relevant to its demand Substitutes: Those other goods which can take the place of the good of interest (bacon vs. ham) Complements: Those other goods whose use will enhance the value of the good of interest. (bacon and eggs) What are substitutes and complements for oil

Substitutes vs. Complements A good is defined as a “Substitute” when a rise in its price leads to a shift out/up in the demand curve for the good of interest. A good is defined as a “Complement” when a rise in its price leads to a shift in/down in the demand curve for the good of interest.

Cross Price Elasticity Cross price elasticity is the % effect on the quantity demanded of a % change in another price. Goods with positive cross-price elasticities are called substitutes Goods with negative cross-price elasticities are called complements Complements Substitutes

Cross Price Elasticity We measure the effect of income on demand for a good as % effect on demand of a 1% increase in related price: f. Ex. For substitutes, cross price elasticity is positive (f > 0). For complements , cross price elasticity is negative (f < 0). qD = a - b×p + f × pk pk = ln(Price of Related Good)

Chap. 3, 4 Commodity Markets

Why are commodity prices so volatile? Oil Prices Link Why are commodity prices so volatile?

Price Sensitivity and Equilibrium Effects When supply or demand curves shift, the effect will be felt in some combination of changes in prices and quantities. The degree to which changes in either supply or demand are felt in quantity changes rather than price changes is determined by price sensitivity of both demand and supply.

What determines price elasticity? AVAILABILITY OF SUBSTITUTES SHARE OF INCOME A price increase will lead to a shift away from the use of a product and toward other products. Price elasticity will be stronger if there are readily available substitutes for a good. A price increase for one good reduce income available for purchases for all goods Price elasticity will be stronger if a good makes up a big chunk of income. World Bank Tobacco Download

Comparisons of Demand Price Elasticities Price Elasticities of Other Goods Salt .1 Coffee .25 Tobacco .45 Movies .9 Housing 1.2 Restaurant Meals 2.3 Commodities have very inelastic demand. Estimate of elasticity of demand for oil in the US is .061 J.C.B. Cooper, OPEC Review, 2003)

Elasticities Extreme P D D Q Perfectly Inelastic Demand (Insulin) Perfectly Elastic Demand (Clear Pepsi) D Q

. Steeper (less elastic) demand curve means that a supply shift will have a smaller impact on quantity and bigger impact on price. S' P S ① P1** ② P2** ⓪ P* D2 D1 Q Q2** Q* Q1**

Elasticity of Supply Elasticity of supply curve depends on the ability of production sector to ramp up supply without increasing the marginal cost of production. A good that is produced with readily available factors w/o a need for time consuming investment will have an elastic supply curve.

Elasticities: Supply P S S Q Perfectly Inelastic Supply (Van Gogh Paintings) P S Perfectly Elastic Supply (Foot Massage) S Q

. Steeper (less price sensitive) supply curve means that a demand shift will have a smaller impact on quantity and bigger impact on price. S1 P S2 ① P1** ② P2** ⓪ P* D' D Q Q* Q1** Q2**

Algebra of Equilibrium Effects If demand or supply elasticities are big, effects of supply or demand change on equilibrium price will be small

Income Elasticity of Oil Assume a world income elasticity of .5 and an increase of world income equal to 5%. Demand shifts out by 2.5%. Would oil production supplied increase by 2.5%? Region Income Elasticity China 0.7 OECD 0.4 ROW 0.6 Source: OECD study qD = a - b×p + m × y Δ qD = m × Δ y

Market Equilibrium (Spreadsheet Problem) At what price and quantity (to closest $5) will the oil market clear? P QD QD´ QS 60 83,035 85,111 81,350 65 82,704 84,771 81,611 70 82,398 84,458 81,854 75 82,114 84,167 82,080 80 81,850 83,896 82,292 85 81,602 83,642 82,492 90 81,369 83,403 82,680 95 81,149 83,178 82,860 100 80,941 82,965 83,030

Algebra of Equilibrium Effects 2.5% Shift in Demand Curve

Price Elasticity and Time

Elasticity of Demand Short-term vs. Long-term It takes time to find substitutes for goods or to adjust consumption behavior in response to a change in prices. The long-run demand response to a price rise is larger than the short-run. Price elasticity of demand is more negative in the long run than in the short run. .

Oil Demand much more elastic in long run than short-run (J.C.B. Cooper, OPEC Review, 2003)

Price Elasticity of Supply Firms also find it easier to adjust production in the long-run than the short run. Long-run price elasticity of supply is typically greater than short-run OECD study suggests price elasticity of oil supply is .04 in short run and .35 in long run.

Speculation & Supply Some commodities have a time dimension. Producers have a choice about when to bring goods to market. If producers believe prices will be higher in the future, they have an incentive to delay shipment to the future. Higher price expectations will shift the supply curve inward. Note: This won’t work for apples, oranges or other perishable commodities.

Expectations of Increased Prices in the Future Lead to Higher Prices Today! ① P** P* ⓪ Q** Q* Q

CONTANGO

Speculation & Demand For some storable commodities (e.g. gold) or durable goods, expectations of future price hikes might also lead consumers to start buying immediately. Higher price expectations will shift demand curve outward.

Even higher prices! P D' S' S D ② P*** P** ① P* ⓪ Q Q** Q***

Bubbles If current prices can be driven by expectations of even higher prices in the future…and…investors pile into commodities whose price has risen, then this could generate a feedback loop featuring rapidly rising prices Think about for fun. Too theoretical for exam.

Bubble BURSTS? St. Louis Fed Database

Expected Income Effect Households are forward looking. If they expect income in the future they will increase spending today. Optimism (or pessimism) about future income will shift demand curve.

Learning Outcomes Solve for equilibrium price and quantities using graphical supply and demand model or spreadsheet supply and demand schedules or simple linear algebra. Explain qualitatively and calculate quantitatively, the likely consequences for equilibrium prices and quantities resulting from exogenous shifts in supply and demand. Calculate elasticities using the midpoint method.

Learning Outcomes Distinguish substitutes/complements, luxuries/necessities/inferior goods. Identify the impact of demand & supply elasticity on price and quantity volatility in the short and long run. Identify the impact of expectations of the future on current prices.