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## Supply and Demand Models

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**Supply and Demand Models**Chapter 3,4**Volatile oil prices**St. Louis Fed FRED database**Prices and Production 1996-2011**BP Statistical Review of World Energy**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 Oil2010**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**Natural Logarithm:**p = ln(P) qD = ln(QD) Log-linear Demand qD = a - b × p 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)**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:**Price Elasticity:The % impact on quantity**demanded/suppliedof a 1% change in price**Midpoint Method**• 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.**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**Differences in logarithms approximate midpoint measure of %**changes z1 – z0 ≡ ln(Z1) – ln(Z0) ≈ %Z/100**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 SupplyIf 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 DemandIf 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**P 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?**Algebra of Equilibrium**QD = a - b×P QS = c + d ×P Linear Functions a - b×P* = c+d×P* (a-c) = (b+d) ×P***Algebra of Equilibrium**qD = a - b×p qS = c + d ×p Log Linear Functions a - b×p* = c+d×p* (a-c) = (b+d) ×p***Algebra of Equilibrium**qD = 11.53 - .05×p qS = 11.14 + .04 ×p Log Linear Functions 11.53 - .05×p* = 11.14+.04×p* (.39) = .09 ×p* 3=11.316**If you know q* and p*, then use antilog function to get Q***and P***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.**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* 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* 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.**A Shift in the Demand Curve: Equilibrium Effect: Movement**along the supply curve increases quantity supplied; movement along demand curve ameliorates quantity demanded. S P Along demand curve Along supply curve ① P** ⓪ D′ P* D Q* Q** Q**A Shift in the Supply 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?**What Shifts the Demand Curve? What Shifts the Supply Curve? Price of Inputs Price of Related Goods Technology/Nature Expected Future Prices Market Entry • Price of Related Goods • Income • Consumer Preferences • Expected Future Prices • Expected Future Income**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)