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Lecture # 04a Demand and Supply (end) Lecturer: Martin Paredes

Lecture # 04a Demand and Supply (end) Lecturer: Martin Paredes. Other Elasticities. In general, for the elasticity of “Y” with respect to “X”:  Y,X = ( % Y) = ( Y /Y) = d Y . X ( % X ) ( X /X) d X Y. Other Elasticities.

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Lecture # 04a Demand and Supply (end) Lecturer: Martin Paredes

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  1. Lecture # 04a Demand and Supply (end) Lecturer: Martin Paredes

  2. Other Elasticities • In general, for the elasticity of “Y” with respect to “X”: • Y,X= (% Y) = (Y/Y) = dY . X • (% X) (X/X) dX Y

  3. Other Elasticities • Price elasticity of supply: measures curvature of supply curve • (% QS) = (QS/QS) = dQS . P • (% P) (P/P) dP QS

  4. Other Elasticities • Income elasticity of demand measures degree of shift of demand curve as income changes… • (% QD) = (QD/QD) = dQD . I • (% I) (I/I) dI QD

  5. Other Elasticities • Cross price elasticity of demand measures degree of shift of demand curve when the price of another good changes • (% QD) = (QD/QD) = dQD . P0 • (% P0) (P0/P0) dP0 QD

  6. Source: Berry, Levinsohn and Pakes, • "Automobile Price in Market Equilibrium," • Econometrica 63 (July 1995), 841-890. • Example: The Cross-Price Elasticity of Demand for Cars

  7. Source: Gasmi, Laffont and Vuong, "Econometric Analysis of Collusive Behavior in a Soft Drink Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311. • Example: Elasticities of Demand for Coke and Pepsi

  8. How to Estimate Demand and Supply Equations Use Own Price Elasticities and Equilibrium Price and Quantity Use Information on Past Shifts of Demand and Supply

  9. Use Own Price Elasticities and Equilibrium Price and Quantity • Choose a general shape for functions • Linear • Constant elasticity • Estimate parameters of demand and supply using elasticity and equilibrium information • We need information on ε, P* and Q*

  10. Example: Linear Demand Curve • Suppose demand is linear: QD = a – bP • Then, elasticity is Q,P = -bP/Q • Suppose P = 0.7 Q = 70 Q,P = -0.55 • Notice that, if  = -bP/Q  b = -Q/P • Then b = -(-0.55)(70)/(0.7) = 55 • …and a = QD + bP = (70)+(55)(0.7) = 108.5 • Hence QD = 108.5 – 55P

  11. Example: Constant Elasticity Demand Curve • Suppose demand is: QD = APε • Suppose again P = 0.7 Q = 70 Q,P = -0.55 • Notice that, if QD = APε A = QP-ε • Then A = (70)(0.7)0.55 = 57.53 • Hence QD = 57.53P-0.55

  12. Example: Broilers in the U.S., 1990 Price • Observed price and quantity .7 0 70 Quantity

  13. Example: Broilers in the U.S., 1990 Price • Observed price and quantity .7 Linear demand curve 0 70 Quantity

  14. Example: Broilers in the U.S., 1990 Price • Observed price and quantity .7 Constant elasticity demand curve 0 70 Quantity

  15. Example: Broilers in the U.S., 1990 Price • Observed price and quantity .7 Constant elasticity demand curve Linear demand curve 0 70 Quantity

  16. Use Information on Past Shifts of Demand and Supply A shift in the supply curve reveals the slope of the demand curve A shift in the demand curve reveals the slope of the supply curve.

  17. Example: Shift in Supply Curve • Old equilibrium point: (P1,Q1) • New equilibrium point: (P2,Q2) • Both equilibrium points would lie on the same (linear) demand curve. • Therefore, if QD = a - bP • b = dQ/dp = (Q2 – Q1)/(P2 – P1) • a = Q1 - bP1

  18. Example: Identifying demand by a shift in supply Price Supply Market Demand 0 Quantity

  19. Example: Identifying demand by a shift in supply Price New Supply Old Supply Market Demand 0 Quantity

  20. Example: Identifying demand by a shift in supply Price New Supply Old Supply • P2 • P1 Market Demand 0 Q2 Q1 Quantity

  21. This technique only works if the curve we want to estimate stays constant. • Example: Shift in Supply Curve • We require that the demand curve does not shift

  22. Price Supply Demand 0 Quantity

  23. Price New Supply Old Supply Old Demand New Demand 0 Quantity

  24. Price New Supply • Old Supply P2 • P1 Old Demand New Demand 0 Q2 = Q1 Quantity

  25. Summary • 1. Example of a simple micro model of supply and demand (two equations and an equilibrium condition) • 2. Elasticity as a way of characterizing demand and supply • Factors that determined elasticity • Estimating demand and supply • From own price elasticity and equilibrium price and quantity • From information on past shifts, assuming that only a single curve shifts at a time.

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