Market Equilibrium & Comparative Statics Dr. Jennifer P. Wissink ©2011 John M. Abowd and Jennifer P. Wissink, all rights reserved.

Market Equilibrium We will consider the market for compact disc players. Recall that we will define the following for our market: The type and style of CD players. The quality of the CD players. All other attributes of the generic CD player. A time frame that applies to our market for CD players. Demanders are the buyers of CD disc players. QxD = f(PX, Ps, Pc, I, T&P, Pop) Suppliers are the sellers of CD players. QXS = g(PX, Pfop, Poc, S&T, N) The CD player market is a perfectly competitive market. demand function QSx Px supply function QDx

Market Equilibrium (Verbal) A place of “rest”. Equilibrium: a price where the quantity demanded equals the quantity supplied. In notation: Find a PX* so that: QXD(PX*) = QXS(PX*)

Market Equilibrium (Table) At P* = $17, the QD = QS=23 So Q*=23

Market Equilibrium (Table) Note: If P>17 you are not at an equilibrium. Why? Suppose P=$30 QD=10 and Qs=36 surplus=26 units Price would tend to fall. There would be an increase in quantity demanded and a decrease in quantity supplied as the price falls.

Market Equilibrium (Table) Note: If P<17 you are not at an equilibrium. Why? Suppose P=$15 QD=25 and Qs=21 shortage=4 units Price would tend to rise. There would be an increase in quantity supplied and a decrease in quantity demanded as the price rises.

Market Equilibrium (Graph) The market equilibrium occurs at the intersection of the supply and demand curves. Let’s drop the subscript X, ok? Price Demand Supply surplus Phigh P*=17 At P* = $17, QD = QS = 23 So Q* = 23 Plow shortage 23 Quantity

Market Equilibrium (Equations) Two equations and Two unknowns Equations: Demand and Supply Curves Unknowns: P and Q To find P*, set QD = QS Recall: QD = 40 - P and QS = 6 + P So for an equilibrium: (40 - P*) = (6 + P*) 34 = 2P* or P* = 34/2 so... P*=$17 To find Q*, plug P* into either the demand or supply equation. Q*=23 = 40 - 17 or Q*=23 = 6 + 17 SIMPLE AS THAT!? Then what....

Comparative Statics Use the model to make predictions. Something changes in the market. Something that changes demand. Something that changes supply. Something that changes both! Something the government does to prevent a natural market equilibrium. Would get a new equilibrium. Compare one equilibrium with another equilibrium and see what happens to P* and Q*. Compare two equilibria - compare two static situations - comparative statics!

Recall Demand & Supply Curves The demand curve QD = f(P) given Ps, Pc, I, T&P, Pop The supply curve QS = g(P) given Pfop, Poc, S&T, N Comparative Statics Summary: EVENT P* Q* ↑D Up ↓D Down ↑S ↓S ↑D ↑ S ?

Comparative Statics: Increase in Demand  increase in P* and Q* D shifts to right. No longer in equilibrium: At P=$17 there’s a shortage Price will rise. As price rises, there is a reduction in quantity demanded along new demand curve AND an increase in quantity supplied along original supply curve. Get new P* and Q* at P*=22 and Q*=28. Price 17 23 Supply Quantity Demand New Demand 22 28

Comparative Statics: Decrease in Demand  decrease in P* and Q* D shifts to left. No longer in equilibrium: At P=$17 there’s a surplus. Price will fall. As price falls, there is an increase in quantity demanded along new demand curve AND a decrease in quantity supplied along original supply curve. Get new P* and Q* at P*=14.5 and Q*=20.5. Price Demand Supply New Demand 17 14.5 20.5 23 Quantity

Comparative Statics: Increase in Supply  decrease in P Comparative Statics: Increase in Supply  decrease in P* & increase in Q* S shifts to right. No longer in equilibrium: At P=$17 there’s a surplus. Price will fall. As price falls, there is a reduction in quantity supplied along new supply curve AND an increase in quantity demanded along original demand curve. Get new P* and Q* at P*=14.50 and Q*=25.5. Price 17 23 Supply Quantity Demand New Supply 14.5 25.5

Demand Generated Examples: 3 Different Markets – 3 Different Stories

Question How would an increase in family income change the demand for air travel? What would happen to the market price and quantity?

Air Travel Market Price P Q Supply of Air Travel Quantity Increased family income increases the demand for air travel – assuming it’s a normal good. Old Demand for Air Travel New Demand for Air Travel New price = P* and new quantity supplied = new quantity demanded = Q*. P* Q* Equilibrium price and quantity both rise.

Question How would an increase in the price of software change the demand for computers? What would happen to the market price and quantity?

Computer Market An increase in the price of software, a complement, decreases the demand for computers. Price P Q Supply of Computers Quantity Old Demand for Computers New Demand for Computers New price = P* and new quantity supplied = new quantity demanded = Q*. P* Q* Equilibrium price and quantity both fall.

Question How would an increase in the price of Cornell men’s hockey tickets change the demand for women’s basketball tickets? What would happen to the market price and quantity?

Cornell Women’s BB Market An increase in the price of CU men’s hockey tickets, a substitute, increases the demand for women’s basketball tickets. Price P Q Supply of Women’s Basketball Quantity Old Demand for Women’s Basketball New Demand for Women’s Basketball P* Q* New price = P* and new quantity supplied = new quantity demanded = Q*. Equilibrium price and quantity both rise.

Supply Generated Examples: 2 Different Markets – 2 Different Stories

Question How would heavy rains in the Gironde valley in September change the supply of fine red wine? What would happen to the market price and quantity?

Red Wine Market Bad weather ruins grapes and leads to a decreased supply that intersects the original demand curve to the left of the original equilibrium. Price P Q Old Supply of Red Wine Quantity Demand for Red Wine New Supply of Red Wine New price = P* and new quantity supplied = quantity demanded = Q*. P* Q* Equilibrium price rises and equilibrium quantity falls.

Question How would a decrease in the price of wood pulp change the supply of paper? What would happen to the market price and quantity?

Paper Market The decreased price of wood pulp, an input price, increases the supply of paper. Price P Q Old Supply of Paper Quantity Demand for Paper New Supply of Paper New price = P* and new quantity supplied = quantity demanded = Q*. P* Q* Equilibrium price falls and equilibrium quantity rises.

Review of Results Increased demand: equilibrium price and quantity both increase. Decreased demand: equilibrium price and quantity both decrease. Increased supply: equilibrium price decreases while quantity increases. Decreased supply: equilibrium price increases while quantity decreases.

Other Applications... Many such application exist. Could go on and on and on..... How about this: Suppose more than one thing happens at the same time???? Last case... The Market: Automobile Gasoline Market in U.S. = gas Regular Grade The first two weeks of September The Events: Heavy Labor Day weekend and back to college travel expected AND AT THE SAME TIME Some Persian Gulf event increases crude oil prices (crude oil is an input in making gas) The Consequences Labor Day & back to school travel plans  increase in the demand for gas higher crude oil prices  decrease in the supply of gas Comparative Statics Result? What’s your prediction on what happens to P* and Q*?

Answer! Predict that equilibrium gas prices go up for sure! Prediction on equilibrium quantity depends on what is assumed about the relative magnitudes of the shifts. IF demand shifts more than supply Q* will also increase IF supply shifts more than demand Q* will decrease Important to know what you know and know what you DON’T KNOW. Draw the pictures for yourself and check it out.