1 Supply and Demand Chapter 2

2 introduction why did the price of gasoline rise (around %16.33) after hurricane Katrina (new orleans: August 2005)and hurricane rita (Texas: September 2005), although price of crude oil did not change significantly? By early October 2005, %30 of U.S. refining capacity was shut down by the 2 storms. by how much would the price (P) have fallen if 1/2 of the capacity came back? to answer such questions, we use a model of supply and demand.

3 demand a product’s demand curve (D) shows how much buyers of the product want to buy (Q D )at each possible price (P), holding all other factors that affect demand constant. Demand curve slopes downward to reflect the negative relationship between (P) and (Q d ) Factors affecting demand (population growth, tastes, income, prices of other goods, government regulations.

4 PP QdQd QdQd D D’ a. Demand Curve: Movement along D b. Shift of Demand Curve: other factors

5 Make sure to know the following: 1. substitutes and complements 2. inferior and Normal goods 2. Movements Along vs. Shifts of the demand curve. Assignment 1

6 Demand functions it shows the amount of quantity demanded for each possible combination (P) and other factors. Q d =D(P, other factors) or: Q x d = 5 - 2P x +4P y -0.25P z M where: Q x d quantity demand of X per unit of time,P x is the price of X, P y is price of y, P z is the price of z, and M is income.

7 according to this D function: Q x d = 5 - 2P x +4P y -0.25P z M if Py =$0.5, Pz =$4, and M=$30,000, then: demand for x becomes: Q x d = Px if corn is free (P x =0), then then Q x d =15 thats figure (a)

8 figure (b) shows shift in demand due to one of the factors affecting demand (not Px) if Py is $0.5 then Q D X = 9 while it is 11 when Py = $1.

9 Ex. Suppose that Q x d = 5 - 2P x +4P y -0.25P z M Px = $0.5, Py=$4, and M=$30,000. At what price of good X that demand will be 8? Ans.: Q x d = 15-2Px, or 15-2Px=8 therefore Px=$3.5 if Py is $1now, then Px=$4.5 so Q D X =8. Assignment 2: in-text exercise 2.1

10 supply this is the 2nd part of the market S curve shows how much sellers of a product want to sell at each possible price, holding fixed all other factors (determining S).

11 PP QsQs QsQs S S’ a. Supply Curve: Movement along S b. Shift of Supply Curve: other factors S

12 if P=3, then Q s =9 if P=2, the Q s =4 positive relationship between P and Q s when P is higher, producing and selling the product is more profitable. Other factors: technology, input cost, price of other outputs, taxes and subsidies

13 supply functions Q x s = S(P, other factors), Q x s = 9 + 5P x - 2P F -0.2P z Ps

14 Market Equilibrium after knowing D and S for a product, next step is to determine equilibrium P and Q. Thats when Q s =Q d The market clears at P e. Market prices tend to adjust so that Qs=Qd

S D Equilibrium in the Market

S D Excess S Excess D

17 ex.: Q d =15-2P and Q s =5P-6, what is the equilibrium price? Q s =Q d P=3 and Q E =9 Assignment III: in-text exercise 2.2

18 Changes in market equilibrium if P f fall from $2.5 to $2, and P z fall from $8 to $6, the supply curve will shift outward after the shift, the market is not in equilibrium (at p=$3). there is excess of ?

19 S 3 S’ D P Q A B

20 S 3 S’ D P Q A B As a result of excess S, P falls

21 S S’ D P Q A BB C 10

22 When prices change, the supply function becomes: Q x S =5P x - 2.5, using the same D function: P x = 5P x -2.5 Px=2.5 and Q x D =15- 2(2.5)=10 and Q x S =5(2.5) =10 SR and LR changes in market equilibrium. Assignment 4: Graph D vs. S changes: Change D while S is fixed Change S while D is fixed Change both and show the effect of relative size of change.

23 Elasticities of D and S To measure responsiveness of changes in D and S. ε xy =% ∆X / %∆Y Values ε that are further than 1 means greater responsiveness.

24 Price elasticity of D ε d = %∆Q d / %∆ P = (∆Q/Q) / (∆P/P) Factors determining ε d measuring small price changes.

25 elasticity of linear d this is a straight line D curve, the demand function takes the form: Q d = A - BP, Calculating elasticity: ε d = (∆Q d /∆P)(P/Q), (∆Q d /∆P) is the change is Qd for each $ that the P increase. for a linear D, this is just (-B).

26 to show that, using a linear D curve, for any ∆ P the change in D is: ∆ Q= -B( ∆ P), divide both sides by ∆ P: (∆Q d /∆P) = -B. therefore, elasticity of demand for a straight line is: ε d = -B (P/Q).

27 ε along linear D curve Q d x =15-2P P Q ε = -2(6/3)= -4 ε = -2(3.75/7.5)= -1 ε = -2(1.75/12)= -1/4

28 ε along linear D curve Q d x =15-2P P Q ε = -2(6/3)= -4 ε = -2(3.75/7.5)= -1 ε = -2(1.75/12)= -1/4 D is more elastic at higher P than than at lower P

29 dividing (∆Q d /∆P)(P/Q) by ∆Q d /∆Q d : ε d = 1 /(∆P/∆Q d ) * (P/Q) where (∆P/∆Q d ) is the slope if the linear D curve. Note: using our D function Q x d = 15-2P x, the slope is (- 1/B) or (-1/2).

30 P Q S S’ S D D QQ’ P’ P Horizontal D: Perfectly Elastic Vertical D: Perfectly inelastic

31 P Q S S’ S D D QQ’ P’ P Horizontal D: Perfectly Elastic Vertical D: Perfectly inelastic Slope = 0 ε d = ∞ Slope = ∞ ε d = 0

32 Using absolute value: D is elastic if |ε d | > 1 D is inelastic if |ε d | < 1

33 elasticities of non-linear d the slope of the tangent line to a curve at a point is the “slope of the curve” at that point. for a small P changes starting at price P, the ratio ( ∆ P/ ∆ Q)=the slope of the demand curve at point A.

34 AB C slope= ∆ P/ ∆ Q slope = ∆ P’/ ∆ Q’ slope= ∆ P”/ ∆ Q” Q’ Q” Q P’ P” P

35 constant elasticity D curve is knows as isoelastic D curve. is has the same elasticity at every price. D function takes the general form: Q d =A(P -B ), WHERE A>0, B>0. ε d = -B

36 slope= ∆ P/ ∆ Q= 1 slope = ∆ P’/ ∆ Q’= C-E D: D function: Q d = 1 00/P

37 total Expenditure and elasticity of D elasticity of D shows how TE changes when P increases and we move along the D curve. TE=PQ TE will increase for a small P increase when D is inelastic and decrease when D is elastic. Since Total revenue (TR) always =TE, the same is true for sellers’ revenue. (TR and ε d )

38 price elasticity of s ε d = (1/( ∆ P/ ∆ Q))*(P/Q), where ( ∆ P/ ∆ Q) is the slope of S curve. Perfectly elastic S. Perfectly inelastic supply.

39 other elasticities income elasticity of demand cross-price elasticity of demand