Supply and Demand

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 (QD)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 (Qd) • Factors affecting demand (population growth, tastes, income, prices of other goods, government regulations.

4. a. Demand Curve: Movement along D b. Shift of Demand Curve: other factors P P 7.5 D’ D Qd Qd 15 15

5. Make sure to know the following:1. substitutes and complements2. inferior and Normal goods2. 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. • Qd=D(P, other factors) • or: Qxd = 5 - 2Px +4Py -0.25Pz +0.0003M • where: Qxd quantity demand of X per unit of time,Px is the price of X, Py is price of y, Pz is the price of z, and M is income.

7. according to this D function: • Qxd = 5 - 2Px +4Py -0.25Pz +0.0003M • if Py =$0.5 , Pz =$4, and M=$30,000, then: • demand for x becomes: Qxd =15 - 2Px • if corn is free (Px=0), then then Qxd =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 QDX = 9 while it is 11 when Py = $1.

9. Ex. Suppose that Qxd = 5 - 2Px +4Py -0.25Pz +0.0003M • Px = $0.5, Py=$4, and M=$30,000. At what price of good X that demand will be 8? • Ans.: Qxd = 15-2Px, or 15-2Px=8 • therefore Px=$3.5 • if Py is $1now, then Px=$4.5 so QDX=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. a. Supply Curve: Movement along S b. Shift of Supply Curve: other factors P P S S S’ Qs Qs

12. if P=3, then Qs=9 • if P=2, the Qs=4 • positive relationship between P and Qs • 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 • Qxs = S(P, other factors), • Qxs = 9 + 5Px - 2PF -0.2Pz - 1.25Ps

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

15. Equilibrium in the Market S 3 D 9

16. Excess S S 3 Excess D D 9

17. ex.: Qd=15-2P and Qs=5P-6, what is the equilibrium price? • Qs=Qd • P=3 and QE=9 • Assignment III: in-text exercise 2.2

18. Changesinmarketequilibrium • if Pf fall from $2.5 to $2, and Pz 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. P S S’ A B 3 D Q 9 12.5

20. As a result of excess S, P falls P S S’ A B 3 D Q 9 12.5

21. P S S’ A B B 3 2.5 C D Q 10 9 12.5

22. When prices change, the supply function becomes: • QxS =5Px - 2.5, using the same D function: • 15 - 2Px = 5Px -2.5 • Px=2.5 and QxD=15- 2(2.5)=10 and QxS=5(2.5) - 2.5 =10 • SR and LR changes in market equilibrium. • Assignment 4: Graph D vs. S changes:Change D while S is fixedChange S while D is fixedChange 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. • εxy=%∆X / %∆Y • Values ε that are further than 1 means greater responsiveness.

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

25. elasticity of linear d • this is a straight line D curve, the demand function takes the form: Qd = A - BP , • Calculating elasticity:εd = (∆Qd/∆P)(P/Q), • (∆Qd/∆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:(∆Qd/∆P) = -B. • therefore, elasticity of demand for a straight line is:εd =-B (P/Q).

27. P ε along linear D curve Qdx=15-2P ε = -2(6/3)= -4 6 ε = -2(3.75/7.5)= -1 3.75 ε = -2(1.75/12)= -1/4 1.5 Q 7.5 3 12

28. P ε along linear D curve Qdx=15-2P ε = -2(6/3)= -4 6 ε = -2(3.75/7.5)= -1 3.75 ε = -2(1.75/12)= -1/4 1.5 Q 7.5 3 12 D is more elastic at higher P than than at lower P

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

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

31. Vertical D: Perfectly inelastic Horizontal D: Perfectly Elastic S S D S’ S’ P D P P’ Q Q’ Q Slope = 0 εd =∞ Slope = ∞ εd =0

32. Using absolute value: • D is elastic if |εd| > 1 • D is inelastic if |εd| < 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. slope =∆P’/∆Q’ C P’ slope=∆P”/∆Q” P” B A P slope=∆P/∆Q Q’ Q Q”

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:Qd=A(P-B), WHERE A>0, B>0. • εd = -B

36. C-E D: D function: Qd=100/P slope =∆P’/∆Q’=1 2 1 slope=∆P/∆Q=1 50 100

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 εd)

38. price elasticity of s • εd = (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