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Chapter 2

Chapter 2. Shifts in Supply and Demand Influence Price. Economists Love Competitive Markets Demand Coal. Qd = f (Pc-, Psb+, Pcm-, Y, T+/-, Pol+/-, #buy+) Ceteris Paribus hold constant everything but P & Q . P. D. Q. World Coal Use by Sector.

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Chapter 2

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  1. Chapter 2

  2. Shifts in Supply and Demand Influence Price

  3. Economists Love Competitive Markets Demand Coal Qd = f (Pc-, Psb+, Pcm-, Y, T+/-, Pol+/-, #buy+) Ceteris Paribus hold constant everything but P & Q P D Q

  4. World Coal Use by Sector

  5. Economists Love Competitive Markets Demand Coal Qd = f (Pc, Psb, Pcm, Y, Tech, Policy, #buy) Ceteris Paribus hold constant everything but P & Q +/- +/- - +/- - + + P D Q

  6. Supply Suppliers Qs = f(Pc, Pf, Psm, Pby,T, Pcy, #sel) + - - + + +/- + P S Q

  7. Sum Up Where are coal reserves Conversions E1 in unit 1, (u1) or E2 in unit 2 (u2) conversion is units of 1 per unit of 2 (u1/u2) Energy Content

  8. Sum Up Qualitative create D and S hold all variables but P&Q constant started to look behind supply P S D Q

  9. Behind Supply • for firm to maximize profits •  = P*Q – TC = P*Q – FC – VC(Q) • competitive firms take price as given • f.o.c. • /Q = P - TC/Q = P - VC(Q)/ Q = 0 • MC ↑ • 2.o.c • 2/Q2 = - TC2/Q2 = - MC(Q)/ Q<0 • MC(Q)/ Q>0 • operate where price equals marginal variable cost • short run supply equals marginal cost curve

  10. Typical Competitive Firm Cost Short Run Supply S P P P MC2 MC1 Psr AVC1 AVC2 D Q Q1 Q2 Q Q Q1 +Q2 Si = MCi above AVC Market is horizontal sum

  11. Where They Cross Determines P & QSupply = Demand P S Pe Model Building Blocks D Qe Q

  12. Out of Equilibrium P S Price too high PH PL Price too low D Q Qs Qd

  13. Shift in DChange in Qs – movement along S P S Pe' Pe Pe" D"(decrease)← D D' (increase)→ Q Qe" Qe Qe'

  14. Shift in S Movements along the D curve S"(decrease)← P S S' (increase)→ Pe" Pe Pe' D Qe' Qe" Qe Q

  15. More than one ChangeCoal Mine Productivity Per Miner Increases S P →S' Pe Pe' D Q PQ Qe Qe'

  16. 1.Chinese Coal Mine Productivity 2. Plus Cheaper Sequestration P ↓ Q ↑ P ↑ Q↑ S S P S' Pe' Pe Pe Pe' D D →D' Q Q Qe Qe' Qe Qe'

  17. Supply and DemandBuilding Blocks-Two markets Natural Gas Coal if all market - general equilibrium

  18. Two Markets • Qdo = a + bPo +cPg + dY • Qso = e + fPo + gPG + hCost • Cost Exogenous • Y Exogenous • Qdg = i + jPo + kPg + lY • Qsg = m + nPo + oPG + pCost • Qdo = Qso • Qdg = Qsg • 6 endogenous variables, 6 equations

  19. Supply and Demand Building Blocks Dynamic -Two time periods Time 1 Time 2 n time periods

  20. Trade Models- Two Areas in World S2 S1 P S1 S1+S2 D1+D2 D1 D2 D Qw Q1 Q2

  21. Market Power Seller P S D Q

  22. Market Power Buyer P S D Q

  23. Quantitative ModelsChapter 2&3 Buyers Qd = f(Pc, Psb, Pcm, T, Pot, Pcy, #buy) Suppliers Qs = f(Pc, Pf, Psm, Pby,T, Pcy, #sel) Functions – with numbers often start with qualitative model to get intuition

  24. Quantitative S-D Example Qd =99 - 2Pc + 1Psb - 2Pcm + 0.1Y Qs =30 + 1Pc – 1Pk - 0.2Pl - 0.4Pnr Pc = price of coal Psb = price of substitute to coal (natural gas) =1 Pcm = a complement to coal =10 Y = income = 200 Pk = price of capital = 20 Pl = price of labor = 40 Pnr = price of other natural resources used in production of coal = 10

  25. Qd = 99 - 2Pcd + Psb - 2Pcm + 0.1Y Qs =30 + 1Pcs – 1Pk - 0.2Pl - 0.4Pnr Qd = 99 - 2Pcd + 1 - 2*10+0.1*200 = 100 -2Pcd Qs = 30 + Pcs – 1*31 - 0.2*30 - 0.4*10 = -11 + 1Pcs

  26. Model02.xls: Worksheet S&D

  27. Inverse Demand Qd = = 100 -2Pcd Qs = -11 + 1Pcs Sometimes want price as function of quantity invert Qd = 100 -2Pcd solve demand for Pcd 2Pcd = 100 – Qd → Pcd = 50 – (1/2)Qd invert Qs = -11 + 1Pcs solve supply for Pcs Pcs = 11 + Qs

  28. Graph and Forecast Pd = 50 – (1/2)Qd Ps = 11 + Qs Forecast P & Q Pd = Ps 50 – (1/2)Q = 11 + Q 50-11 = Q+(1/2)Q 39 = (3/2)Q Q = (2/3)39 = 26 Pd = 50– (1/2)26 = 37 Ps = 11 + 26 = 37 P 60 S 40 P = 37 20 D 50 100 Q = 26 Q

  29. Is Equilibrium Stable? Price above Equilibrium Pd = 50 – (1/2)Qd Qd=100 – 2Pd Ps = 11 + Qs Qs = -11 + Ps What if P = 40 Qd=100 – 2*40 = 20 Qs = -11 + 40 = 29 Excess quantity supplied P↓ P 60 S P = 40 20 D Qd = 20 Qs = 29 100 Q

  30. Quantitative • Need numbers for ceterus paribus values • Substitute in to Qd and Qs • Qd = f(Pd) is demand • Qs = f(Ps) is supply • Solve for P and Q • Sometimes inverse is easier or more useful • Solve for price as a function of quantity • Pd =f-1(Qd) is inverse demand • Pd =f-1(Qd) is inverse demand • We graph the inverses

  31. General Equilibrium Model (1)Think about but not to be tested • Markets for all products • all factors or production • consumers buy • m final goods: a,b,c,…. • at prices pb, pc, pd,…. • their demand for final goods: db, dc, dd,…. • consumers own and sell • n factors of production: qt, qp, qk, …. • at prices pt, pp, pk, … • their supply/of n factors: st, sp, sk,… • m + n unknown prices

  32. General Equilibrium Model (2)Think about but not to be tested • in real world things are priced in money • $/liter, etc • in simplest G.E. model no money • pick a numeraire good • its price is one • m + n - 1 unknown prices • equilibrium in household sector • stpt+ sppp+ skpk+ …. = da + dbpb+ dcpc+ …. • income = expenditure • If holds for each household, holds for market

  33. General Equilibrium Model (3)Think about but not to be tested producers buy n factors of production demand: dt, dp, dk, producers produce m end use goods s demand: st, sp, sk, m commodities and n factors there are m+n unknowns quantities m + n - 1 unknown prices total: 2m + 2n - 1 unknowns

  34. General Equilibrium Model (4)Think about but not to be tested • Consumer • Demand for goods (m-1 independent) • da= da(pt, pp, pk, …, pb, pc, pd,…) • Supply of factors (n) • st= st(pt, pp, pk, …, pb, pc, pd,…) • Producers • Demand for factors (n) • dt= dt(pt, pp, pk, …, pb, pc, pd,…) • Supply of goods m • sa= sa(pt, pp, pk, …, pb, pc, pd,…)

  35. Last Time - Sum Up Qualitative create D and S hold all variables but P&Q constant P S D Q

  36. Models for PolicyWhat if Government Sets Maximum Price of 30 Shortages Likely to be black market Could to subsidize What would subsidy cost? To get suppliers to produce 40 Need Ps=11+40 =51 Cost (51-30)(40)=840 P 60 S Ps = 51 P = 30 D Qs = 19 Qd = 40 100 Q

  37. What happens with following policies? P 60 S Pmax Pmin D 100 Q Controls Non-binding

  38. Demand Price Elasticity Q responsiveness to price P P2 P1 Dlr D1 Qlr Q Q2 Q1 may change over time

  39. Back to 1973 Oil Market S79 OPEC Supply Shocks 73&79 P S73 P79 Dlr D1 Q82 Q Q79

  40. Elasticity Definition How much quantity responds to price d = % change quantity % change in price If d = –0.5 price goes up by 100%, quantity demanded falls by % change quantity = % change in price* d = 100%*-0.5 = 50%

  41. Let’s Develop Formal Definition d = % change quantity % change in price Qd *100 d = Qd Pd *100 Pd Q2-Q1 = Q1 P2 - P1 P1

  42. Suppose We Have Price Increase P Q $2.00/g 500 106 g/d $3.00/g 400 106 g/d Qd d = Qd Pd Pd (400 106 g/d – 500 106 g/d) 500 106 g/d ($3.00 g – $2.00 g) $2.00 /g = -0.20/0.5 = -0.4 (no units)

  43. Lets Go Back to Lower Price P Q $2.00/g 500 106 g/d $3.00/g 400 106 g/d Q2 – Q1 d = Q1 P2-P1 P1 (500 – 400) 400 = (1/4) = (2– 3) -(1/3) 3 = -(1/4)(3/1) = - 3/4 = - 0.75

  44. Sum Up Computing Arc Elasticities d = % change quantity % change in price Qd d = Qd Pd Pd Q2-Q1 = (Q1+ Q2)/2 P2 - P1 (P1+ P2)/2

  45. Sum Up Elasticity = Responsiveness to Price • x = % change quantity • % change in X • Q could be quantity demanded • Q could be quantity supplied • X could be Price • X could be income • X could be the price of a substitute • (cross price elasticity) • X could be any other variable that influences Q • Q likely more responsive in long run than short run

  46. More Convenient for Elasticity Qs and Qd responsiveness to other variables x = % change quantity % change in Q x = Q = Q X XX Q X Take limit as X→0 x = Q X X Q

  47. Where do they come from? Estimate whole function market data Qd = f(Pd, Y, Ps, Pc, . . ., etc. ) εp = Q P P Q Function Forms linear: Q = a – bP εp= -b(P/Q)

  48. Linear Function P |Elastic| > 1 a/b D |Unit Elastic| = 1 =- =-1 Q = a - bP p = -b(P/Q) Graph: P = 0 then Q = a -b*0 = a  = -b(0/a) = 0 Q = 0 = a-bP then P = a/b  = -b(a/b)/0 = - P = (a/b)/2 then Q = a - b(a/b)/2) = a - a/2 = a/2  = -b(a/b)/2/(a/2) = -1 a/2b |Inelastic| (1,0) =0 a Q a/2

  49. Demand Price Elasticities and RevenuesHow Does Price Change Revenue TR = PQ = PQ(P) TR/P = Q + (Q/P)*P =Q(1+ (Q/P)*(P/Q)) Sign of TR/P = sign (1+εp) TR/P < 0 when (1+εp)<0 subtract -1 from both sides εp<-1 = Q(1+εp) (elastic) Raising price lowers revenue Lowering price raises revenue

  50. Demand Price Elasticities and Revenues TR/P < 0 when εp<-1 elastic P and TR opposite direction P TR P TR TR/P = 0 when (1+εp)=0 εp= -1 unitary elasticity TR/P > 0 when (1+εp)>0 0> εp> -1 P TR? P TR?

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