Supply Demand De nitions Q P Q P Taxation P price of good per unit Q quantity demanded able and willing vector of shift variables Ex income price of other goods taste and preferences taxes subsidies p price of good per unit Q quantity supplied vector of shift variables on the supply side Ex technology price of inputs Excise tax legally imposed on sellers Sales tax tax legally imposed on buyers Legal incidence of taxation who is legally obligated to pay the tax Economic incidence of taxation who actually bears the burden of the tax Example This is the same regardless of where the tax is directly applied Assume Q 200 P Q 10 2P Let T tax rate per unit Case 1 Excise Tax of 15 per unit Before tax Q Q 10 2P 200 P P 70 Put this back into any equation Q 200 70 130 After tax q 130 Ps PD T PD gross price price paid by buyers inclusive of tax PS net rice price received by sellers net of tax Always solve for the side you re doing the tax on Q 10 2P Q 200 P Step 1 PS PD T PD 15 Step 2 Rewrite S D functions Step 3 Substitute result from step 1 into Q in step 2 to get new supply function Q 10 2 P 15 Q 10 2P 30 40 2P Vertical gap T what is the intuition behind this result Sellers will sell 130 units if they receive at least 70 before tax 85 15 given to govt 70 70 0 70 Step 4 Set new S curve equal to D curve and solve for P 40 2PD 200 PD PD 80 Step 5 Using PS PD 15 solve for PS Note PD is the intersection of S2 D1 PS 80 15 65 where does this show up on the graph Case 2 Sales tax of 15 unit is imposed on buyers PS sticker price Step 1 PD PS T PS 15 Step 2 Q 200 P Q 10 2 P Step 3 Substitute step 1 into Q Q 200 PS 15 Q 200 PS 15 Q 185 PS the new demand function Intuition some consumer is willing to pay up to and no more than 70 for the 130th unit w o tax 55 15 70 70 0 70 Step 4 set new D function equal to S function solve for equilibrium P where D2 S1 intersect 10 2PS 185 PS PS 65 PS is always the same regardless of where tax is Step 5 Solve for PD using PD PD 15 PD PS 15 65 15 80 Under what circumstances will buyers or sellers bear the entire burden of tax meaning dPD T eS elasticity of supply change in Q dQ x P change in P dP Q eD elasticity of demand change in Q dQ x P change in P dP Q These are measures of buyer seller sensitivity to price change dPD eS dT eS eD e 2 70 130 14 13 e 1 70 130 7 13 dP 14 13 14 x 13 2 3 dT 14 13 7 13 13 21 P 70 P 80 If eS eD Example dQ 1 dP 1 2 dP dT 1 2 dP dT If supply is perfectly elastic eS P 10 Q P 10 Q 0 1 Buyers pay entire tax burden when S is perfectly elastic e 0 Intuition Sellers have excellent alternative uses of resources e g they can sell to someone else just as easily OR 2 Buyers pay entire tax burden when D is perfectly inelastic e 1 Intuition Buyers have poor alternatives Per Unit Subsidy Let Z subsidy rate PS PD Z The bene ts of a subsidy are equally split just like with taxes Example L 100 W L 200 W W effective wage received by suppliers of labor workers W effective wage received by demanders employers Wage W Wm Value placed on fringe bene t V W Wm Cost of fringe bene t C Wm money wage Before fringe bene ts 100 Wm 200 Wm Wm 150 After FB Assume C 30 V 10 L 90 W L 100 W 100 W 30 L 200 W 200 W 30 L 170 W 120 W 140 Step 1 new L and L Step 2 set new L and L equal to each other 170 W 90 W W 130 Employee W 130 10 140 180 Employer W 130 30 160 150 Price Changes When V C wage will go down both are worse off When V C wage will go up both are better off When V C there will be no difference Ex Q 100 P Q 20 P Price ceiling a legal maximum price Binding PC P P Effects Sellers are less willing to sell Shortage When Q Q Increase in the use of non money price competition Waiting in line queueing Political in uence Violence Binding PC increase in non money competition increase in non monetary cost of acquiring a good time increase PTotal Pmoney non monetary cost Claim PC Pm decrease but increase in NMC more than Pm goes down Solve Ceiling is imposed P goes down 60 50 To nd P Q 20 50 30 What is Q at D At what P will Q also be to 30 Why Q 100 P P 100 30 70 Scarcity fewer units Now assume there are ration tickets entitles buyer to one unit at p 50 Total issued by government equals whatever Q is at p 30 in this case Willing to pay 100 for 1st unit will to pay 50 for ticket and then 50 for good distance between D and PC at Q No difference than plain price ceiling PT P PRT 70 DRT SRT PRT 20 QRT 50 PRT derived from the graph QRT 30 Consumer Producer Surplus De nitions Refers to a maximum amount someone is willing to pay for a certain of units Area under the curve Total Value total bene t total willingness to pay Marginal value marginal bene ts marginal willingness to pay The maximum amount one is willing to pay for one more unit MV change in TV dTV the derivative of TV change in Q dQ Assumption diminishing MV MV falls as quantity rises Total value goes up at a slower rate than MV Always downward sloping but not always linear Example Q TV MV 0 0 1 10 10 2 19 9 3 27 8 4 34 7 Price re ects MV Will keep buying until MV P Will buy good up to Q which P MV Suppose p 8 consumers are price takers MV and D are the same Area under D curve or MV curve TV P a bQ inverse D curve Same as MV a bQ TV MV Q dQ a bQ TV aQ 1 2 bQ Surplus Consumer Surplus CS Measures net gains from trade to consumers TV is willing to pay PQ actual expenditures on good De nition CS TV PQ Steps 1 For the given P nd Q 2 Label areas 3 TV A B PQ B CS …