Chapter 16: Equilibrium

Transcription

1 Econ Microeconomic Analysis Chapter : Equilibrium Instructor: Hiroki Watanabe Spring Watanabe Econ Equilibrium / Review Market Clearance Tax Who Pays the Tax? Tax Incidence First Theorem Summary Watanabe Econ Equilibrium / Definition Definition. (Equilibrium) A market is in equilibrium when total quantity demanded by buyers equals total quantity supplied by sellers. Watanabe Econ Equilibrium /

2 Definition Watanabe Econ Equilibrium / Definition Agent Individual Aggregate Buyer A Seller Watanabe Econ Equilibrium / Definition A brief review on where D(p) and S(p) come from. Watanabe Econ Equilibrium /

3 Ch Demand Quick Review Example. (Marshallian Demand with Cobb-Douglas Utility) Liz s solution to utility maximization problem max C, T ( C, T ) = C T subject to = p C C + T constitutes a Marshallian demand φ C (p C ) = p C, via tangency condition MWTP( C, T ) = p C. Watanabe Econ Equilibrium / Ch Demand Quick Review Tea x T (cups) Indifference Curves Budget Line (p C =) Cheesecakes x C (slices) Watanabe Econ Equilibrium / Budget Line (p C =) Ch Demand Quick Review Marginal Willingness to Pay, Price p ($/slice) C Demand Curve Cheesecakes x C (slices) Watanabe Econ Equilibrium /

4 Ch Supply Quick Review Example. (Supply with Decreasing Returns to Scale) Jack s solution to profit maximization problem max y π(y) = py y (with MC(y) = y) constitutes supply via marginal condition s(p) = p, MC(y) = p. Watanabe Econ Equilibrium / Ch Supply Quick Review TC(y) TR(y) w/ p= TR(y) w/ p= Total Cost, Total Revenue ($) Cheesecake y (slices) Watanabe Econ Equilibrium / Ch Supply Quick Review Individual Supply s(p) Marginal Cost, Price p ($/slice) Cheesecake y (slices) Watanabe Econ Equilibrium /

5 Patch Them Together Individual Supply s(p) Individual Demand φ c (p) MC(y), MWTP(x), Price p ($/slice) Cheesecake y or x C (slices) Watanabe Econ Equilibrium / Patch Them Together Fact. (Price Equals...) If Liz and Jack is maximizing their objective function ( ( ) or π(y)), Agent Price is = to Because of Buyer MWTP( ) tangency condition Seller MC(y ) marginal condition Assuming p T = for Liz and p > p MES for Jack. Watanabe Econ Equilibrium / Patch Them Together Marginal Willingness to Pay MWTP(x) Market Price p MWTP, Price (cups or $/slice) Cheesecake y (slices) Watanabe Econ Equilibrium /

6 Patch Them Together Marginal Cost MC(y) Market Price p Marginal Cost, Price ($) Cheesecake y (slices) Watanabe Econ Equilibrium / Definition. (Equilibrium Price) Equilibrium price p satisfies Remark S(p ) = D(p ). p(> p ) leaves excess supply because S(p) > D(p). Price drops till the gap closes. p(< p ) leaves excess demand because S(p) < D(p). Price increases till the gap closes. Watanabe Econ Equilibrium / Watanabe Econ Equilibrium /

7 Watanabe Econ Equilibrium / Watanabe Econ Equilibrium / Fact. (Three Conditions of Equilibrium) If the market is in equilibrium, three conditions are met: p b = MWTP( ). p s = MC(y ). p b = p s = p. Watanabe Econ Equilibrium /

8 Tax and Equilibrium A quantity tax is a tax of t paid on each unit traded. Definition. (Tax on Different Agents) Sales tax is levied on buyers. Excise tax is levied on sellers. Watanabe Econ Equilibrium / Tax and Equilibrium Question. (Tax and Equilibrium) How are prices affected? How is the quantity traded affected? Who pays the tax? Watanabe Econ Equilibrium / Tax and Equilibrium Answer. (Tax and Equilibrium) Splits in two. Gets smaller most of the times. It doesn t matter who pays the tax. What matters is tax incidence. Watanabe Econ Equilibrium /

9 Clearing Market with Tax A tax rate t makes the price paid by buyers including tax, p b (whatever goes out of Liz s pocket), higher by t from the price received by sellers after paying tax, p s (whatever Jack takes in his pocket). p b p s = t. Even with a tax the market must clear. Quantity demanded by buyers at price p b must equal quantity supplied by sellers at price p s : D(p b ) = S(p s ). Watanabe Econ Equilibrium / Clearing Market with Tax Market clearing conditions: p b p s = t D(p b ) = S(p s ). Note that these two conditions apply no matter if the tax is levied on sellers or on buyers. A sales tax rate t has the same effect as an excise tax rate t. Watanabe Econ Equilibrium / Excise Tax Proposition. (Excise Tax Raises Marginal Cost) Excise tax t inflates marginal cost MC(y) by t dollars. Watanabe Econ Equilibrium /

10 Excise Tax Jack has to update his PMP Example. as follows: max y π(y) = p b y (TC(y) + ty). Marginal condition updates as follows: p b = MC(y) + t(= p s + t). Watanabe Econ Equilibrium / Excise Tax Marginal Cost, Price p ($/slice) Individual Supply s(p) Individual Supply s(p) with t= Cheesecake y (slices) Watanabe Econ Equilibrium / Sales Tax Proposition. (Sales Tax Reduces Marginal Willingness to Pay) Sales tax t drops marginal willingness to pay MWTP( ) by t dollars. Watanabe Econ Equilibrium /

11 Sales Tax Liz has to update her UMP Example. as follows: max C, T ( ) = C T subject to m = (p C +t) C + T. Tangency condition updates as follows: MWPT( ) = (p C +t) p s = MWTP( ) t(= p b t) Watanabe Econ Equilibrium / Sales Tax p= MWTP(x * ) p= MWTP(x * ) Marginal Willingness to Pay, Price p ($/slice) C Cheesecakes x C (slices) Watanabe Econ Equilibrium / Post-Tax Equilibrium Conclude: Excise tax lifts supply curve by t. Sales tax drops demand curve by t. Getting back to the tax? Question., does it matter who pays Watanabe Econ Equilibrium /

12 Post-Tax Equilibrium Aggregate Supply with Tax Watanabe Econ Equilibrium / Post-Tax Equilibrium Price consumers face is p b =. Price firms face is p s =. Jack receives $ per slice, out of which he pays $ as excise tax. Transaction volume is q =. Watanabe Econ Equilibrium / Post-Tax Equilibrium Aggregate Demand with Tax Watanabe Econ Equilibrium /

13 Post-Tax Equilibrium Price consumers face is p b =. Liz pays $ a slice and then pays $ as sales tax. Price firms face is p s =. Transaction volume is q = as before. Watanabe Econ Equilibrium / Post-Tax Equilibrium It doesn t matter who pays the tax. Watanabe Econ Equilibrium / Post-Tax Equilibrium Aggregate Demand with Tax Aggregate Supply with Tax Watanabe Econ Equilibrium /

14 Post-Tax Equilibrium Excise or sales, Jack gets the same reduced profit and Liz achieves the same reduced utility level. What matters is: how reduced are they? Watanabe Econ Equilibrium / Tax Incidence When the excise tax is imposed, it s just the sellers who take on the tax burden? Technically yes, but the buyers also have to face a higher price than before and share the tax burden as well. Watanabe Econ Equilibrium / Tax Incidence Definition. (Tax Incidence) Tax Incidence measures how tax burden is divided between buyers and sellers, defined by tax burden on buyers tax burden on sellers = (p b p )q t (p p s )q t. Watanabe Econ Equilibrium /

15 Tax Incidence Aggregate Supply with Tax Watanabe Econ Equilibrium / Tax Incidence & Elasticity In the previous example, the tax burden was equally split between buyers and sellers. Not always. Proposition. (Tax Incidence & Elasticity) Inelastic party takes on larger tax burden than elastic party. Watanabe Econ Equilibrium / Tax Incidence & Elasticity Aggregate Supply with Tax +/ Watanabe Econ Equilibrium /

16 First Fundamental Theorem of Welfare Economics Proposition. (First Fundamental Theorem of Welfare Economics) Provided that preferences are well-behaved and there are perfectly competitive complete markets, then equilibrium allocation is efficient. Watanabe Econ Equilibrium / First Fundamental Theorem of Welfare Economics Fact. embodies the first fundamental theorem. What if MC(q ) MWTP(q )? Watanabe Econ Equilibrium / First Fundamental Theorem of Welfare Economics How do we measure the efficiency of the economy as a whole? Definition. (Total Surplus) Total surplus measures the overall performance of the economy. It is defined by TS := CS + PS(+Tax Revenue). Watanabe Econ Equilibrium /

17 First Fundamental Theorem of Welfare Economics Note that the equilibrium achieves the maximum total surplus possible. Watanabe Econ Equilibrium / First Fundamental Theorem of Welfare Economics Watanabe Econ Equilibrium / Tax Creates Deadweight Loss Tax creates deadweight loss due to deviation from the equilibrium. unless demand or supply is perfectly inelastic. Watanabe Econ Equilibrium /

18 Tax Creates Deadweight Loss Aggregate Supply with Tax Watanabe Econ Equilibrium / Tax Creates Deadweight Loss Subsidy is a negative tax. Tax creates deadweight loss. Does that mean subsidy will create a negative deadweight loss, i.e., makes the economy better than the equilibrium allocation? Watanabe Econ Equilibrium / Tax Creates Deadweight Loss Aggregate Supply with Subsidy Watanabe Econ Equilibrium /

19 Market equilibrium realizes maximum total surplus. Tax incidence and elasticity. Watanabe Econ Equilibrium / consumer surplus, CS, see consumer surplus deadweight loss, efficiency, elasticity, equilibrium,,, excise tax,,, first fundamental theorem of welfare economics, marginal condition,,, marginal cost,, marginal willingness to pay,, marshalian demand, Marshallian demand, MC(y), see marginal cost MWTP( ), see marginal willingness to pay p b, see price paid by buyers φ, see Marshallian demand price paid by buyers, price received by sellers, profit maximization problem,, PS, see producer surplus p s, see price recieved by sellers q, see transaction volume sales tax,,, subsidy, t, see tax rate tangency condition,,, tax incidence, tax rate, tax revenue, total surplus, transaction volume, TS, see total surplus utility maximization problem,,