TaxSubsidyGeneral EquilibriumExchange Economy4 buyer’s price3.5 3 2.5 2 1.5 1 0.5 QQ10 0 4.5 5 D A B C D S’ P0 PD PS S P 0 1 2 3 4 5 6 7 8 9 10 Q Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 1 Tax 14.01 Principles of Microeconomics, Fall 2007 Chia-Hui Chen October 26, 2007 Lecture 18 Tax, Subsidy, and General Equilibrium Outline 1. Chap 9: Tax 2. Chap 9: Subsidy 3. Chap 16: General Equilibrium 4. Chap 16: Exchange Economy 1 Tax Government impo ses a $1 tax on every unit sold (see Figure 1), as discussed in Lecture 17. The buyer’s price is shown on the y-axis. The consumer surplus Figure 1: Tax . and producer surplus both decrease: ΔCS = −(A + B), ΔP S = −(C + D). Government revenue ΔG = A + C.Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2 2 Subsidy P So the deadweight loss is DW L = B + D. The burden o f a tax is shared by consumers and producers; the relative amount borne by consumers and producers depends on re lative elasticities of demand and supply. • If the demand is inelastic (see Figure 2), 10 9 8 7 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 10 S D A B C DPS P0 PD Q Figure 2: Tax Burden on Buyers, Relative Inelastic Demand Curve. ΔCS = −(A + B), ΔP S = −(C + D), buyers bear most of the burden of the tax. • If the supply is inelastic (see Figure 3), ΔCS = −(A + B), ΔP S = −(C + D), producers bear mos t of the burden of the tax. Pass-through fraction is the percentage of a tax borne by consumers. It tells the fraction of tax ”passed through” to consumers through higher price. If ED = 0, say the demand is p e rfectly inelas tic (see Figur e 4), buyers bear all of the tax burden: ES = 1. ES − ED2 Subsidy 30 2 4 6 8 10012345678910QPSDABCDPSP0PDFigure 3: Tax Burden on Producers, Relative Inelastic Supply Curve.Figure 4: Tax Burden on Buyers, Perfectly Inelastic Demand Curve.Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MITOpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD MonthYYYY].P 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 Q Q100 DCPA E B PS 0 PB S D 0 1 2 3 4 5 6 7 8 9 10 Q Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 4 2 Subsidy Figure 5: Subsidy. 2 Subsidy Government subsidizes $1 fo r each unit sold (see Figure 5). In this case, sellers’ price is higher than buyers’ price: PB = PS + 1. The consumer surplus increases by ΔCS = A + B; and the producer surplus increases by ΔP S = C + D. Government expenditure equals the whole area between PB and PS under the quantity Q1 ΔG = −(A + B + C + D + E). The deadweight loss is DW L = E. Likewise we can discus s the benefit of subsidy: • if ED is small, namely, the demand is mo re inelastic, the benefit of subsidy ES goes mostly to buyers; • if ED is large, namely, the supply is more inelastic, the benefit of subsidy ES goes mostly to sellers.Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 5 3 General Equili brium 3 General Equilibrium Partial equilibrium . Ignores effects form other markets. General equilibrium. Simultaneous determination of the prices a nd quanti-ties in all relevant markets, taking into account feedback effects. Feedback effect. The price or quantity adjustment in one market caused by price and q uantity adjustments in related markets. Example (DVD and Movie Tickets Markets). The price of a DVD is $3, and the price of a movie ticket is $6 at equilibrium. Now tax $1 on the movie ticket (see Figure 6). The specific process of price change is listed as follows: MOVIE TICKET : ′ SM → SM , Price change:6 → 6.35 ; DVD : The price change of movie tickets shifts the demand curve of DVD. DV → DV ′ , Price change:3 → 3.5; MOVIE TICKET : The price change of DVD shifts the demand curve of movie tickets. → D ′ DMM , Price change:6.35 → 6.75; and so on. The final equilibrium prices are P (M OV IET ICKET ) = 6.85; P (DV D) = 3.58. If we ignore the feedback effects, we might underestimate the price change bought by the tax.6 10 9 S * M 8 SM 7 6 5 4 DM 3 2 1 0 0 2 4 6 8 10 Q P 10 9 8 7 SV 6 5P 4 3 DV * 2 0 1 QV QV * DV 0 1 2 3 4 5 6 7 8 9 10 Q Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 3 General Equili brium (a) Price Change of Movie Ticket. (b) Price Change of DVD. Figure 6: General Equilibrium of DVD and Movie Ticket Markets.6 OB 5 4 3 2 1 A(7F,1C)=B(3F,5C) OA 0 0 1 2 3 4 5 6 7 8 9 10 Food Clothing Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 7 4 Exchange Economy 4 Exchange Economy Assume that: • there are two consumers A and B; • there are two goods, food and clothing; • the quantities of food and clothing are 10 and 6, and A has 7 food and 1 clothing, while B has 3 food and 5 clothing; • they know each others’ preferences; • transaction cost is zero. The edgeworth box is shown in Figure 7. Figure 7: Edgeworth