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Chapter One The Market

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The Theory of Economics does not furnish a body of settled conclusions immediately applicable to policy. It is a method rather than a doctrine, an apparatus of the mind, a technique of thinking which helps its possessor to draw correct conclusions --- John Maynard Keynes

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Economic Modeling u What causes what in economic systems? u At what level of detail shall we model an economic phenomenon? u Which variables are determined outside the model (exogenous) and which are to be determined by the model (endogenous)?

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Modeling the Apartment Market u How are apartment rents determined? u Suppose –apartments are close or distant, but otherwise identical –distant apartments rents are exogenous and known –many potential renters and landlords

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Modeling the Apartment Market u Who will rent close apartments? u At what price? u Will the allocation of apartments be desirable in any sense? u How can we construct an insightful model to answer these questions?

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Economic Modeling Assumptions u Two basic postulates: –Rational Choice: Each person tries to choose the best alternative available to him or her. –Equilibrium: Market price adjusts until quantity demanded equals quantity supplied.

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Modeling Apartment Demand u Demand: Suppose the most any one person is willing to pay to rent a close apartment is $500/month. Then p = $500 Q D = 1. u Suppose the price has to drop to $490 before a 2nd person would rent. Thenp = $490 Q D = 2.

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Modeling Apartment Demand u The lower is the rental rate p, the larger is the quantity of close apartments demanded p Q D . u The quantity demanded vs. price graph is the market demand curve for close apartments.

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Market Demand Curve for Apartments p QDQD

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Modeling Apartment Supply u Supply: It takes time to build more close apartments so in this short-run the quantity available is fixed (at say 100).

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Market Supply Curve for Apartments p QSQS 100

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Competitive Market Equilibrium u “low” rental price quantity demanded of close apartments exceeds quantity available price will rise. u “high” rental price quantity demanded less than quantity available price will fall.

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Competitive Market Equilibrium u Quantity demanded = quantity available price will neither rise nor fall u so the market is at a competitive equilibrium.

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Competitive Market Equilibrium p Q D,Q S 100

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Competitive Market Equilibrium p Q D,Q S pepe 100

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Competitive Market Equilibrium p Q D,Q S pepe 100 People willing to pay p e for close apartments get close apartments.

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Competitive Market Equilibrium p Q D,Q S pepe 100 People willing to pay p e for close apartments get close apartments. People not willing to pay p e for close apartments get distant apartments.

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Competitive Market Equilibrium u Q: Who rents the close apartments? u A: Those most willing to pay. u Q: Who rents the distant apartments? u A: Those least willing to pay. u So the competitive market allocation is by “willingness-to-pay”.

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Comparative Statics u What is exogenous in the model? –price of distant apartments –quantity of close apartments –incomes of potential renters. u What happens if these exogenous variables change?

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Comparative Statics u Suppose the price of distant apartment rises. u Demand for close apartments increases (rightward shift), causing u a higher price for close apartments.

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Market Equilibrium p Q D,Q S pepe 100

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Market Equilibrium p Q D,Q S pepe 100 Higher demand

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Market Equilibrium p Q D,Q S pepe 100 Higher demand causes higher market price; same quantity traded.

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Comparative Statics u Suppose there were more close apartments. u Supply is greater, so u the price for close apartments falls.

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Market Equilibrium p Q D,Q S pepe 100

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Market Equilibrium p Q D,Q S 100 Higher supply pepe

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Market Equilibrium p Q D,Q S pepe 100 Higher supply causes a lower market price and a larger quantity traded.

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Comparative Statics u Suppose potential renters’ incomes rise, increasing their willingness-to- pay for close apartments. u Demand rises (upward shift), causing u higher price for close apartments.

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Market Equilibrium p Q D,Q S pepe 100

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Market Equilibrium p Q D,Q S pepe 100 Higher incomes cause higher willingness-to-pay

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Market Equilibrium p Q D,Q S pepe 100 Higher incomes cause higher willingness-to-pay, higher market price, and the same quantity traded.

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Taxation Policy Analysis u Local government taxes apartment owners. u What happens to –price –quantity of close apartments rented? u Is any of the tax “passed” to renters?

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Taxation Policy Analysis u Market supply is unaffected. u Market demand is unaffected. u So the competitive market equilibrium is unaffected by the tax. u Price and the quantity of close apartments rented are not changed. u Landlords pay all of the tax.

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Imperfectly Competitive Markets u Amongst many possibilities are: –a monopolistic landlord –a perfectly discriminatory monopolistic landlord –a competitive market subject to rent control.

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A Monopolistic Landlord u When the landlord sets a rental price p he rents D(p) apartments. u Revenue = pD(p). Revenue is low if p 0 u Revenue is low if p is so high that D(p) 0. u An intermediate value for p maximizes revenue.

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Monopolistic Market Equilibrium p QDQD Low price Low price, high quantity demanded, low revenue.

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Monopolistic Market Equilibrium p QDQD High price High price, low quantity demanded, low revenue.

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Monopolistic Market Equilibrium p QDQD Middle price Middle price, medium quantity demanded, larger revenue.

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Monopolistic Market Equilibrium p Q D,Q S Middle price Middle price, medium quantity demanded, larger revenue. Monopolist does not rent all the close apartments. 100

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Monopolistic Market Equilibrium p Q D,Q S Middle price Middle price, medium quantity demanded, larger revenue. Monopolist does not rent all the close apartments. 100 Vacant close apartments.

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Perfectly Discriminatory Monopolistic Landlord u Imagine the monopolist knew everyone’s willingness-to-pay. u Charge $500 to the most willing-to- pay, u charge $490 to the 2nd most willing- to-pay, etc.

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Discriminatory Monopolistic Market Equilibrium p Q D,Q S 100 p 1 =$500 1

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Discriminatory Monopolistic Market Equilibrium p Q D,Q S 100 p 1 =$500 p 2 =$490 12

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Discriminatory Monopolistic Market Equilibrium p Q D,Q S 100 p 1 =$500 p 2 =$490 12 p 3 =$475 3

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Discriminatory Monopolistic Market Equilibrium p Q D,Q S 100 p 1 =$500 p 2 =$490 12 p 3 =$475 3

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Discriminatory Monopolistic Market Equilibrium p Q D,Q S 100 p 1 =$500 p 2 =$490 12 p 3 =$475 3 pepe Discriminatory monopolist charges the competitive market price to the last renter, and rents the competitive quantity of close apartments.

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Rent Control u Local government imposes a maximum legal price, p max < p e, the competitive price.

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Market Equilibrium p Q D,Q S pepe 100

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Market Equilibrium p Q D,Q S pepe 100 p max

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Market Equilibrium p Q D,Q S pepe 100 p max Excess demand

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Market Equilibrium p Q D,Q S pepe 100 p max Excess demand The 100 close apartments are no longer allocated by willingness-to-pay (lottery, lines, large families first?).

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Which Market Outcomes Are Desirable? u Which is better? –Rent control –Perfect competition –Monopoly –Discriminatory monopoly

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Pareto Efficiency u Vilfredo Pareto; 1848-1923. u A Pareto outcome allows no “wasted welfare”; u i.e. the only way one person’s welfare can be improved is to lower another person’s welfare.

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Pareto Efficiency u Jill has an apartment; Jack does not. u Jill values the apartment at $200; Jack would pay $400 for it. u Jill could sublet the apartment to Jack for $300. u Both gain, so it was Pareto inefficient for Jill to have the apartment.

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Pareto Efficiency u A Pareto inefficient outcome means there remain unrealized mutual gains-to-trade. u Any market outcome that achieves all possible gains-to-trade must be Pareto efficient.

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Pareto Efficiency u Competitive equilibrium: –all close apartment renters value them at the market price p e or more –all others value close apartments at less than p e –so no mutually beneficial trades remain –so the outcome is Pareto efficient.

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Pareto Efficiency u Discriminatory Monopoly: –assignment of apartments is the same as with the perfectly competitive market –so the discriminatory monopoly outcome is also Pareto efficient.

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Pareto Efficiency u Monopoly: –not all apartments are occupied –so a distant apartment renter could be assigned a close apartment and have higher welfare without lowering anybody else’s welfare. –so the monopoly outcome is Pareto inefficient.

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Pareto Efficiency u Rent Control: –some close apartments are assigned to renters valuing them at below the competitive price p e –some renters valuing a close apartment above p e don’t get close apartments –Pareto inefficient outcome.

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Harder Questions u Over time, will –the supply of close apartments increase? –rent control decrease the supply of apartments? –a monopolist supply more apartments than a competitive rental market?

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An algebraic Model of Supply and Demand Supply as a function of price Demand as a function of price Market equilibrium To be solved for p*,q D *,q S * = endogenous variables; a,b,c,d = exogenous parameters

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Does an Equilibrium exist? Is the equilibrium stable?

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Equilibrium

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Comparative Statics – Taxing rents

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b=0 no price increase SupplyDemand P* t p*-t q q s =-a p E

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b>0 price increase Supply Demand q p t P1P1 P-t E0E0 E1E1 P0P0 q 0 q1q1

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Frage: Subvention

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