1 The Upside-down Economics of Regulated and Otherwise Rigid Pricesby Casey B. Mulligan and Kevin K. Tsui

2 Types of price regulationJoint price-quantity regulation Conscription = price ceiling + supply mandate Price ceiling with limits on purchasing Price floor with limits on selling Price regulation alone This paper emphasizes ceilings rather than floors much of health, (some) rent control, insurance, banking Competition occurs on non-price dimensions

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4 Come back to the quantity part

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6 Figure 1. Claims on gross tenant-occupied housing output, 2006Gross output = tenants’ payments. Vacant properties have zero output. The vacant slice’s share of NOS is the vacancy rate. It’s a mistake to hold the product fixed. It’s a mistake to focus on wait time. The theory says that it would be a mistake for the market to adjust only on wait time. The data says that they adjust more than that.

7 Creating more square feet with the same cubic feetImage credit:

8 Industry Tastes and Technologyg(n,q) = cost of producing quantity n with non-price attributes q Y(n,q) = services produced by n and q positive first derivatives and positive cross derivatives comparative statics are the same replacing q with F(q), F > 0 Tastes: u(Y, all other goods) = consumer utility. Linear in AOG Derivative summaries at a point {n,q} u:  = magnitude of price elas. of the demand for Y g: = “elasticity of supply of quality” > 0 gnn describes the supply of quantity Y:  = elasticity of subs. (and rts) > 0 g & Y: cxY, related to expansion path u, g, Y: “Market multiplier” β (u does not contribute much) Everyone is identical. Could use semi elasticities. Elasticity of supply of quality rules out increasing returns. ? [n,q] chart of isoquant and isogn showing mm vs 1 ? 𝜃 1+𝜃 ≡ 𝑔 𝑞 /𝑛 𝑔 𝑛𝑞 𝜎≡ 𝑌 𝑛 𝑌 𝑞 𝑌 𝑌 𝑛𝑞

9 Figure 2. Scale and substitution effects on the services delivered by the controlled good.q Expansion path Scale effect Substitution effect Isoquants of Y(n,q) n

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11 Of course there are two things going on. Come back to the quantity part

12 Equilibrium concepts Quality-regulated equilibriumNo restrictions on prices Market determines quantity n Price-regulated equilibrium Producers choose a quality limit x, but prices must comply Consumer choose n (and q), given the quality limit Both are competitive The two are isomorphic, UNLESS the quality ceiling increases the equilibrium price 𝑴 𝒀 𝒏,𝒒 𝒀 𝒏 𝒏,𝒒 =𝒑= 𝒈 𝒏 (𝒏,𝒒)

13 Figure 4B. The services provided by the controlled good,with separable conditional cost: supply shift is second order. Services price Services demand Supply with efficient quality We assume that services demand curve is stable: either type of regulation just moves along the services demand Services amount 𝑌 𝑢𝑛𝑟𝑒𝑔

14 A Price Ceiling Causes Inefficiently Low QuantityMonthly rent (per apartment) Deadweight loss from fall in number of apartments rented S $1,400 1,200 E 1,000 Price ceiling 800 600 D (from Krugman-Wells) Figure Caption: Figure 5-3: A Price Ceiling Causes Inefficiently Low Quantity A price ceiling reduces the quantity supplied below the market equilibrium quantity, leading to a deadweight loss. The area of the shaded triangle corresponds to the amount of total surplus lost due to inefficiently low quantity transacted. 1.6 1.8 2.0 2.2 2.4 Quantity of apartments (millions) Quantity supplied with rent control Quantity supplied without rent control

15 Figure 3. The demand for raw quantity with a quality ceiling.𝒀 𝒏,𝒒 =𝒏𝒒 Price of quantity 𝑾𝑻𝑷 𝒏,𝒒 =𝑴 𝒀 𝒀 𝒏 =𝑴 𝒏𝒒 𝒒 Which is a better substitute for quality (at the margin): Quantity? (𝜎>𝜂) Other goods? (𝜎<𝜂) (As drawn), 𝑑𝑛 𝑑𝑞 <0, 𝑑𝑝 𝑑𝑞 <0, producers benefit from dq < 0 𝝈<𝜼 Each curve has equal area 𝝈>𝜼 Raw quantity (n) 𝑛 𝑢𝑛𝑟𝑒𝑔 𝑛 𝑟𝑒𝑔

16 The demand for raw quantity with various quality ceilings.𝒀 𝒏,𝒒 =𝒏𝒒 Each curve has the same area. The point of the envelope is just to show where all of the other curves would be.

17 Producer surplus and the supply of raw quantitywith a quality ceiling. Price of quantity 𝒅𝒏=𝟎 𝒅𝒑<𝟎 𝒈 𝒏𝒒 𝒏,𝒒 vs 𝒈 𝒒 𝒏,𝒒 𝒏 i.e., 𝜽 vs 𝟎 𝒈 𝒏 𝒏,𝒒 We assume theta > 0 𝒈 𝒏𝒒 𝒏,𝒒 𝒅𝒒=𝒅𝒑 𝒅𝑹𝒆𝒗𝒆𝒏𝒖𝒆=𝒏𝒅𝒑 𝒈 𝒒 𝒏,𝒒 𝒅𝒒 Raw quantity (n) 𝑛

18 Joint production interpreted𝑍 𝑛 =factors used to produce raw quantity 𝑍 𝑞 =factors used to add quality 𝑔 𝑛,𝑞 = 0 𝑛 𝑆 𝑛 𝑍 𝑛 𝑑 𝑍 𝑛 𝑛𝐺(𝑞) 𝑆 𝑞 𝑍 𝑞 𝑑 𝑍 𝑞 0 𝑛 𝑆 𝑛 𝑍 𝑛 𝑑 𝑍 𝑛 0 𝑛𝐺(𝑞) 𝑆 𝑞 𝑍 𝑞 𝑑 𝑍 𝑞 Cost of raw quantity Cost of adding quality Factor-supply curves: 𝑆 𝑛 , 𝑆 𝑞 >0, 𝑆 𝑛 ′ , 𝑆 𝑞 ′ ≥0 𝜃= 𝑆 𝑞 𝑍 𝑞 𝑆 𝑞 ′ 𝑍 𝑞 𝑍 𝑞 ≥0

19 Producer surplus and the supply of raw quantitywith a quality ceiling. Price of quantity 𝒅𝒏>𝟎 𝒅𝒑=𝟎 𝒈 𝒏 𝒏,𝒒 extra surplus Raw quantity (n) 𝑛 𝑢𝑛𝑟𝑒𝑔 𝑛 𝑟𝑒𝑔

20 Quality regulation changes the compositionof producer surplus. Factors for producing raw quantity Factors for adding quality Factor price Factor price Factor supply Factor supply Factor quantity Factor quantity Cannot necessarily sign Zq 𝑍 𝑛,𝑢𝑛𝑟𝑒𝑔 𝑍 𝑛,𝑟𝑒𝑔 𝑍 𝑞,𝑢𝑛𝑟𝑒𝑔 𝑍 𝑞,𝑟𝑒𝑔 𝑔 𝑛,𝑞 = 0 𝑛 𝑆 𝑛 𝑍 𝑛 𝑑 𝑍 𝑛 𝑛𝐺(𝑞) 𝑆 𝑞 𝑍 𝑞 𝑑 𝑍 𝑞

21 Is quality a pseudoprice?Price coordinates supply and demand given quality Quality coordinates supply and demand given price price 1/quality Supply Supply Demand Demand quantity quantity Auction analogy

22 Is quality a pseudoprice?There is likely a region where demand slopes up 1/quality Supply 𝒑= 𝒈 𝒏 (𝒏,𝒒) 𝜎=𝜂 unstable 𝒑=𝑴 𝒀 𝒏,𝒒 𝒀 𝒏 𝒏,𝒒 Beta exceeds 1 iff demand crosses supply from above. Price ceiling shifts supply up (less quality) and demand to the right. Demand quantity Note: p is held fixed.

23 Price regulation: compliance becomes interdependent An example with elastic quality supply. wn is the factor price for Zn Own quality supplied MC pricing 𝐺 𝑞 =𝑝− 𝑤 𝑛 𝑤 𝑛 = 𝑆 𝑛 𝑁 𝑄 Market supply of quantity market quantity N depends on market quality Q Aggregate consistency 𝑞=𝑄 𝐺 ′ 𝑞 𝑑𝑞=𝑑𝑝− 𝑆 𝑛 ′ 𝑁 ′ 𝑑𝑄 Change to “quality does not clear the market in the same way” 𝑑𝑞= 𝑑𝑝 𝐺 ′ 𝑞 +𝛽𝑑𝑄 , 𝛽≡− 𝑆 𝑛 ′ 𝑁′ 𝐺 ′ 𝑞 Interdependent compliance efforts

24 The market multiplier illustrated with a quality ceiling.Price of quantity Supply with efficient quality Supply with regulated quality mm = ratio of red to green (at the margin) The “normal” side of the Jevon’s paradox. Next slide needs to establish three things: WTP up is sufficient but not necessary for quantity up, WTP direction is sigma-eta direction, WTP is necessary but not sufficient for mm > 1 Raw quantity 𝑛 𝑢𝑛𝑟𝑒𝑔 𝑛 𝑟𝑒𝑔

25 Market multiplier: as a function of tastes and technologyEquilibrium quantity change per unit dx 𝛽(𝑛,𝑥)≡ 𝐷 𝑥 𝑛,𝑥 / 𝐷 𝑛 𝑛,𝑥 𝑔 𝑛𝑞 𝑛,𝑥 / 𝑔 𝑛𝑛 𝑛,𝑥 Supply-curve shift per unit dx (quantity dimension) 𝐷 𝑛,𝑥 ≡𝑀 𝑌 𝑛,𝑥 𝑌 𝑛 𝑛,𝑥 − 𝑔 𝑛 𝑛,𝑥

26 Figure 5A. Equilibrium quality vs. the price ceilingThe role of the market multiplier Price ceiling 𝛽=1 𝛽∈(0,1) 𝑝 2 𝛽>1 𝑝 1 𝛽=1 𝛽∈(0,1) Increasing eta moves the unreg equil from the mm > 1 region to the right-hand mm (0,1) region, because, especially with inelastic supply, demand reduction helps relax the price constraint 𝑝 0 𝛽=0 Quality 𝑥 2 𝑥 1

27 Figure 5B. Equilibrium quantity vs. the price ceilingThe role of the market multiplier, assuming gnn > 0 Price ceiling 𝛽∈(0,1) 𝛽=1 𝑝 2 𝛽>1 𝑝 1 𝛽∈(0,1) 𝛽=1 𝑝 0 𝛽=0 𝛽<0 Raw quantity 𝑛 1 𝑛 2

28 Figure 5C. Equilibrium quality vs. the price ceilingExample: the multiplier exceeds one at the unregulated allocation Price ceiling 𝑝 2 R U 𝑝 𝑢 𝑝 1 Quality 𝑥 𝑟 𝑥 2 𝑥 𝑢 𝑥 1

29 Equilibrium quality vs. the price ceilingExample: the multiplier is almost one at the unregulated allocation Price ceiling R U 𝑝 𝑢 Quality 𝑥 𝑟 𝑥 𝑢

30 a pecuniary externality becomes a true externalityMarket multiplier: a pecuniary externality becomes a true externality Lagrangian for a “planner” who faces a limit p on marginal cost ℒ≡𝑢 𝑌 𝑛,𝑥 −𝑔(𝑛,𝑥)+ 𝑝− 𝑔 𝑛 𝑛,𝑥 𝜆 Planner’s benefits and costs of quantity 𝑀 𝑌 𝑛,𝑥 𝑌 𝑛 (𝑛,𝑥)=𝑝+𝜆 𝑔 𝑛𝑛 (𝑛,𝑥) The market ignores this piece  possible death spirals

31 Necessary and sufficient conditionsCeiling increases quantity (𝜷>𝟎) Quality reduces WTP (𝝈>𝜼) Unstable (𝜷>𝟏)

32 Ceiling increases quantity (𝜷>𝟎) Quality reduces WTP (𝝈>𝜼)Jevons Paradox Ceiling increases quantity (𝜷>𝟎) Quality reduces WTP (𝝈>𝜼) Unstable (𝜷>𝟏) Make coal less efficient: less energy per ton. Fixed amount of energy: more tons of coal. Jevons paradox: energy usage declines so much that tons go down

33 Producer surplus and the supply of raw quantitywith a price ceiling. Price of quantity 𝑆𝑖𝑔𝑛 𝑑 𝑑𝑝 𝑛𝑝−𝑔 𝑛,𝑥 =𝑆𝑖𝑔𝑛 1 1+𝜃 −𝛽 𝒈 𝒏 𝒏,𝒒 𝛽=1 extra surplus 𝛽=0 Raw quantity (n) 𝑛 𝑢𝑛𝑟𝑒𝑔 𝑛 𝑟𝑒𝑔

34 Figure 6. Qualitative effects of price regulationby the market multiplier value at the unregulated allocation Impact of regulation Definitions n = quantity pn = expenditure x = quality limit u = social surplus g = total cost mm= market multiplier pu = unregulated price pr = regulated price  = elasticity of q supply n, pn w/ mm ≥ 1 n w/ mm  (0,1) (pn  g) w/ mm  (1/(1+),1) pu  pr u w/ mm < 1 x w/ mm < 1 n, pn w/ mm < 0 (pn – g) w/ mm < 1/(1+) u, (u + g – pn), x w/ mm ≥ 1 Note: Assumes that supply is not perfectly elastic

35 Figure 6. Qualitative effects of price regulationby the market multiplier value at the unregulated allocation Impact of regulation Definitions n = quantity pn = expenditure x = quality limit u = social surplus g = total cost mm= market multiplier pu = unregulated price pr = regulated price  = elasticity of q supply n, pn w/ mm ≥ 1 n w/ mm  (0,1) pu  pr n, pn w/ mm < 0 Note: Assumes that supply is not perfectly elastic

36 𝑛 𝑢𝑛𝑟𝑒𝑔 𝑛 𝑟𝑒𝑔 𝑌 𝑟𝑒𝑔 𝑌 𝑢𝑛𝑟𝑒𝑔Figure 4A. The raw quantity of the controlled good, with quality regulation and 𝜎=𝜂 on the relevant parts of demand. Figure 4B. The services provided by the controlled good, with separable conditional cost: Y-supply shift is second order. Supply with efficient quality Services shadow price Supply with inefficient quality p Willingness to pay Services demand Supply with regulated quality Supply with efficient quality Raw quantity Services amount 𝑛 𝑢𝑛𝑟𝑒𝑔 𝑛 𝑟𝑒𝑔 𝑌 𝑟𝑒𝑔 𝑌 𝑢𝑛𝑟𝑒𝑔

37 Price regulation comparative statics𝛽<1 𝑑𝑛 𝑑𝑝 =− 𝛽 1−𝛽 1 𝑔 𝑛𝑛 𝑑𝑞 𝑑𝑝 = 1 1−𝛽 1 𝑔 𝑛𝑞 𝐷 𝑛,𝑥 ≡𝑀 𝑌 𝑛,𝑥 𝑌 𝑛 𝑛,𝑥 − 𝑔 𝑛 𝑛,𝑥 𝛽(𝑛,𝑥)≡ 𝐷 𝑥 𝑛,𝑥 / 𝐷 𝑛 𝑛,𝑥 𝑔 𝑛𝑞 𝑛,𝑥 / 𝑔 𝑛𝑛 𝑛,𝑥

38 Waiting Model 1: a symptom of low inventoriesq = vacancy rate, a.k.a., inventory ratio The resource cost of the vacancy rate q is proportional to n. Vacancy rate goes in Y(n,q) because it enhances the average value of the units consumed. E.g., fewer stockouts. If Y(n,q) = nf(q), then 𝜎=1. Model 2: Customer in the production function “Revenue misspecification” problem Model 3: First-come, first served; lotteries; waiting tax Would not be an equilibrium outcome in our model, unless these mechanisms reduced marginal costs

39 Summary Quality competition with homogeneous buyers and sellersA price ceiling can increase the quantity traded It increases supply, and by increasing demand (𝜎>𝜂) or by not decreasing it too much. Not a litmus test for imperfect competition A price ceiling can increase expenditure A price ceiling can benefit producers A price ceiling can create worse-than-first-order losses 𝑆𝑖𝑔𝑛 1 1+𝜃 −𝛽 𝛽≥1