The Upside-down Economics of Regulated and Otherwise Rigid Prices

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

2. Types of price regulation • Joint 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

6. Figure 1. Claims on gross tenant-occupied housing output, 2006

7. Industry Tastes and Technology • Technology • g(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)

8. 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

11. Equilibrium concepts • Quality-regulated equilibrium • No 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

12. Figure 4B. The services provided by the controlled good, with separable conditional cost: supply shift is second order. Services demand Services price Supply with efficient quality Services amount 0

13. Figure 3. The demand for raw quantity with a quality ceiling. Price of quantity (As drawn), , producers benefit from dq < 0 Which is a better substitute for quality (at the margin): Quantity? () Other goods? () Raw quantity (n) 0

14. The demand for raw quantity with various quality ceilings.

15. Producer surplus and the supply of raw quantity with a quality ceiling. Price of quantity vs i.e., vs Raw quantity (n)

16. Joint production interpreted Cost of raw quantity Cost of adding quality Factor-supply curves:

17. Producer surplus and the supply of raw quantity with a quality ceiling. Price of quantity extra surplus Raw quantity (n)

18. Quality regulation changes the composition of producer surplus. Factors for adding quality Factors for producing raw quantity Factor price Factor price Factor supply Factor supply Factor quantity Factor quantity

19. Is quality a pseudoprice? Quality coordinates supply and demand given price Price coordinates supply and demand given quality 1/quality price Supply Supply Demand Demand quantity quantity

20. Is quality a pseudoprice? There is likely a region where demand slopes up 1/quality Supply unstable Demand quantity Note: p is held fixed.

21. 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) Raw quantity

22. Figure 5A. Equilibrium quality vs. the price ceiling The role of the market multiplier Price ceiling Quality

23. Figure 5B. Equilibrium quantity vs. the price ceiling The role of the market multiplier, assuming gnn > 0 Price ceiling Raw quantity

24. Figure 5C. Equilibrium quality vs. the price ceiling Example: the multiplier exceeds one at the unregulated allocation Price ceiling R U Quality

25. Equilibrium quality vs. the price ceiling Example: the multiplier is almost one at the unregulated allocation Price ceiling R U Quality

26. Market multiplier: a pecuniary externality becomes a true externality Lagrangian for a “planner” who faces a limit p on marginal cost Planner’s benefits and costs of quantity The market ignores this piece  possible death spirals

27. Necessary and sufficient conditions Ceiling increases quantity () Quality reduces WTP Unstable (

28. Jevons Paradox Ceiling increases quantity () Quality reduces WTP Unstable (

29. Producer surplus and the supply of raw quantity with a price ceiling. Price of quantity extra surplus Raw quantity (n)

30. Figure 6. Qualitative effects of price regulation by the market multiplier value at the unregulated allocation Definitions Impact of regulation 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 0 n, pn w/ mm < 0 Note: Assumes that supply is not perfectly elastic

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

32. Waiting • Model 1: a symptom of low inventories • q = 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 . • 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

33. Summary • Quality competition with homogeneous buyers and sellers • A price ceiling can increase the quantity traded • It increases supply, and • by increasing demand () 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