Why is real estate market an oligopoly?

1. Why is real estate market an oligopoly? DRE Research Seminar 15 February 2006 James D. Shilling University of Wisconsin- Madison School of Business Tien Foo Sing National University of Singapore Department of Real Estate

2. Presentation Outline • Introduction – Bertrand’s Paradox • Basic model and assumptions • A mono-centric city model with capacity constraints • A Multi-nodal urban land market model • Differentiated markets in Hotelling’s linear space • Mergers and predatory pricing strategies • Variable price structure • Conclusions & future extensions

3. Industrial organization and real estate market • Industrial organization (IO) literature is expanding rapidly • Issues relating to functioning of market, like market structure, incomplete information, and predatory strategies, exit and entry deterrence etc. • Limited IO studies in real estate market • Real estate market has unique features for IO study because of the inherent spatial characteristics • Differ by location (distance from city centre), by property type (sub-markets), by countries/cities (institutional features) • Real estate market provide a good platform for IO studies • Products are typically heterogeneous – differentiated by location and by type • Information is inefficient/imperfect • Supply side constraint – fixity in land / density control through zoning

4. Basic model and assumptions • A static game theoretic model with two players • They develop homogenous products at a fixed location, xi • Two firms compete on prices to optimize profits • Information complete and decisions are simultaneous • Demand function is given as Di(pi, pj) = a – bpi + dpj • b = demand elasticity; d = cross-elasticity of substitution • Such that 0 < d < b • The market is pareto-efficient • In Nash equilibrium, duopoly firms earn zero profits • Prices will be driven down to equal to costs • The result is welfare sub-optimal • Bertrand’s Paradox

5. Bertrand’s Nash Equilibrium Rj pi Ri Nash equilibrium pi*=pj* =c pi* pj pj*

6. Bertrand’s paradox and real estate market • Real estate markets are not monopoly, and they are dominated by several players, and the number of players in each market varies • The responsiveness of the market may vary across cities and sub-markets • Is real estate market a special test case that rejects Bertrand’s paradox? • If not, why are the following questions not answered? • Why are mergers and predatory strategy not operative in real estate market? • Is the real estate market welfare sub-optimal? • Could developers earn more than zero profits? • What factors that drive an oligopoly real estate market?

7. Why is real estate market an oligopoly? • In manufacturing technology, the adoption of flexible technology promote concentration of market (Eaton and Schmitt, 1994) • Firms avoid diversification and expansion of basic products, and thus reduce fixed costs • Ownership structure is irrelevant, and mergers and cartels are welfare optimal strategies that lead to concentration of market • Flexible technology is not applicable to real estate markets • Land is fixed and immobile, and ownership of lands is a prerequisite of any development activities • Is oligopoly structure of real estate market welfare optimal? why? • Other forces limiting concentration of real estate market: • Capacity constraint (The Edgeworth’s solution, 1987) • Differentiated products/ spatial characteristics of real estate market • Imperfect information • Dynamic market / repeated strategies

8. Flexible Production Structure by Eaton and Schmitt (1994) Xi Xj Xh

9. Limiting forces: (1) Capacity constraint • In a mono-centric city where both developers co-exist at xi • Supply is inelastic and density on each land parcels is controlled by zoning • Maximum density is binding in each market at xi, • such that • Capacity constraint is imposed by , where [0  1] • Demand functions: • In Nash Equilibrium

10. Fraction of maximum market demand, () Cross-elasticity of substitution, (d) Elasticity of Demand, (b) Capacity constraint and demand structure

11. Proposition 1: • Capacity constraint,, in a duopoly market is a function of the demand elasticity, b, and cross elasticity of substitution, d. In a market with highly substitutable products, and where buyers are less insensitive to price changes, i.e. inelastic demand, a developer requires a higher capacity constraint of m in order to preempt entrants and earn monopoly return ■ • In a market with highly substitutable product, developers are required to increase their capacity substantially to preempt entry and obtain monopoly profit • This is commonly observed in highly homogenous market, and lower end housing markets

12. Limiting forces: (2) • A multi-nodal urban land model • Spatial features are incorporated using Hotelling’s linear city kernel (1929) • (x, q) = [(x1, q1), (x2, q2), …. ,(xN, qN)] • where , [m = (1, 2)] indicates a bi-nodal urban market • [x1 < x2 < x3 <….. xN] • distance vector is a continuous function that increases in an equally space distance, • Two developers, each of them establishes competitive edge at the two city centroids

13. Cost structure in Hotelling’s linear city

14. Solving for optimal market boundary • Assume that price is inelastic • Aggregate profit functions over a distance, (|Xi, xi|): • In Nash equilibrium, [p*1 = p*2 = MC*i(x1)] • Equilibrium price is equal to the marginal cost of the second most efficient developer: • MC*i(x1) = max [MC1(xi), MC2(xi)] • Market boundary where both developer earn optimal profits is derived as:

15. (c) (a) (d) (e) (b) X* Aggregate Profits in duopoly market

16. Optimal market boundary, (x*) Size of linear city, (X2 – X1) Market Share of developer 1, () Optimal market boundary of duopoly

17. Aggregate Profit for developer 1, ( 1) Size of linear city (X2 – X1) Market Share of developer 1, () Aggregate profit of developer 1

18. Proposition 2: • Given the optimal market boundary that gives welfare-optimal return to each of the developers, , aggregate profits of the developers increase with an increase in the linear size of a bi-modal city. However, the aggregate profits of developers will be lower, if they face an increasing capacity constraint. • Both developers are better off when the city size is expanded • Aggregate profits decreases when capacity is raised by either one of the developer • The above two conditions are sufficient to reject a monopoly market

19. Entry and mergers in real estate market • Proposition 3: • There are positive profits for new entrants to establish strong foothold in space along the linear city, , and the profits of incumbents will be eroded with the new entrants. The loss in profits for incumbents as indicated by shaded area (a) and dotted area (c) is dependent on the location at which the new entrants possess competitive edge in their production technology. The loss for incumbent developer m increase, when is smaller. • Proposition 4: • Merger of two developers with established home market reputation in adjacent markets are welfare optimal. However, there are no externality effects on the developer outside the merger. The profit level of the developer not involved in the merger remains unchanged.

20. (c) (a) (d) (e) (b) X* Effects of entry and mergers

21. In a multi-nodal city with elastic demand • Demand function: qi = Di(pi, pj) • Proposition 5: • In an elastic market where demand is responsive to price changes, the profits of developers will be an increasing function in the cross-elasticity of substitution, d, and an decreasing function in the demand elasticity, b.

22. Variable price structure • Utility function of buyers: • Profit function • Proposition 6: • When the marginal rate of increase in unit cost is lower than the marginal disutility rate, developers will be able to maximize the profit by stretching their market boundary outward from their home-base. When [t < r], there is no incentive for developers to expand their market boundary, and it would be better off for the developer to focus only on its home-market where he has competitive advantages.

23. Limitations & possible extensions • Reputation of developers • D1(p1, p2) = a – (b-)p1 + dp2 • Incomplete information on cost structure • Location dependent capacity constraints • Different sub-market and switching costs

24. p1,a p1,b Xs Urban land pricing structure for two different uses

25. Conclusion • For manufacturing firms with homogenous products, flexible production technology promotes market concentration (Eaton and Schmitt, 1994) • Costly to expand basic products • In real estate market, flexible production technology is not applicable • Ownership in real estate market is critical • Fixity in supply and capacity is constrained • Using Hotelling’s linear city kernel, models with two city centroids were developed • Given capacity constraints, and also that cost structure of developers is tied to location advantage • Forces that promote concentration of market are ineffective • Real estate market is an oligopoly, yet there is no reason to reject that the market is welfare sub-optimal • Empirical hypotheses can be developed to further verify propositions that reject concentration of ownership in real estate market • Thank you!