2. Housing © Allen C. Goodman, 2000

3. Importance Necessity – We must have shelter. Importance – For most households, it is the single most important item of consumption. It is also, particularly in Western countries, the largest store of wealth. Durability – Housing lasts a long time. Most estimated depreciation rates are no higher than about 1%, and in many places houses last hundreds of years.

4. Importance, cont. Spatial Fixity – With only minor exceptions, housing cannot be transported. Indivisibility – Households cannot mix units to get what they want. Heterogeneity – Housing can have a great number of characteristics. One can think of a large number, and differential preferences over: –Quantity –Quality –Location –neighborhood

5. Importance, cont. Nonconvexities in production – Rehabilitation, conversion, demolition, and reconstruction involve discontinuous changes. Why? It is generally easier to change housing quality discontinuously, rather than through continuous upgrading. Informational asymmetries – Information is not perfect. Potential occupants don’t know everything about dwelling units. Landlords and tenants must interact without perfect information Transactions costs – Can run to 10% or more of the cost of the unit.

6. Two Other Terms Homogeneous – You can summarize housing in one dimension, i.e. through expenditures. Speak of housing as a number of units, possibly indexed by location. Heterogeneous – Composed of many features. Particularly important when considering individual demand and supply features.

7. Homogeneous Analysis Rent Control – One market p q S D p* q* pc qc Shortage

8. Homogeneous Analysis Rent Control – Two Markets p q S D p* q* pc qc Shortage Uncontrolled Du Su D´uD´u pu*

9. Housing Policy Early U.S. policy involved building and/or renting new units. Called public housing. (Parenthetically) U.S. has much smaller direct government involvement than most other countries. In 1960s (and possibly before), it became clear that this was terribly expensive. Many economists lobbied for various types of cash-based aid.

10. In-kind transfers What would you like, $100 for housing, or $X that you could spend any way you want? Housing Other Goods A B C

11. If we give money … What will happen to demand? What will happen to supply? Quantity Price D S D´D´

12. Supplies of Land and Housing LAND First L = L A + L U dL = dL A + dL U dL U = - dL A Land Price L E s = -E d (L A /L U ) EsEs -c s E d = LULU LALA

13. Muth Estimates agricultural demand elasticity  -1.2, so urban supply elasticity is about +1.2. Supply of housing services? Early estimates were  +14. What do we know about flat curves? –Little or no increasing returns to scale –Constant costs, indicative of competition.

14. Long run housing I use an analysis from Vernon Henderson. Q = housing; K = capital L = land; R = Rent r = payment to capital. Start with: Q(u) = Q (K(u), L(u)) Profit (  ) is:  = p(u)Q(K(u), L(u)) – rK(u) – RL(u) We get standard maximization, where MR = MC. Zero profits imply that unit costs must always vary through land costs to equal output prices.

15. What happens as land rents (hence housing prices) change? KEY – Profit doesn’t change as they move. Therefore: Q(u) [  p(u)/  u] = L(u) [  R(u)/  u](1.13) Rearranging (1.13), leads to, for land rent: [  R(u)/  u] = [Q(u)/ L(u)] [  p(u)/  u] (1.14) Divide both sides by R(u), and multiply RHS by p(u)/p(u), leads to: [  R(u)/  u]/R(u) = [p(u)Q(u)/ R(u)L(u)] {[  p(u)/  u]/p(u)} (1.16) Q = housing; K = capital L = land; R = Rent r = payment to capital. LHS: Pct. Change in Rents RHS: Pct. Change in Prices, multiplied by 1/rental share – Call rental share  L.

16. [  R(u)/  u]/R(u) = (1/  L ) {[  p(u)/  u]/p(u)}(1.16) Define elasticity of substitution as:  =  ln (K/L)/  ln (R/r). So:  ln (K/L)/  u =  dln (R/r)/  u = (  /  L )  ln p(u)/  u. Since r doesn’t change, dln (R/r) = dln R. So, a 1%  in housing prices  a (  /  L ) increase in capital land ratio Most of the time, we don’t see density changing as fast as factor costs, so  < 1. If  = 0.7 and  L = 0.1, we see that a 1%  in housing prices  a (0.7 / 0.1), or 7% increase in capital land ratio. Also, land rents change much more quickly than housing prices: Q = housing; K = capital L = land; R = Rent r = payment to capital.

17. This is simple to see: p(u) = s K r + s L R(u)  p(u)/  u = s L  R(u)/  u  R(u)/  u = (1/s L )  p(u)/  u This also means that factor shares aren’t constant as implied in Cobb-Douglas production functions that are otherwise very serviceable. This is a LR analysis. It assumes that people live in house trailers. Yet, for many aggregate analyses, a lot of the predictions are really pretty good. It is also important to note (over and over) that when we talk about housing price, we are talking about unit price. This is why it is sometimes very important to deal w/ expenditures, rather than price. NEXT: Demand Q = housing; K = capital L = land; R = Rent r = payment to capital.