RE5004 Chap.4 Four-Quadrant Market Adjustment
Four-Quadrant Market Adjustment
Close four linked markets
Space demand determines rent for a stock, capitalization maps rent to asset value, construction responds to price and replacement links completions back to stock. Long-run equilibrium requires every relation to hold together.
Trace shocks beyond the first round
A lower cap rate can raise asset price while eventual construction expands stock and lowers rent.
Lower depreciation can increase stock while reducing annual completions. These results become intuitive once stocks and flows remain separate.
Protect units around the loop
Rent is a flow price for space, asset price capitalizes that flow, construction is a completion flow per period and stock is measured at a point in time. The replacement identity connects the last two without making them interchangeable.
A steady state can contain positive construction because completions offset depreciation; it requires zero net stock change, not zero gross building activity.
Use comparative statics as a closed comparison
A shock enters one relation, but the other markets feed back until a new joint equilibrium is reached.
The first-round capitalization effect of a lower cap rate is therefore different from the final rent effect after construction expands stock. Begin with the shifted curve, walk through rent, price, completions and stock, and return to the starting market. A direction list is credible only when the last link supports the first.
What this chapter covers
- 01
Space-market rent determination
- 02
Capitalization and asset value
- 03
Construction response
- 04
Replacement and stock flow
- 05
Published numerical equilibrium
- 06
Long-run comparative statics
Worked example · free
Verifying the published tuple
- 2Check space demand.
- 3Check replacement and construction price.
- 3Check capitalization and units.
Key terms
- Space Market
- The market where stock and occupancy demand determine rent.
- Asset Market
- The market capitalizing rental income into property value.
- Replacement Construction
- Completion flow required to offset depreciation of stock.
- Comparative Statics
- Comparison of old and new equilibria after an exogenous change.
- Capitalization Rate
- The rate linking rent to asset price.
Four-Quadrant Market Adjustment FAQ
Why can price rise while rent falls?
A lower cap rate first raises asset price, stimulating construction. The larger long-run stock lowers the rent required to clear the space market, even while asset value remains higher. The apparent contradiction disappears once the initial capitalization step is separated from the final closed loop.
Rent and price are linked, but both are endogenous and the intervening stock response changes the rent entering the final capitalization relation.
Why can completions rise while stock falls?
With higher depreciation, a smaller sustainable stock can require a larger annual replacement flow. Construction is a flow and stock is a level, so their directions need not match. The identity compares completions per period with the loss rate applied to the remaining stock. Inspecting construction alone cannot reveal net expansion unless depreciation, demolition or conversion losses are also known.
What does comparative statics leave out?
It compares two steady states but does not reveal timing, overshooting or the path between them. Vacancy, construction lags and credit are needed to explain the transition. A comparative-static result can say final stock is higher without saying when projects start, whether rent peaks first or how financing synchronizes delivery. Those dynamic questions belong to a separate mechanism rather than to extra arrows in the table.
How can you tell whether a proposed equilibrium is complete?
Substitute the candidate values into every relation and require the final capitalization step to reproduce the starting rent. Space demand must match stock, completions must replace depreciation, construction cost must match asset price and price must capitalize back into rent. Passing only three equations leaves one market adjusting, so the tuple is not a joint long-run equilibrium.
Assessment move
Draw the loop R to P to C to S before every shock. State the entry quadrant, walk through each response, reconcile the stock-flow identity and close the loop at rent. Beside each symbol, write its unit: rent flow, asset value, completion flow or physical stock. Recompute the published equilibrium by checking all four relations and reject any tuple that closes only three.
For shock practice, divide the answer into first-round and final effects; this is essential for cap-rate changes, where initial price capitalization induces a stock response that moves final rent in the opposite direction. Use the replacement identity as an audit whenever construction and stock move differently.
Then compare the direction chain with space-market clearing: extra stock should not require a higher clearing rent under unchanged demand. End by stating the model boundary—two steady states are compared, while timing, vacancy overshooting and credit require the cycle framework. This routine turns the quadrant diagram into a causal proof rather than a memorized matrix.
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