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alth effect argument considers households that optimise consumption decisions over their lifecycle to maximise utility．An unexpected permanent increase in the value of an asset owned by the household will increase lifetime wealth，which the household wants to run down over the remainder of its life. Since housing costs will also rise，the effect on non-housing expenditure will be dampened. If I assume that households are Finitely-lived, i.e. I abstract from dynastic considerations and bequest motives，this should lead to an unambiguous increase in consumption by households whose holdings of household equity exceed the level of housing services required over the remainder of their life. The impact on other households depends on the form of the rise in house prices, and the manner in which they expect to consume housing services over their lifetime．

3.1.1.1 House Price Changes
　Considering first the issue of house prices，we must distinguish between the effect of a Once-and-for-all increase in prices，and a change in the growth rate of house prices. Houses can be bought as a consumption good, for owner-occupation, or as an investment good，to be rented out．The supply of houses is highly inelastic，even in the medium run，so the total housing stock is approximately constant．
　In my first stylised scenario I consider all exogenous，overnight doubling in the price of houses．I assume a constant exogenous rate of household formation，equal to the rate of household destruction．Ceteris paribus，a doubling in the purchase price of houses means young households will find it cheaper to rent rather than buy a house，expanding the demand for rental property．To increase the number of properties available for renting， landlords must buy houses at the new market price．If I assume the housing market is competitive，rent on the marginal rental property will equate the cost of rental housing services and the cost of owner-occupied housing services．This occurs when the cost of renting has also doubled．Renters are worse off, as they now face higher lifetime rents. Owner occupiers may be better off，if the increase in wealth exceeds the rise in their housing costs．
I notice that I have assumed house price changes to be exogenous. To be confident that house price changes cause changes in consumption growth，I would prefer to know the underlying cause of a change in house prices，So that I could be certain it was unrelated to consumption．

3.1.1.2 Consumption of Housing Services
The existence of transaction costs and heterogeneity between houses create significant housing market frictions and lagged responses．If there is a positive (exogenous) shock to house prices this period，equilibrium will not be immediately reached，and house prices will continue to adjust in subsequent periods[ Hendry (1984) creates a model in which there may be “positive feedback of increasing house prces to demand” *pp226, emphasis in original)][ Muellbauer and Murphy (1990) find” strong evidence of the powerful instability of the housing market” (pp366), showing this is not merely a theoretical possibility. ]．Hence households that were previously indifferent between renting and owning now have all incentive to buy，hoping that any
house they purchased would rapidly rise in value，and providing a hedge against the risk of rising rents．Such an action is rational，and forms a Nash equilibrium[ Nash (1950), Nash (1951)]：if renters