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Unformatted text preview: Section Notes Susan E. Stratton 1 Cost of housing regulations B ( H ) gives us the benefit of housing C ( H ) gives us the cost of housing L units of land available units of land needed per hous All houses are identical. All land is controlled by the producer, but the producer is a pricetaker in the market for housing. How do we find market equilibrium in the absence of regulation? 1. Solve the producers profit maximization problem. max H pH C ( H ) (1) subject to land availability. Suppose that each house needs units of land. This gives us a Lagrangian which looks like L = pH C ( H ) + L H (2) which gives us p = C ( H * ) + . 2. Look at consumers utility maximization behavior. Consumers always purchase where p = B ( H * ) , i.e. the price must be equal to the marginal benefit of housing in equilib rium. 3. Combine to get B ( H * ) = C ( H * ) + or the marginal benefit of housing equals the marginal cost of constructing housing plus the shadow value of the required land. Now, we consider a regulation which limits the acres available for development, increases the cost of units, and delays completion by 1 year. Lets figure out the new equilibrium. Well begin by considering the market oneyear from now and the discount back. How do we find equilibrium now? 1 1. Solve the producers new profit maximization problem. Let the new cost curve be C 1 ( H ) . We know have max H pH C 1 ( H ) (3) subject to L L L where L is the number of acres were conserving. Since theThus we need to write a Lagrangian L = pH C 1 ( H ) + L L H (4) whose firstorder conditions are p C 1 ( H ) = 0 (5) and H = L L. (6) This tells us that H = L L 2. Look at consumer behavior. Consumers always set B ( H ) = p so we know that the market clearing price must be the marginal benefit at the restricted acreage or...
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This note was uploaded on 04/02/2008 for the course ECON 102 taught by Professor Sunding during the Fall '07 term at University of California, Berkeley.
 Fall '07
 Sunding

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