optionValueRegulation - Section Notes Susan E Stratton 1...

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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 α units of land needed per hous All houses are identical. All land is controlled by the producer, but the producer is a price-taker 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 α units of land. This gives us a Lagrangian which looks like L = pH - C ( H ) + λ ¯ L - αH (2) which gives us p = C ( H * ) + αλ . 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 * ) + αλ 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. Let’s figure out the new equilibrium. We’ll begin by considering the market one-year from now and the discount back. How do we find equilibrium now? 1
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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 αL ¯ L - ˆ L where ˆ L is the number of acres we’re conserving. Since theThus we need to write a Lagrangian L = pH - C 1 ( H ) + λ ¯ L - ˆ L - αH (4) whose first-order conditions are p - C 1 ( H ) - αλ = 0 (5) and αH = ¯ L - ˆ L. (6) This tells us that H = ¯ L - ˆ L α 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 p = B ¯
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