Can be measured by a single number q αpβyθ

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: Can be measured by a single number q= α(p^β)(y^θ) q=housing consumption p=price per unit of housing y=income Β=negative price elasticities of demand θ=positive income elasticities of demand To estimate the magnitude of these elasticities, multiply both sides by P to yield: qp= α(p^β+1)(y^θ) If applicable to renter, qp = total rent If applicable to owner, p=purchase price, pq=value of the house pq(housing expenditure) denoted by E , representing either Rent or Value E = α(p^β+1)(y^θ) Take natural logarithms to get logE=γ+(β+1) logp+θlogy (gamma)γ=logα(alpha) Equation gives housing expenditure as a function of the price p and income y β is negative bc when price rises, demand falls β close to 0 → almost inelastic When price rises, demand doesn’t change much -1<β(hat)<0 Income rises, demand rises 0<θ(hat)<1 → housing consumption rises less than proportionally with income θ(hat) → income rises, the proportion of people’s income they spend on housing falls The percentage, share they spend reduces, demand rises Ex. ) millionaire doesn’t care about loans/mortgages on average, spends 30% of income on housing but that 30% doesn’t mean anything If you are rich, the percentage is higher and lower if you are poor Hedonic Approach : housing is a bundle of attributes Instead of being written as U(c,q), it is written as U(c,a1,a2,...am) where Ai is the level of the ith housing attribute, of which there are M in total (c is “bread” consumption) Consumers have demands for individual attributes rather than generalized housing commodity
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c=non-housing consumptions A1,A2,...Am = attributes of housing Hedonic price function: Housing value = δ0 + δiAi δ(hat)i = implicit price ex.) 1.)housing value = 36 + 5.2(sqft) + 0.89(lot size) + 830(fireplace) - 1270(two-car garage) - 0.07(age)(sq.ft) On avg. how much people value each attribute On avg., people value a fireplace at $830 2.) demand for each attribute δ(hat)i=(gamma)γ0+γiAi + γ1 income +γ2 family size γ(hat)i: slopes of demand function for attributes -Issue with housing is there are many attributes but only one housing price- Annual user-cost of housing Renters-->landlords→(pq) pay: price per sq. ft, pay rent homeowners-->owner-occupier→ pay:down payment (one-time from savings), mortgage, property taxes, insurance and maintenance, depreciation (1.2% per year), capital gains V: value of house I: mortgage interest rate H: property tax rate G: rate of capital gains D: rate of depreciation iV + hV + dV - gV V=(v)(q) (where v = value per sq. ft) (i+h+d-g)(v)(q) US taxation Homeowner Landlords 100(30, income tax rate) Mortgage deductible Property Taxes Tax deductible (deductible) $20(-6) Depreciation(value relatively small) x (deductible) mortgage Capital Gains(big incentive for owning homes) x taxable $5(-1.5)
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Rent(big incentive for owning homes) x taxable Property tax -America encourages home ownership -You pay 30-6-1.5=22.5(buying the house helped you save those 2 things(property tax and capital gains) τ =income tax rate 20-6 → (1- τ ) iV + (1- τ ) hV + dV - gViV - τ iV Owner-occupier user-cost= [(1- τ )(i+h)+d-g]v per sq. ft
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