Problem $5$

$(4$ points$)$

Some cities have rent control $("$ceiling$")$ laws that limit the monthly rent on apartments. Consider a local market for apartments where the demand and supply are given by:

Demand: $p=20000-0\mathrm{.}05x$ and Supply: $p=600+0\mathrm{.}003x.$

a$.$ What is the equilibrium number of apartments rented $(x)$ in the free market?

b$.$ What is the equilibrium rent $(p)?$

c$.$ If rent is controlled by a celing of $$1443\mathrm{.}40$ per unit, what is the number of apartments rented?

d$.$ What subsidy would result in the same rent to tenants $($$$1443\mathrm{.}40)--$but without the problem of housing shortages?

$x=$

$(1$ point$)$

apartments

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$435$

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