Question

Part III: Problems Chapter 1 e There are two types of apartments, inner ring and outer ring. . The price of outer ring apartments is fixed and equal to po. . There is a fixed supply of inner ring apartments equal to N". The cost to the land-lord of renting the short run is zero, up until N. Then it is infinite. . The total possible number of renters that would live in the inner ring is Nd N. This is the maximum number that might want to live in the inner ring. to the University is lower by the amount ci-to, for renter i· 0, is the type of person i and a higher 0 reflects higher costs of transport, while t is a scaling paramter. The only reason to pay more for an inner ring apartment is to save on transportation costs. . The distribution of types is uniformly distributed and ranges from (0,1]. In English this means that the type of an individual ranges from 0 and 1, inclusive. A consumer with type 0 has no of type 1 has the maximum transport costs of t; a consumer of type 1/2 has transport costs of t/2, and so on. Uniform distribution simply means that the of people of any type is the same. It also means that the cumulative proportion of renters with a type less than θ is θ. So if θ-.25 then 25% of renters are type 0.25 or less and 75% of renters have a type greater than 0.25.

Answer 1

From point 2, it is clear that the price of outer ring apartment is an exogenous variable. This means that the price of the outer - ring apartments is taken as determined by factor not mentioned in the problem. rightarrow From point 3, it is a short case and supply is fixed for the inner - ring apartment, hence the supply curve is vertical. rightarrow From point 4, the inner - ring apartment market an equilibrium price. rightarrow From the last point, theta is continuously increasing from 0 to 1 as we move from the inner apartment to the outer - ring apartment. G) From the equation, we derive in part (e): putting the respective values 1000 = (1000 + 1000 theta) - p gives, p = 1000 At equilibrium, Demand = supply, p - 1000*(1/2) = $ 500 which gives theta = 1/2 Rent for the inner ring apartment is p = 1000*(1/2) = $ 500 Rent for the outer ring apartment = $ 1000 and $ 500 for transportation