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Question: 6 the rental market for apartments in a university town...

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6. The rental market for apartments in a University town. The assumptions follow Varians model in Chapter 1: . 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 an apartment in 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 Apartments in the inner ring and outer ring are identical, except that the cost of transportation to the University is lower by the amount ci to, for renter i. θί Is the type of person i and a higher θ 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,. In English this means that the type of an individual ranges from 0 and 1, inclusive. A consumer with type 0 has no transport costs; a consumer 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 proportion 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. (a) What is the benefit for a typei of living in an inner ring apartment relative to an outer ring (b) What is the cost for a type of living in an inner ring apartment relative to an outer ring (c) For typei what is their maximum willingness to pay for an inner ring apartment? What does it (d) If the rent for an outer ring apartment is pS1, 000 and t$1,000, what is the type of renter apartment? apartment? depend on? who is just indifferent (the marginal type) between living in the inner ring and the outer ring for inner ring rent equal to i. $1,000 ii. $1.250 iii. $1,500 iv. $ 1,750 v. $2,000 (e) For any rent (call it p), any t, and any p what is the number of renters who would like to live in the inner ring? That is, what is the demand function for inner ring apartments? (f) What is the equilibrium rent assuming a competitive market for apartments? (g) If 1,000, N500, 1,000, and N,000 what is the equilibrium rent for an apartment? Which types live in the inner ring? The outer ring? (h) Explain why at the equilibrium price in (g) a voluntary trade between a θ = 0.75 and θ = 0.25 is not possible?

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