Question

Economics Apartment Question: Inner and Outer Ring

» 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 N8. The cost to the land-lord of renting an apartment in the short run is zero, up until Ns. 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 = t0, for renter i· 0, 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 [0,1]. 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

Answer 1

Let us infer a few things from your question which will help us in subparts of the question.

• 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 factors not mentioned in the problem.
• From point 3, it is a short run case and supply is fixed for the inner-ring apartment, hence the supply curve is vertical
• From point 4, the inner-ring apartment market attains an equilibrium price.
• From the last point,  $\theta$ is continuously increasing from 0 to 1 as we move from the inner apartment to the outer-ring apartment.

a) The person who lives in the inner-ring apartment will have low transportation cost than the one who lives in the outer-ring apartment. The reason is as we move from inner-ring apartment to outer-ring one cost of transportation increases.

b) For the inner ring apartment, the demand of the apartment is greater than supply, hence renter has to pay higher rent than the outer-ring apartment.

c) Maximum willingness to pay for the inner-ring apartment can be written as

willingness to pay = $p^{o} + t\theta$   i.e; rent of the outer-ring apartment + cost of transportation.

For maximum willingness; $\theta$ = 1, hence the above equation became $p^{o} + t$ .

It depends on the rent of outer-ring apartment and scaling parameter.

d) If a person is indifferent between apartments it means his maximum willingness to pay matches the equation we derive in the above part.

Therefore, the maximum willingness to pay is 1000+ 1000 = $ 2000.

Hence, option (v) is correct.

e) The demand function for inner ring apartment; = $N^{d} = (p^{o} + t\theta )-p$

This is the demand function because demand negatively related to the price of inner ring apartment and positively related to outer ring apartment.

f) If we assume a competitive market then equilibrium exists where the demand of apartment is equal to the supply of apartment.

g) From the equation, we derive in part (e); putting the respective values

1000 = (1000+1000$\theta$) - p

gives, p = 1000$\theta$

At equilibrium, Demand = Supply, p-1000$\theta$ = 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.

h) The voluntary trade at $\theta = 0.25$ and $\theta = 0.75$ is not possible because at this

rent of the outer-ring apartment = 1000 + 250 = $1250; at $\theta = 0.75$; rent of outer-ring apartment = $1750

rent of inner-ring apartment = 1000*(0.25) = $250 ; at $\theta = 0.75$; rent of inner-ring apartment = $ 750

because it creates large gap between what they are paying versus what they have to pay after trade,