SECTION B: ANSWER ALL QUESTIONS. Write down your answers CLEARLY in the booklet

Question

SECTION B: ANSWER ALL QUESTIONS. Write down your answers CLEARLY in the booklet and show your works. Correct answers without explanations are eligible for full marks, wrong answers without explanations get zero marks, and wrong answers with correct solution steps get partial marks. (60 MARKs) Question 21 (30 marks) Consider a residential builder who is deciding how much open space to include in a suburban condominium development. Individuals who will live in the development are willing to pay more for their suites if the development includes some open space. Suppose that the marginal private benefit that the developer receives as a result of this factor is MPB = 100-05S, where s is the amount of open space, measured in square feet. However, open space is costly to the developer, since it restricts the amount of housing that he can build open space has an opportunity cost. Suppose that the marginal cost of open space to the developer is given by MC S. Residents outside the development t also derive a benefit from having some open space in the development some space may be provided as a park that they can use, or it may be that including some open space makes the development esthetically more appealing. Suppose that these marginal external benefits are given by MEB 50-0.25S. (a) Find the equilibrium level of open space, that is, the level that the developer will choose taking only his own interests into account. (4 marks) What is the marginal social benefit (MSB) of open space in this case? Depict (b) MPB, MEB, MSB and MC in a diagram. (8 marks) Find the efficient amount of open space, that is, welfare of the community. How does the efficient amount of ope (c) the level that maximizes the n space compare with the equilibrium amount that you calculated in part a.? Explain the intuition behind your finding (8 marks) (d) Essay Question How can the community induce the developer to incorporate the efficient level of open space into the project? Explain in detail the various alternatives and assess their feasibility and drawbacks. (10 marks)

Explanation / Answer

Solution a. The equilibrium level of open space that is the level that the developer will choose taking only his own interests into account is the level of S for which MB=MC

This gives 100-0.5S =S which implies S=100/1.5=66.67

Solution b. The marginal social benefit (MSB) of Open space in this case is by given by adding the MB and MEB curves that gives the MSB=150-0.75S  

Solution c: The efficient amount of open space that is the level that maximizes the welfare of the community is given by as the efficien amount of open space satisfies MSB=MC or 150-0.75S=S, which implies S=150/1.75=85.7.

The efficient amount of open space is more than the equilibrium amount of open space that we calculted in i.e 66.67

Solution d: The community  induce the developer to incorporate the efficient level of open space into the project is can be given by the below solution

The solution is to subsidize the provision of open space.This can be obtained as.the required subsidy equals the level of MEB at the efficeint level of open space,so the efficient subsidy would be equal 50-0.25S ,,S in this case is 85.7,,,so 50-0.25(85.7)=28.6 per unit.

With the above subsidy the marginal benefit of open space to the developer becomes MB+subsidy=128-0.5S.

Now the developer will choose the level of S for which 128.6-0.5S=S, which implies S =128.6/1.5=85.7,,,i.e the efficient amount .So there are different alternatives.

The community could also require that the developer must include this amount of open space or it allow the developer to build to a higher density if the project includes a certain amount of open space

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