Supply and Demand and Demand Curve

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1. Assume there is a well-defined geographic area of a city. The area is composed exclusively of apartments and is populated by low-income residents. The people who live in the area tend to stay in that area because (1) they cannot afford to live in other areas of the city, (2) they prefer to live with people of their own ethnic group, or (3) there is discrimination against them in other areas of the city. Rents paid are a very high percent of peoples’ incomes. (a) Would the demand for apartments in this area be relatively inelastic or relatively elastic? State why. (b) Would the supply of apartments in this area be relatively inelastic or relatively elastic? State why.

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(c) Draw the demand and supply curves as you have described them, showing the initial equilibrium price and quantity. Label carefully. (d) Now assume the government creates a rent supplement program. Under this program, the renter is required to pay 30% of income in rent. Any additional rent is paid by the government. For example, a low-income person with an income of $1,000 a month would be required to pay $300 in rent (30%). If the rent is $500, the other $200 would be paid by the government. Analyze the results of this program. Show the changes on the graph and explain what will result. Who gains and who loses from this program? (e) Instead, now assume that the government decides to provide a building subsidy to people who build apartments in this low-income area. A certain percent of their costs will be paid by the government. Analyze the results of this program. Show the results on the graph and explain what will result. 2. Assume that the demand curve for paper of a certain type is given by Qd = 200 − 5p, where Qd is the number of pounds demanded per year and p is the price per pound. The supply of function of this type of paper is given by Qs = 40 + 3p, where Qs is the number of pounds provided. (a) What is the equilibrium price? (b) What is the equilibrium quantity supplied and demanded? (c) What is the total surplus (consumer surplus+producer surplus) at the equilibrium price? (d) Now assume that the government imposes a tax of $8 per each pound sold, paid by the consumers, which reduces the quantity sold and demanded to 85 pounds. In this case, what are the price and the consumer surplus? 3. Consider a credit market with a single type of lender who is risk neutral, and 2 different types of borrowers: borrowers of type g (good) who repay loans with probability qg , and borrowers of type b (bad), who repay loans with probability qb , with qg > qb - that 2

is, the good borrowers (g types) are more likely to repay than the bad borrowers (b types). There are a large number of borrowers. (a) Assume that the lender can differentiate the g type of borrowers from the b type of borrowers -that is, there is full information. This means he can charge each type of borrower a different interest rate. Assume also that the supply of credit is perfectly elastic. Suppose that the lender wants to earn a return of r percent from each group of borrowers - good and bad. What is the interest rate he will charge to the two types of borrowers? (Hint: Lender has to take the repayment rate into consideration, to ensure he earns an effective interest rate of r.) (b) Now assume the lender cannot observe the different types of borrowers. In this case, he must charge a single interest rate to all borrowers. Let λ be the fraction of good borrowers among all borrowers. What is the interest rate r1 that the lender will charge all borrowers so that his expected return is still r? (c) Why will the interest rate r1 that you calculated in (b), induce adverse selection? Explain clearly. (d) Explain carefully why the adverse selection problem will lead to credit rationing in this market - that is, there are borrowers willing to borrow but lenders are unwilling to raise interest rates and lend. 4. A firm produces output according to the following production function: q = f (L, K) =...
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