Exercise 2

Due Wednesday 9/13

Please note that the parts below are completely separate: part B does not involve any of the information from part A, etc.

Part A

1. Suppose that a researcher has collected willingness to pay and willingness to accept data from the pool of potential buyers and sellers of a particular good, and has found that the data can be summarized by the equations below:
   
   WTP = 700 - 2*Q
   
   WTA = 100 + 4*Q
   
   Please graph the two equations and solve for the market equilibrium price and quantity. Be sure to label the axes, show the numerical value of each intercept, and indicate the equilibrium clearly.
2. Calculate consumer, producer and social surplus for the equilibrium in question A1.
3. Now suppose that a new regulation limits the total number of trades in the market to 50 or less. How many of the trades from question A1 would be eliminated? Assuming that only the least valuable trades are eliminated, what is the total dollar value of social surplus lost due to the regulation? In this situation, term "least valuable" means the trades that generate the least social surplus, which will be the ones to the right of the Q=50 line.
   
   Please note that you only need to calculate the lost amount of total social surplus; you do not need to find the new market price, nor do you have to figure out what happens to CS and PS separately.
4. Copy your graph from A1 and then show the effect of the regulation in A3. As in A1, be sure to label the graph thoroughly.

Part B

1. Suppose that the following information has been obtained about a second market:
   
   WTP =120 - 0.05*Q
   
   WTA = 20
   
   That's not a typo: there's no Q in the WTA equation. That means the suppliers are willing to sell any number of units as long as they receive at least $20 for each one. Please graph the two equations, find the market equilibrium, calculate consumer and producer surplus, and show everything on a well-labeled diagram.
2. Now suppose that a regulation reduces the number of trades in this market by 20%. That is, suppose that the last 20% of the trades you calculated in B1 do not occur. Please calculate the lost social surplus. How much of that is consumer surplus? Producer surplus? Discuss briefly.

Part C

1. Suppose that a third market has two different types of buyer. The willingness to pay for an individual buyer i of each type is given below, where WTPi means the willingness to pay for buyer i and Qi is buyer i's quantity:
   
   Type 1: WTPi = 100 - 0.5*Qi
   
   Type 2: WTPi = 100 - Qi
   
   Please solve for the demand curve for each type (that is, the quantity demanded as a function of the price P).
2. In the market as a whole, there are 5 type-1 buyers and 10 type-2 buyers. Please use your results from C1 to obtain an equation for the overall market demand.
3. The market supply for the good is given by the equation below:
   
   Qs = 20*P
   
   Please find the equilibrium price and quantity in the market.
4. Using your results from C3, find the quantity each individual buyer will purchase, the amount of consumer surplus each will receive, and the total consumer surplus received by the buyers as a group.
5. Finally, calculate the producer surplus and the total social surplus produced by the market.