Question

You will take on the role of the benevolent social planner. Remember the sole objective of a benevolent social planner is to maximize total surplus. Below are two lists of numbers. The top list represents the opportunity costs of a number of firms that supply an unspecified commodity. The bottom list includes the willingness to pay of a number of buyers who desire to purchase this unspecified commodity. Using these lists answer the following questions.

Sellers and their Opportunity Costs:

Trampled by Turtles 7

Dispatch 8

Valerie June 7

Daft Punk 2

JoshRitter 3

Delfonics 5

Yola 2

Los Lobos 5

Che Apalache 4

Buyers and their Willingness to Pay:

Dolly 4

Loretta 8

Crystal 10

Ernest 5

Dwight 7

Rosanne 10

Ronnie 7

Clint 5

Tracy 9

1. How many exchanges should occur? (1 point)

2. What is the total surplus of each exchange that occurs? Give the seller’s letter, the buyer’s letter, and the total surplus of this pair’s exchange. (1 point)

3. What is total surplus for the entire market? (1 point)

4. Assume that a price ceiling is imposed upon this market. No unit will be permitted to trade for a price above $4.50.

a. What is quantity supplied at this price? (1 point)

b. What is quantity demanded at this price? (1 point)

c. How many exchanges occur? (1 point)

5. Assume that the government has decided to impose a $3 tax per unit, to be paid by the sellers. A seller who does not sell a unit pays no tax. Therefore, the tax is like a cost increase of $3. A seller’s cost will really be $3 above the listed opportunity cost.

a. How many exchanges will occur? (1 point)

b. What is the total surplus of each exchange that occurs? Give the seller’s number, the buyer’s number, and the total surplus of this pair’s exchange. (1 point)

c. What is total surplus for the entire market? (1 point)

d. Is there any deadweight loss? If so, what is it? (1 point)

Answer 1

1) The person with highest willingness to pay will be able to buy first and the person with lowest opportunity costs will be able to sell first. And the exchange would occur only when willingness to pay is higher than the opportunity cost.

So, arranging the willingness to pay in descending order, we get, 10,10,9,8,7,7,5,5,4

Arranging the opportunity cost to the buyer in ascending order, we get, 2,2,3,4,5,5,7,7,8.

Here we can see that it is only till the 6th numbers that the willingness to pay is higher than the opportunity costs. So in total only 6 units will be sold.

2) The exchanges and the total surplus will be

Seller	Buyer	Total surplus
Y	C	10-2 = $8
D	R	10-2 = $8
J	T	9-3 = $6
C	L	8-4 = $4
L	R	7-5 = $2
D	D	7-5 = $2

3) The total surplus of the entire market =

= 8+8+6+4+2+2

= $30.

4) a) Now, if the price ceiling of $4.5 is imposed, the quantity supplied at this price will be only 4 units, because only the sellers whose opportunity cost of production is less than $4.5 will be willing to sell the good.

b) The total quantity demanded at the price of $4.5 will be 8 units, because all the people who are willing to pay more than $4.5 will be wanting to buy the good.

c) As the demand is of 8 units but the supply is of only 4 units, the number of exchanges that would occur will be 4. So, total number of exchanges that would occur at a price ceiling of $4.5 will be 4.

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