Problem Set 3 W11 Key

8/7/2019 Problem Set 3 W11 Key

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Econ 200B Winter 2011 - Key

Problem Set 3 - Distributed: 01/25/11

Textbook Problems

Chapter 4:

2 & 3: Answer in the text

6. The total amount of sellers rents and consumers surplus is maximized when the quantity

demanded equals quantity supplied. The price at which the units are exchanged affects only the

distribution of rents between buyers and sellers.

8. Markets with many buyers and sellers establish a uniform price for a good. Each person

makes purchases or sells the good until his or her marginal value equals that price. Therefore,

everyones marginal values of the good are equal (to the common price). This shows that such

markets exhaust the gains from trade. Although all buyers and sellers engaged in trade have the

same marginal value for the good, this does not imply that everyone buys or sells the same

amount. Most individuals have different marginal value schedules for goods because marginal

values depend on personal tastes and incomes which are not uniform across individuals.

10. Middlemen exist because they produce something of value. They lower the transaction

costs and hence the prices of goods consumers desire. Eliminating the profits of the middlemen

in markets unrestricted by legal barriers against trade would not be in the interest of

consumers because this would result in more costly goods to consumers as more expensive

means are employed to bring seller and buyer together. High transactions costs explain thegeneral absence of truck farmers. It is much cheaper for farmers to do what they do best,

farming, and to pay middlemen to take their produce to retailers.

12 & 16: Answer in the text.

Additional Problems

1. Assume that the supply schedule for the person in problem 2a. above can be linearized.Draw their supply curve. Be sure to label all axes, and intercepts.

See below.


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2. You are a research assistant who finds the schedule of supply and demand for haircutsgiven in the table below.

Price ($/haircut) Q demanded (haircut/day) Q supplied (haircut/day)

0 100 010 80 0

20 60 20

30 40 40

40 20 60

50 0 80

a. Assuming that both supply and demand are linear, draw the supply and demandcurves on a graph. Use only one graph, and be sure to label all relevant points.

Price Supply

Qty

$8

$17

Price

Qty

$50

40 100

$30

S

D

$10


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b. Find the point where supply and demand intersect and label it.See graph

c. At what price and quantity does this happen?Q*=40, p*=$30

d. What are the total gains from trade when the market price and quantity arethose found in part c?

Total gains from trade is the area of the triangle under the demand curve and

above the supply curve on the graph from part a. This area= b*h = 40*($50-

$10)=$800.

e. What is the sellers rent in part d?The sellers rent is the area of the triangle below a straight line drawn from the

price and above the supply curve. This area = (40)*($30-$10)= $400.

f. What is the consumer surplus in part d?The consumer surplus is the area of the triangle below the demand curve and

above a straight line drawn horizontally out from the price. This area =

(40)*($50-$30)= $400. It can also be found from Consumer Surplus = Total Gains

from Trade - Sellers Rent = $800-$400 = $40.

3. Repeat a-f of Question 2 for the supply and demand schedules for running shoes.Price ($/pair) Q demanded (pairs/day) Q supplied (pairs/day)

60 1000 400

70 900 500

80 800 60090 700 700

100 600 800

110 500 900

a. Assuming that both supply and demand are linear, draw the supply and demandcurves on a graph. Use only one graph, and be sure to label all relevant points.


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Note that I had to do some calculations to find the y-intercepts of the demand

and supply curves (p=$160 & p=$20) and the x-intercept of the demand curve

(Q=1600).

b. Find the point where supply and demand intersect and label it.

See graph.

c. At what price and quantity does this happen?Q*=700, p*=$90

d. What are the total gains from trade when the market price and quantity arethose found in part c?

Total gains from trade is the area of the triangle under the demand curve and

above the supply curve on the graph from part a. This area= b*h =

700*($160-$20 )= 700* ($70) = $49,000.

e. What is the sellers rent in part d?The sellers rent is the area of the triangle below a straight line drawn from the

price and above the supply curve. This area = 700*($90-20) = 700 * ($35) =

$24,500.

Price

Qty

$160

700 1600

$90

S

D$20


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f. What is the consumer surplus in part d?The consumer surplus is the area of the triangle below the demand curve and

above a straight line drawn horizontally out from the price. This area = 700*($160-$90)= 700 * ($35) = $24,500. It can also be found from Consumer

Surplus = Total Gains from Trade - Sellers Rent = $49k - $24.5k = $24.5 k.

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Problem Set 3 W11 Key