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Wilfrid Laurier University

Economics

EC238

Karen Huff

Winter

Description

Economics 238OC: Written Assignment #1
Due Friday January 25, 2013 Instructor: K. Hu▯
Written Assignment #1: Economic Tools
This assignment covers two important skills:
1. Partial equilibrium analysis
2. Cost minimization
1. Suppose that the market for some private good involves external costs
like pollution. The supply and demand are described by linear functions
as follows:
PC = 68 ▯ Q D (1)
PP = 8 + 0:5QS (2)
Where PC and PP are the prices paid by consumers and received by
producers respectivelyD and QSare the quantities demanded and
1
supplied, respectively.
There is $24 worth of damage done every time a unit of the good is
produced.
[5] (a) Solve for the equilibrium price and quantity of this market if there
is no tax or subsidy in place.
P = P = P (3)
C P M
QS = Q D= Q M (4)
Use equations 1 and 2 to get:
68 ▯ QM = 8 + 0:5Q M (5)
60 = 1:5Q M (6)
Q M = 40 (7)
1These are sometimes called ‘inverse’ demand and supply functions because they relate
price to quantity, rather than the other way around.
1 Plugging this into either equation 1 or 2 yields:
P = $28 (8)
M
[10] (b) Calculate the total social bene▯ts, total social costs and total net
social bene▯ts associated with the market equilibrium. Show your
calculations and explain the steps brie
y in your own words. (A
diagram may help.)
P
68
S
A
28
B
C
8
D D Q
40 68
In terms of the diagram (which is not drawn to scale), we can ▯gure
out the labelled areas as follows.
1
A = (68 ▯ 28)(40) = $800 (9)
2
1
B = (28 ▯ 8)(40) = $400 (10)
2
1
C = (28 ▯ 8)(40) = $400 (11)
2
D = 8 ▯ 40 = $320 (12)
2 Then
TSB = A + B + C + D = $1;920 (13)
TPC = C + D = $720 (14)
TDC = $24 ▯ 40 = $960 (15)
TSC = TPC + TDC = $720 + $960 = $1;680 (16)
TNSB = $1;920 ▯ $1;680 = $240 (17)
Note that total social cost is made up of total private costs of pro-
duction TPC plus total damage costs (TDC). The damage costs are
not shown on the diagram to make it less messy.
[5] (c) Now suppose that the industry is taxed $27 per unit of the good.
Calculate the equilibrium quantity and prices, showing your work.
PC = P P $27 (18)
t
QD = Q =SQ (19)
The superscript t stands for tax. Use equations 1 and 2 to get:
68 ▯ Q t = 8 + 0:5Q + 27 (20)
t
33 = 1:5Q (21)
Q t = 22 (22)
Plugging this into equation 1 and 2 yields:
t
PC = 46 (23)
P t = 19 (24)
P
[10] (d) Calculate the total social bene▯ts, total social costs and total net
social bene▯ts associated with the tax equilibrium. Show your
calculations and explain the steps brie
y in your own words. (A
diagram will help.) Very brie
y explain in your own words.
Note: Total Net Social Bene▯t can be positive or negative.
3 P
68
A
46
S
B
19
C
D
8 E D
22 68 Q
The TSB is equal to the area under the MSB or demand curve which
corresponds to the area of rectangle (B + C + D + E) and the area
of triangle (A).
B + C + D + E = 22 ▯ 46 = $1;012 (25)
1
A = (68 ▯ 46) ▯ 22 = $242 (26)
2
TSB = $1;254 (27)
The TPC is equal to the area under the MPC or supply curve which
corresponds to (D) which is a triangle plus (E) which is a rectangle.
The total damage cost (not shown on the diagram) will equal the
marginal damages ($24) times the output (22) which is $528.
1
D = (19 ▯ 8) ▯ 22 = $121 (28)
2
E = 8 ▯ 22 = $176

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