Name:_____Solutions__________
SE201: PRINCIPLES OF MICROECONOMICS
Assignment 7: Due Wednesday 10/19/15
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Make sure you show your work and that ALL answers are complete and neatly
written.
Only work that follows these instructions and represents a “Good Faith Effort” to
answer the questions posed will receive a check. (Copying answers from a classmate
without working through the problems is unacceptable conduct).
Stop by during my office hours (MW period 5, 6) if you have questions, or set up
another time to meet with me.
Read Chapters 6 - 9 of your textbook. Answer the following questions that cover efficiency,
government policies, and trade.
1. Assume the world consists of two countries, the U.S. and Mexico. Assume the U.S. sugar
market is perfectly competitive and the market demand is:
Qd  70  2 P
where P is the price per pound, and Qd is the total yearly quantity demanded (in millions
of pounds) in the U.S. The supply of sugar is given by:
Qs  8P
Assume the Mexican sugar market is also perfectly competitive and the market demand
is:
Qd  20  P
where P is the price per pound, and Qd is the total yearly quantity demanded (in millions
of pounds) in Mexico. The supply of sugar is given by:
Qs  4 P
Given the information above, complete all of the following (show your work for each
question on the last two pages marked “worksheets”):
a) Find the equilibrium price and quantity in both markets assuming there is NO
TRADE.
U.S.
PE = $__7__ per pound
Mexico
PE = $__4__ per pound
QE = _56___ million pounds per year
QE = _16___ million pounds per year
b) Find consumer surplus (CS), producer surplus (PS), and total surplus (TS) in each
market, assuming there is NO TRADE.
U.S.
CS = $__784__ million per year
Mexico
CS = $__128__ million per year
PS = $__196__ million per year
PS = $__32___ million per year
TS = $__980__ million per year
TS = $__160__ million per year
c) Find the new equilibrium price paid by consumers, the final price received by
producers, the new consumer surplus (CS), the new producer surplus (PS), tax
revenue generated, and deadweight loss (DWL) in the U.S. if the U.S. government
imposes a tax of $2 per pound on the sellers of sugar.
PC (paid by consumers)
= $__8.60__ per pound
PP (received by producers after paying tax) = $__6.60_ per pound
QE = _52.8_ million pounds per year
Tax revenue = $_105.6_million per year
CS = $_696.96_ million per year
TS = $__871.20 _ million per year
PS = $_174.24_ million per year
DWL = $_3.2_ million per year
d) Find the deadweight loss (DWL) in the U.S. if the U.S. government imposes a price
ceiling of $5 per pound on sugar.
DWL = $_80_ million per year
Now assume there is FREE TRADE between the U.S. and Mexico.
e) Find each of the following. (Hint: To find the world equilibrium price and quantity,
first find the world demand and world supply of sugar.)
PEWorld = $_6_ per pound
U.S.
QEWorld = _72_ million pounds per year
Mexico
QD = _58_ million pounds per year
QS = _48_ million pounds per year
QD = _14_ million pounds per year
QS = _24_ million pounds per year
Imports / Exports (circle one) = 10_mil.
Imports / Exports (circle one) = 10_mil.
CS = $__841___ million per year
PS = $__144____ million per year
CS = $___98___ million per year
PS = $__72____ million per year
TS = $__985__ million per year
TS = $__170___ million per year
Gains from trade = $_5___ million/year
Gains from trade = $_10__ million/year
Worksheets
a)
Price
Price
Supply
Supply
Pe
Pe
Demand
0
Demand
Qe
0
Quantity / year
In U.S.
70-2P = 8P
Pe = $7
Qe = 8(7) = 56 million
Qe
Quantity / year
In Mexico
20-P = 4P
Pe = $4
Qe = 4(4) = 16 million
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b)
Inverse demand in U.S. is P = 35 – 0.5 Q. Inverse demand in Mexico is P = 20 – Q.
Consumer surplus is the area above the equilibrium price but below the (inverse) demand curve.
Producer surplus is the area below the equilibrium price but above the (inverse) supply curve.
CSUS = ½ * (35 – 7)*56 = $784 million/day
PSUS = ½*(7-0)*56 = $196 million/day
TSUS = CS + PS = $980 million
CSMEX = ½ * (20 – 4)*16 = $128 million/day
PSMEX = ½*(4-0)*16 = $32 million/day
TSMEX = CS + PS = $160 million
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c)
Supply with tax
Price
Supply
tax
Pe
Demand
0
Qe
Quantity / time
The inverse supply curve with tax is P = 2 + (1/8)Q which gives a supply curve of Q = 8P – 16. The
new equilibrium (consumer) price paid is where
70 – 2P = 8P – 16
Pc = $8.60
Qe = 52.8 million
Pp = $8.60 - $2 tax = $6.60 is the new price received by producers
CSUS = ½ * (35 – 8.60)*52.8 = $696.96 million/day
PSUS = ½*(6.60-0)*52.8 = $174.24 million/day
Tax revenue US = $2*52.8 = $105.60 million
DWLUS = ½ * ($2)*(56 - 52.8) = $3.2 million/day
Notice that the DWL is exactly equal to the former total surplus (no tax) – (CS + PS + tax revenue) =
$980 – (696.96+174.24 + 105.60) = $3.2 million
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d)
Price
Supply
Pe
Demand
0
Qe
Quantity / year
The price ceiling reduces Qs to 40 million. The DWL is the area between the demand and supply
curves from 40 million to 56 million. (Note that the price on the demand curve corresponding to Q =
40 is $15). So
DWLUS = ½ * ($15-5)*(56 - 40) = $80 million/day
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e)
Price
Supply
Pe
Demand
0
Qe
Quantity / year
Price
Supply
Pe
Demand
0
Qe
Quantity / year
World demand is the horizontal sum of the demand in each country, which is Qd = 90 – 3P.
World supply is the horizontal sum of the supply in each country, which is Qs = 12P.
This yields,
90 – 3P = 12P
Pe = $6 / lb
Qe = 72 million lbs.
At P =$6 lb,
QdUS = 58 million/day
QsUS = 48 million/day
U.S. imports 10 million lbs / day.
QdMEX = 14 million/day
QsMEX = 24 million/day
Mexico exports 10 million lbs / day.
CSUS = ½ * (35 – 6)*58 = $841 million/day
PSUS = ½*(6-0)*48 = $144 million/day
TSUS = CS + PS = $985 million
Gains from trade in U.S. = $5 million (found by comparing TS here to earlier with no trade)
CSMEX = ½ * (20 – 6)*14 = $98 million/day
PSMEX = ½*(6-0)*24 = $72 million/day
TSMEX = CS + PS = $170 million
Gains from trade in Mexico = $10 million (found by comparing TS here to earlier with no trade)