# Karan Assignment 8 Revised

```Assignment 8 Notes

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There are two countries in the world, France and Germany, and both can use workers to produce either cheese
o France can produce either a ton of cheese or a ton of bread with 3 workers.
o Germany can produce a ton of cheese with 6 workers and a ton of bread with 3 workers.
France has 120 workers;
Germany has 150 workers.
Initially, there is no trade between the two countries.
Workers (L)
Germany:
150
France
120
Cheese
150
=
6
120
=
3
150
=
3
120
=
3
PPF: Production Possibilities Frontier
 Line representing the amount of production a country can have between two goods, assuming that it’s at a
maximum level of efficiency (capital being used efficiently, and Natural Rate of Unemployment)
 By knowing how much each country can make, we can create a linear function (y =mx+ b) to represent the PPF
 (Total Cost)*X + (Total Cost)*Y = Total Resources
 Y = mx + B
 Y = (slope)(X) + B
 2x+ 4y = 8
 X + 2y =4
 2y = 4 – x
 Y=2–½x
 The PPF is about opportunity cost and trade-offs.
o How many of each do you make?
o How much will you be giving up to make a ton (of whatever good you’re looking at)?
Solving these types of problems:
 These problems can be solved best by always conceptually understanding what’s going on
o Means having a graph off the PPFs
o Means understanding what input is required to make a ton of each good
 Put in terms of the other good (that you’re not solving for), in order to better compare them
 The relative cost of producing each good
 The relative price of each good in each country
 The opportunity cost of making each good
 What did you have to forego (in terms of producing the other good), in order to make a
ton of this good?
 How many tons of the other good could you make per 1 ton of this good?
 Ex: How much bread can Germany make per ton of cheese?

   ℎ – gives us how much bread Germany can make per ton of cheese

o
50
25
= 2            ℎ
 ℎ        ℎ    2
Means understanding what the relative output is of each good
 Rate of Production
 How much bread can you make for every ton of cheese?
Assignment 8
1. What is each country's cost of producing bread? Write the production possibilities frontier in the
form that shows the cost of producing each good.

Relative prices are equal to the opportunity cost of production.
o If a positive amount of both goods are demanded, in equilibrium, the cost of purchasing a good must
equal the cost to produce the good.
Relative Price:
Comparative Cheese
Cost for 1 ton of Cheese
Cost for 1 ton of Bread
Relative Price
Germany:
6L/ton 50    = 2 tons of bread 3L/ton 25   ℎ= ½ ton of cheese 2
25   ℎ
50
1   ℎ
France
3L/ton 40    = 1 ton of bread 3L/ton 40   ℎ= 1 ton of cheese 1
40   ℎ
40
1   ℎ
1 ton of Bread, it cost ½ tons of cheese
1/2 B + 1C = 25
How much of other good for 1 ton of the good you’re focusing on
How much could Germany have produced instead of a ton of cheese? 2 tons of bread  Cost them 2 tons of bread to make a ton
of cheese
Germany: C =25 – ½ B
Y = 25 – ½ X
C + 1/2 B = 25
France: C = 40 - B
2. Draw the production possibilities frontier for each country. How much bread can France
produce if it produces 10 tons of cheese? How much bread can Germany produce if it produces
10 tons of cheese?

The equation of a line  Y = y-intercept + (slope)X

∆  ℎ
o Slope
=
=how much cheese can you make instead of 1 ton of bread?
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The only reason it’s not the other way around is because I made cheese the y-intercept
Germany:
o y-intercept = max amount of cheese possible = 25
o Slope = how much cheese they could make instead of 1 ton of bread = ½
o PPF  C = 25 – ½ B

Germany:
Y- intercept = 25
25
Slope = = .5
50
10= 25 -.5(B)
10= 25 – ½ *B
-15= - ½ B
B = 30
∆
France:
Y-intercept = 40
Slope = 1
C = 40 - B.
B = 40 – 10
B = 30
Cheese
50
40
30
20
10
10
20
30
40
Germany:
(6 workers per ton)*(10 tons) = 60 workers
150L total – 60L for cheese = 90L for bread
90
=
3
50
France:
(3 workers per ton)*(10 tons) = 30 workers
120L total – 30L for cheese = 90L for bread
90
=
3
3. What is the opportunity cost of producing bread for each country?
First Question was finding how much of each goes into making 1 ton of initial good.
- Finding the Relative Input
Another Outlook  finding how much of the other good is made when we make 1 ton of initial good
- Finding the Relative Output
How much cheese is output per ton of the bread?
Rate of Production
Comparative
Germany:
Cheese: Relative Output
6
25   ℎ
50
France
40   ℎ
40
1
= tons of cheese per bread
3  ℎ
= 2 tons of bread per cheese
2
3
= 1 cheese per bread
3  ℎ
= 1 ton of bread per cheese
PPF: In terms of Labor
Germany:
3B + 6B = 150
B + 2C = 50 - Same as B = 50 – 2C OR C = 25 – ½ B
France
3B + 3C = 120
B + C = 40
To find Opportunity Cost, ask simple question about each good:
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What do I have to give up to get 1 ton? Same shit as Relative Input/Costs
It’s always in terms of the other good  How much of the other good could you have made?
Germany:
France
Cheese
2 tons of bread
1 ton of bread
.5 tons of cheese
1 ton of cheese
4. Suppose the relative price is 1.25 tons of cheese for 1 ton of bread. Are they willing to trade? If
so, who exports bread? Who exports cheese? Assuming they do specialize and trade, draw the
new PPF under trade for each country
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1.25 tons of cheese = 1 ton of bread  Value
Bread is more expensive than C
With PPF, we’re talking about quantity
Amount of bread will be less than cheese
1.25*(Quantity of Bread) = Quantity of Cheese
1
1.25B = 1.25
B = .8C  the exact same thing as 1.25B = C
Opportunity Cost:
o France: 1C = 1B  Relative Cost is 1 ton of B for 1 ton of Cheese
o They want to get cheese or read more efficiently
Opportunity Cost
Germany:
France
Cheese
2 tons of bread
1 ton of bread
.5 tons of cheese
1 ton of cheese

o France can make cheese more efficiently than Germany
o Germany can make Bread more efficiently than France

If Germany can make ½ ton of Cheese for 1 bread
o They want to be able to get more Cheese for bread
o They want it to be higher than .5
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Germany will trade at any rate less than 2 Bread for 1 cheese
France can make 1 bread for 1 cheese
o So they’ll trade between 1 and 2
France
1B <C < 2B
Germany
.5C < B < 1
 exact same thing
Germany will trade Bread at any rate between .5 tons of cheese and 1 ton of cheese (what France makes it at)
Rate of Cheese
.75
1
1.25
France:
Germany:
What’s the trade rate?
#4.) B =1.25C  C = .8B
#5.) 1C = 1.25B  B = .8C
TRADE AT THAT RATE
1.5
1.75
2
2.25
5. Suppose the relative price is 1.25 tons of bread for 1 ton of cheese. Are they willing to trade? If
so, who exports bread? Who exports cheese? Assuming they do specialize and trade, draw the
new PPF under trade for each country.
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1.25 tons of bread traded for 1 ton of cheese
Value of 1 ton of Cheese > Value of 1 ton of Bread
(Amount of Cheese)*1.25 = Amount of Bread
B = 1.25C  C = .8B
Comparative
Germany:
Cheese: Relative Output
2 tons of bread per cheese > 1.25
25   ℎ
50
40   ℎ
France
40
1
= <.8
2
1 ton of bread per cheese < 1.25
= 1 > .8
Better than trading 1 for 1
Max Cheese
Germany:
Produced 50 tons of bread…
40 tons of cheese
50 tons
France
40 tons
Produced 40 tons of cheese
Traded 40 cheese for:
50 tons of bread
Cheese
50
40
30
20
10
10
20
30
40
50
6. Suppose the price of bread in both countries is \$1000/ton. Before the Treaty of Rome (meaning
with no trade), what is the price of 1 ton of cheese in France? What is the price in Germany?
Germany: Price of Bread = \$1000/ton
 25 tons of cheese = 50 tons of bread
o There is half as much so it will be twice as expensive
 Input to make cheese = relative price of producing cheese
o Input to make Cheese = 2 tons of Bread  \$2000
France: Price of Bread = \$1000
Input to make Cheese = 1 ton of Bread  \$1000
7. Suppose that after the Treaty of Rome (with trade) the price of bread remains at \$1000/ton.
What would be the price of cheese under the relative price in Question 4? How about under the
relative price of Question 5?
[Hint: If a country refuses to trade its price under trade is the same as under autarchy.]
a.) 1 ton of Bread = 1.25 tons of Cheese
Value  1.25B = C
1.25*(\$1000)
C= \$1250  more expensive for France
C= \$1,000 for France  they don’t trade
C = \$2,000 for Germany
b.) 1 ton of cheese = 1.25 tons of bread
Value  1.25C = B  C= .8B
\$1000 = 1.25C
C = \$800
8. Suppose that before trade France produced 30 tons of bread and 10 tons of cheese. Assuming
all workers are paid the same wage and labor is the only input of production, what is the
nominal wage before trade? What is the nominal wage after trade?

Nominal Wage = #
120 Workers get same wage
France: B = 30, C = 10
Step i.) Find Labor for each
B  3L  90L
C  3L  30L
Labor for Cheese
1/3LC = 10
LC = 30
1/3LB = 30
LB= 90
Step ii.) Nominal GDP
Nominal GDP = (C)*C + (PB)*B
Total Cost*Cheese + Total Cost* Bread= Total Resources (Nominal GDP)
Nominal GDP = 30*1000 + 10*1000
= \$30,000 + \$10,000 = \$40,000
Step iii.) Nominal Wages
Nominal Wages =
\$40,000
=
120
\$333 per worker
Scenario 1:
Value of 1 ton of bread = Value of 1.25 tons of cheese
C = 1.25B
Price of Bread = \$1000
Price of Cheese to trade = \$1,250
Price of Cheese to produce = \$1,000
Scenario 2:
1 ton of cheese = 1.25 tons of bread
B = 1.25C  .8B = C
Price of bread to Produce = \$1000
Rate
Price of Cheese
France
Sell 1 B for
1.25C
\$800
Value of 10C
\$800* 10 tons=
\$8000
Value of 30B
Total Value of
30B and 10C
Wages
\$30,000
\$38,000
Wages =
\$,

= \$

9. Suppose that the average French consumer buys  tons of bread and  tons of cheese.
(This is 500 pounds of bread and 166.66 pounds of cheese. The French love their bread and cheese…)
Assuming the year before trade is the base year, what is France's real wage before and after

CPI: Consumer Price index (that we can solve for)
o Used to measure inflation vs a base year of 100
o Let’s assume that the CPI before trade = 100
o Therefore, wages are still \$333

CPI = 100*

Inflation =


Nominal GDP before trade = \$40,000
Nominal GDP after trade = \$32,000

−  ℎ
=

100
38,000
CPI = 40,000 ∗ 100 =(.95)100 = 95

Real Wages =
\$316.67
∗ 100
95
∗ 100
= \$333  the deflation (-5% inflation) meant that the \$316.67 wages after trade had the same value as
the \$333 wages before trade opened up
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