Transcript Assignment #1

Assignment #1
Total: 24
Q1) 5
Q2) 7
Q3) 8
Q4) 4
Question 1
• A college student who is cramming for final exams has only six
hours of study-time remaining. Her goal is to get as high an
average score as possible in three subjects: Economics,
mathematics, and statistics. She must decide how to allocate
her time among the subjects. According to the best
estimates, her score in each subject will depend upon the
time allocated to it according to the following schedule. How
should the student allocate her time?
Question 1
Economics
Mathematics
Statistics
Hours of
study
score
Hours of
study
score
Hours of
study
Score
0
20
0
40
0
80
1
45
1
52
1
90
2
65
2
62
2
95
3
75
3
71
3
97
4
83
4
78
4
98
5
90
5
83
5
99
6
92
6
86
6
99
Solution to Question 1 (1)
•
The general rule for allocating a resource efficiently across different
production activities is:
– Allocate each unit of the resource to the production activity where its
marginal benefit is highest.
• She should allocate her first additional hour to the subject in which it will
give her the highest marginal benefit
• Then allocate her second additional hour to the subject in which it will
give her the second highest marginal benefit…..
• Until her six hours of studying are all occupied
Solution to Question 1 (2)
•Using Allocation Rules
Economics
Mathematics
Statistics
Hours
of
study
score
MB
Hours
of
study
score
MB
Hours
of
study
Score
MB
0
20
-
0
40
-
0
80
-
1
45
25 1
1
52
12
3
1
90
10
2
65
2
62
10
5
2
95
5
3
75
20 2
10 4
3
71
9
3
97
2
4
83
8
4
78
7
4
98
1
5
90
7
5
83
5
5
99
1
6
92
2
6
86
3
6
99
0
•She should spend 3 hours on Economics, 2 hours on Mathematics and 1 hour on
Statistics
6
Question 2 (1)
• Suppose that there are 10 million workers in Canada, and that each of
these workers can produce either 2 cars or 30 bushels of wheat in a year.
• a) What is the opportunity cost of producing a car in Canada? What is the
opportunity cost of producing a bushel of wheat in Canada? Explain the
relationship between the opportunity costs of the two goods.
• Opportunity cost of producing a car is 15 bushels of wheat
• Opportunity cost of producing a bushel of wheat is 1/15 cars
•
•
If Canada wants to produce a car, it needs to give up 15 bushels of wheat.
If Canada wants to produce a bushel of wheat, it needs to give up 1/15 cars.
Question 2 (2)
• b) Draw Canada’s production possibilities curve. If Canada chooses to
consume 10 million cars, how much wheat can it consume without trade?
Label this point on the production possibilities curve.
• 10 million workers, each can produce either 2 cars or 30 bushels of wheat
• The maximum amount of cars can produce
- 10 millions workers x 2 cars/worker is 20 million cars
• The maximum amount of wheat can produce
- 10 millions workers x 30 bushels of wheat is 300 million bushels of wheat
• If Canada chooses to consume 10 million cars, it needs to have
- 5 million workers in producing 10 million cars
- Thus, leaving 5 million workers to produce wheat and producing 150
million bushels of wheat without trade
Question 2 (3)
•Canada can consume 10 million cars and 150 million bushels of
wheat without trade
•This point should lie on the curve and is efficient and obtainable
Cars (million
per year)
•Slope = 1/15, or, opportunity cost of producing wheat is 1/15 cars
20
Canada’s PPC
10
0
150
300
wheat (million per year)
Question 2 (4)
• c) Now suppose that the United States offers to buy 10 million
cars from Canada in exchange for 20 bushels of wheat per car.
If Canada continues to consume 10 million cars, how much
wheat does this deal allow Canada to consume? Label this
point on your diagram. Should Canada accept the deal?
Question 2 (5)
•If Canada accepts the deal, it gets 200 million
bushels of wheat, at point A
•This point lies beyond Canada’s PPF which was
initially unattainable without the trade with US
Cars (million
per year)
20
•If Canada continues to consume 10 million car,
then it obtains an extra 50 bushels of wheat
Canada’s PPC
•Canada should accept the deal
A
10
0
150
200
300
wheat (million per year)
Question 3 (1)
• Country A has 1200 units of labor available. It can produce
two goods, apples and bananas. The unit labor requirement in
apple production is 3, while in banana production it is 2. (The
unit labor requirement of a good is the amount of labor
required to produce one unit of that good.) There is another
country, country B, with a labor force of 800. B's unit labor
requirement in apple production is 5, while in banana
production it is 1. Suppose people in both countries have the
same preferences so that, for each country, the following
holds: quantity demanded for apples/quantity demanded for
bananas = price of bananas/price of apples. Find out the
prices of the goods over which they are exchanged. (Hint: the
prices are such that, for each good, the total demand by both
countries is equal to the total supply by both countries.)
Question 3 (2)
Country
To make 1 apple
To make 1 banana
A (1200 units of
labor)
3 labors
2 labors
B (800 units of
labor)
5 labors
1 labor
• Country A
- Opportunity cost to make 1 apple = 1.5 bananas
- Opportunity cost to make 1 banana = 2/3 apple
• Country B
- Opportunity cost to make 1 apple = 5 bananas
- Opportunity cost to make 1 banana = 1/5 apple
• Country A has a comparative advantage on producing apple
• Country B has a comparative advantage on producing banana
Question 3 (3)
• Find the prices of the goods over which they are exchanged
• The most beneficial way to trade is for each country to
specialize completely using all of their available resources
• Country A will produce 400 apples using 1200 units of labor
• Country B will produce 800 bananas using 800 units of labor
Question 3 (4)
Qa
Pb
Q b = Pa
or Pa Qa = Pb Qb
• The preferences from both countries imply that, both
countries,
- i) will demand the same quantity of apples and same
quantity of bananas
- ii) will spend the same amount of money on buying apples
and bananas; therefore, the total spending on apples and
bananas must equal to each country’s total revenue
Country A
Country B
Pa Qa + Pb Qb = Pa Qa
Pa Qa + Pb Qb = Pb Qb
Question 3 (5)
• Thus, find the prices such that, the total spending on apples
and bananas equals to the country’s revenue; and the total
world demand of each good equals to the total world supply
of each good.
• i) Total production of Apple = 400 apples,
- Country A demands 200 apples
- Country B demands 200 apples
• Total production of Banana = 800 bananas,
- Country A demands 400 bananas
- Country B demands 400 bananas
Question 3 (6)
• ii) Each country’s total spending = total income
- Country A: 200Pa + 400Pb = 400Pa
- Country B: 200Pa + 400Pb = 800Pb
• Solving these two equations,
Pa = 2Pb
• If Pb = $1, then Pa = $2
Question 3 (7)
• Pb = $1, Pa = $2
• Country A,
- Produces 400 apples, total income is $800
- Total Demand on apple is 200, total cost on apple is $400
- Total Demand on banana is 400, total cost on banana is $400
• Country B,
- Produces 800 bananas, total income is $800
- Total Demand on apple is 200, total cost on apple is $400
- Total Demand on banana is 400, total cost on banana is $400
• At this price, for each country, total spending on apples and
bananas equals to its revenue
Question 3 (8)
• In equilibrium, Pa = 2Pb
• The world quantity demanded for apple = The world quantity
supplied of apple
• The world quantity demanded for banana = The world
quantity supplied of banana
• No country can benefit from readjusting her consumption
decisions and her production plans
Question 4 (1)
• Q2. From Chapter 3
• How would each of the following affect the U.S. market supply
curve for corn?
 Factors affecting the supply curve
-changes in cost of production
-improvement in technology
-expectation of future prices
-changes in suppliers
-changes in weather
Question 4 (2)
• a) A new and improved crop rotation technique is
discovered.
-This new technique is an improvement in technology
-Enables more crops to be produced with the same inputs
-The supply curve shifts right
• b) The price of fertilizer falls.
-Fertilizer is an input used in the production of corn
-Price of fertilizer falls leads the cost of corn production decrease
-Lower input prices shift the supply curve to right
Question 4 (3)
• c) The government offers new tax breaks to farmers.
-This new tax saving makes farming relatively more profitable than
before
-More people would switch to farming, thus increase in the number
of suppliers
-Supply curve shifts right
• d) A tornado sweeps through Iowa.
-Tornado destroys the corn production
-Supply curve shifts left
End of Assignment 1