Assignment #1

Total: 24 Q1) 5Q2) 7Q3) 8Q4) 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 1Economics 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)

Economics

Hours of

study

score MB

0 20 -

1 45 25

2 65 20

3 75 10

4 83 8

5 90 7

6 92 2

Mathematics

Hours of

study

score MB

0 40 -

1 52 12

2 62 10

3 71 9

4 78 7

5 83 5

6 86 3

Statistics

Hours of

study

Score MB

0 80 -

1 90 10

2 95 5

3 97 2

4 98 1

5 99 1

6 99 0

1

2

3

4

5

6

•She should spend 3 hours on Economics, 2 hours on Mathematics and 1 hour on Statistics

•Using Allocation Rules

• 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 (1)

• 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 (2)

Canada’s PPC

Cars (million per year)

wheat (million per year)

20

10

0

150 300

•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

•Slope = 1/15, or, opportunity cost of producing wheat is 1/15 cars

Question 2 (3)

• 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 (4)

•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

•If Canada continues to consume 10 million car, then it obtains an extra 50 bushels of wheat

•Canada should accept the dealCanada’s PPC

Cars (million per year)

wheat (million per year)

20

10

0150 300

A

200

Question 2 (5)

• 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 (1)

• 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 (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

• 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 (3)

• 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

Qa Pb Q b = Pa or Pa Qa = Pb Qb

Question 3 (4)

Country A Country B

Pa Qa + Pb Qb = Pa Qa Pa Qa + Pb Qb = Pb Qb

• 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 (5)

• 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 (6)

• 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 (7)

• 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 3 (8)

• 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 (1)

• 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 (2)

• 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

Question 4 (3)

End of Assignment 1