Problem 1. Basic Math Review: Use the following sets of information to answer this set of questions.
a. You are told that there are two linear lines in a coordinate graph with x the variable on the horizontal axis and y the variable on the vertical axis. The first line contains the points (5, 10) and (10, 20), while the second line contains the points (0,20) and (10,0). From this information find the equations for lines 1 and 2 and the solution for this set of equations.
b. You are told that there are two linear lines in a coordinate graph with x the variable on the horizontal axis and y the variable on the vertical axis. The first line has a slope of -1 and contains the point (100,100). The second line has a y-intercept of 20 and in addition, you know that every time the x variable increases by 10 units the y variable increases by 20 units. From this information find the equations for lines 1 and 2 and the solution for this set of equations.
c. You are told that there are two linear lines in a coordinate graph with x the variable on the horizontal axis and y the variable on the vertical axis. You are told that initially the two lines can be described by the two equations Y = 10 – X and Y = X. Then, you are told that at every y value the amount of the x variable has increased by 5 units for the first equation (Y = 10 – X). What is the initial solution for the original two equations? What is the new equation for the first line after the described change? What is the new solution for the revised set of equations?
d. You are told that there are two linear lines in a coordinate graph with x the variable on the horizontal axis and y the variable on the vertical axis. The first line is a vertical line where the value of x is always equal to 10 no matter what the value of y. The second line has a slope equal to -2. The solution for the two equations is given by (10,80). What are the equations for the two lines?
Problem 2. PPF and Opportunity Cost: The table below provides information about the production possibility frontier for Economy Z. This economy’s PPF is linear between each of the points given in the table (thus, the PPF is linear between points A and B, linear between points B and C, but not linear between points A and C). Use this information to answer this set of questions.
Butter per Year Guns per Year
(in pounds) (number of guns)
A 100 0
B 80 50
C 60 90
D 40 120
E 20 140
F 0 150
a. Suppose that Economy Z is currently producing at point C. What is the opportunity cost of producing 20 more pounds of butter?
b. Suppose that Economy Z is currently producing at point C. What is the opportunity cost of producing 30 more guns?
c. Suppose that Economy Z is currently producing at point D. What is the opportunity cost of producing one more pound of butter?
d. Suppose that Economy Z is currently producing at point B. What is the opportunity cost of producing one more gun?
e. Draw a sketch of Economy Z’s PPF with Butter on the x-axis and guns on the y-axis. Does this PPF exhibit increasing opportunity costs with regard to gun production? Explain your answer.
f. Looking at your sketch of Economy Z’s PPF from part (e), does this PPF exhibit increasing opportunity costs with regard to butter production? Explain your answer.
g. Suppose that Economy Z is currently producing 70 pounds of butter. Is it possible for Economy Z to also produce 75 guns at the same time given their resources, technology and the time period?
h. Suppose that Economy Z is currently producing 25 pounds of butter and 110 guns. Is this point of production both feasible and efficient? Explain your answer.
Problem 3. PPF and Comparative Advantage: Suppose there are two individuals: Bob and Sue. Both Bob and Sue produce two different goods: clarinets and drums. Each of them have the same amount of resources, the same technology, and the same amount of time to spend producing clarinets and drums. If Bob devotes all of his time, resources, and technology to producing clarinets he is able to produce 1000 clarinets and 0 drums. When Bob devotes all of his time, resources and technology to producing drums he is able to produce 500 drums and 0 clarinets. If Sue devotes all of her time, resources, and technology to producing clarinets she is able to produce 800 clarinets and 0 drums. When Sue devotes all of her time, resources and technology to producing drums she is able to produce 500 drums and 0 clarinets. Assume that the PPFs for both Bob and Sue are linear PPFs.
a. Draw a graph of Bob’s PPF with clarinets on the vertical axis and drums on the horizontal axis. Label the graph carefully and completely. Draw a second graph of Sue’s PPF with clarinets on the vertical axis and drums on the horizontal axis. Label the graph carefully and completely.
b. Fill in the blank for the following statements:
i. _______ has the absolute advantage in producing clarinets.
ii. _______ has the absolute advantage in producing drums.
iii. _______ has the comparative advantage in producing clarinets.
iv. _______ has the comparative advantage in producing drums.
c. Currently Bob and Sue each devote half of their time and half of their resources to the production of clarinets. The rest of their time and resources goes toward producing drums. Currently Bob and Sue do not trade with one another. Fill in the following table given this information.
Clarinets Drums
Bob
Sue
Total Production
d. Now, suppose that Bob increases his production of clarinets by one unit while Sue decreases her production of clarinets by one unit. They both adjust their production of drums so that they stay on their respective PPFs. Complete the table below based on these assumptions.
Clarinets Drums
Bob
Sue
Total Production
e. Did total production of the two goods increase or decrease in part (d) relative to part (c)? Explain your results.
f. Now, suppose that Bob decreases his production of clarinets by one unit while Sue increases her production of clarinets by one unit.
They both adjust their production of drums so that they stay on their respective PPFs. Complete the table below based on these assumptions.
Clarinets Drums
Bob
Sue
Total Production
g. Did total production of the two goods increase or decrease in part (f) relative to part (c)? Explain your results.
h.How do your results in parts (d) and (f) relate to the concepts of specialization, comparative advantage and trade? Explain your answer.
i. What is the range of prices in terms of drums for which 1 clarinet will trade? What is the range of prices in terms of drums for which 100 clarinets will trade?
Problem 4. PPF and Comparative Advantage: Suppose there are two countries: Micro and Smalltime. Both countries produce two goods: corn and wheat. Currently both countries do not trade with each other. Assume that each country uses only labor to produce corn and wheat and that both countries have an equal amount of labor available to use. The following table provides information about the number of hours of labor needed to produce one unit of wheat or one unit of corn in each of the two countries. Assume that the PPFs for both countries are linear PPFs.
Labor Hours Needed to Labor Hours Needed to
Produce One Unit of Corn Produce One Unit of Wheat
Micro 2 hours of labor 8 hours of labor
Smalltime 3 hours of labor 6 hours of labor
a. Construct a PPF for Micro and a PPF for Smalltime illustrating their PPFs for a given amount of labor. You will need to specify what amount of labor you are assuming that the two countries have available (you should choose equivalent amounts of labor for the two countries). Make sure you label your graphs clearly and completely. Put wheat on the vertical axis and corn on the horizontal axis in both of your graphs.
b. Which country has the absolute advantage in producing corn?
c. Which country has the absolute advantage in producing wheat?
d. What is the opportunity cost of producing one unit of corn in Micro?
e. What is the opportunity cost of producing one unit of wheat in Micro?
f. What is the opportunity cost of producing one unit of corn in Smalltime?
g. What is the opportunity cost of producing one unit of wheat in Smalltime?
h. Suppose that both countries have exactly 48 hours of labor available to them. Can Micro, with its 48 hours, produce 4 units of wheat and 10 units of corn? Explain carefully your answer paying attention to how many hours of labor are needed to produce this level of output if Micro does not specialize and does not trade.
i. Suppose that both countries have exactly 48 hours of labor available to them. Can Smalltime, with its 48 hours, produce 4 units of wheat and 10 units of corn? Explain carefully your answer paying attention to how many hours of labor are needed to produce this level of output if Smalltime does not specialize and does not trade.
j. Suppose that both countries have exactly 48 hours of labor available to them. Can Micro and Smalltime produce 8 units of wheat and 20 units of corn if they specialize and then trade with one another? Explain carefully your answer paying attention to how many hours of labor are needed to produce this level of output and what item each country will produce.