Homework 1-
1. For each of the following sets of information please write an equation that represents accurately this information. Assume that all relationships are linear.
a. The line contains the points (x, y) = (10, 15) and (6, 11).
b. The line contains the point (x, y) = (10, 15) and has a slope of -2.
c. The line contains the point (x, y) = (20, 10) and you also know that each time the variable on the horizontal axis increases by two units the variable on the vertical axis increases by four units.
d. The line contains the y-intercept 30 and you also know that each time the variable on the vertical axis decreases by two units the variable on the horizontal axis decreases by four units.
e. The line contains the x-intercept 40 and you also know that each time the variable on the vertical axis increases by two units the variable on the horizontal axis decreases by four units.
2. In each part of this question you are given information about two linear relationships. Use this information to write the two equations and then use these two equations to solve for a solution that is true simultaneously for both equations.
a. The first line contains the points (x, y) = (10, 10) and (30, 10) and the second line contains the points (x, y) = (0, 15) and (30, 0).
b. The first line contains the point (x, y) = (10, 20) and has a slope of 5. The second line contains the point (x, y) = (5, 5) and has a slope of -2.
c. The first line contains the point (30, 0) and has a slope of -1. The second line contains the point (0, 15) and has a slope of 1.
d. The first line contains the point (6, 2) and you also know that each time the variable on the vertical axis decreases by two units the variable on the horizontal axis increases by 1 unit. The second line contains the point (3,3) and you also know that each time the variable on the vertical axis increases by two units the variable on the horizontal axis also increases by two units.
3. Joe, a baker, makes cookies and cakes. The following table provides five production combinations of cookies and cakes that Joe can make. Each combination lies on Joe's production possibility frontier (PPF). Furthermore, Joe's PPF is linear between each given point in the table: e.g., his PPF is linear between points A and B, B and C, C and D, etc. Use this information to answer this set of questions.
|
Production Combination
|
Cookies
|
Cakes
|
|
A
|
1000
|
0
|
|
B
|
800
|
70
|
|
C
|
600
|
120
|
|
D
|
300
|
160
|
|
E
|
0
|
200
|
a. What is the opportunity cost of producing one more cake if Joe is currently producing at combination A?
b. What is the opportunity cost of producing one more cake if Joe is currently producing at combination B?
c. What is the opportunity cost of producing one more cake if Joe is currently producing at combination C?
d. What is the opportunity cost of producing one more cake if Joe is currently producing at combination D?
e. What is the opportunity cost of producing one more cookie if Joe is currently producing at combination E?
f. What is the opportunity cost of producing one more cookie if Joe is currently producing at combination D?
g. What is the opportunity cost of producing one more cookie if Joe is currently producing at combination C?
h. What is the opportunity cost of producing one more cookie if Joe is currently producing at combination B?
4. This question reviews some pretty simple math in an attempt to make your aware that you know how to change an index number. This question allows you to practice this technique in a familiar setting so that later in the course when we do this in an economics context it might seem more familiar. Tom's chemistry class has had three exams. The exams in the class are all given the same weight in the grading scale, but each exam has a different number of total possible points. On the first exam Tom made a 60 out of 75 points, on the second exam Tom made a 51 out of a possible 60 points, and on the third exam Tom made a 40 out of 50 points.
a. What is Tom's grade on the first exam if the first exam score was converted to a 100 point scale?
b. What is Tom's grade on the second exam if the second exam score was converted to a 100 point scale?
c. What is Tom's grade on the third exam if the third exam score was converted to a 100 point scale?
d. On a 100 point scale with each exam given the same weight in the calculation, what is Tom's average grade?
e. If Tom wants to raise his average grade and the fourth exam has 60 points, how many points must Tom get on this exam?
5. Suppose that there are two countries, Orange and Yellow. Both countries produce tires and radios. Suppose that these two countries only use labor to produce these two goods (this is just a simplifying assumption to make our work easier). Orange has 200 hours of labor available while Yellow has 100 hours of labor. The following table tells you how many hours of labor are needed in each country to produce one tire or one radio.
|
|
Hours of Labor Needed to Produce One Tire
|
Hours of Labor Needed to Produce One Radio
|
|
Orange
|
2 hours of labor
|
4 hours of labor
|
|
Yellow
|
5 hours of labor
|
4 hours of labor
|
a. Given the above information, draw two graphs. In the first graph draw Orange's production possibility frontier with tires measured on the horizontal axis and radios measured on the vertical axis. In the second graph draw Yellow' production possibility frontier with tires measured on the horizontal axis and radios measured on the vertical axis.
b. What is Orange's opportunity cost of producing one tire?
c. What is Orange's opportunity cost of producing one radio?
d. What is Yellow's opportunity cost of producing one tire?
e. What is Yellow's opportunity cost of producing one radio?
f. Which country has the comparative advantage in producing tires?
g. Which country has the comparative advantage in producing radios?
h. What range of trading prices would be acceptable to both countries in terms of tires if the countries decided to trade 20 radios?
i. What range of trading prices would be acceptable to both countries in terms of radios if the countries decided to trade 15 tires?
6. Suppose that there are two countries, Monrovia and Sergovia. Each of these countries produces only two types of product: gadgets and widgets. The production of these two goods requires only labor. Furthermore, each country always produces on its production possibility frontier (PPF) and each country has a linear PPF. You are given the following information about the amount of labor that is needed in each country to produce gadgets and widgets.
|
|
Hours of Labor Needed to Produce One Gadget
|
Hours of Labor Needed to Produce One Widget
|
|
Monrovia
|
4 hours of labor
|
1 hour of labor
|
|
Sergovia
|
2 hours of labor
|
2 hours of labor
|
You are also given the following information about the current level of production of gadgets and widgets.
|
|
Current Level of Gadget Production
|
Current Level of Widget Production
|
|
Monrovia
|
175
|
100
|
|
Sergovia
|
50
|
150
|
a. If Monrovia only produces gadgets, what is the maximum amount of gadgets it can produce given the above information?
b. If Monrovia only produces widgets, what is the maximum amount of widgets it can produce given the above information?
c. If Sergovia only produces gadgets, what is the maximum amount of gadgets it can produce given the above information?
d. If Sergovia only produces widgets, what is the maximum amount of widgets it can produce given the above information?
e. Which country has the comparative advantage in the production of gadgets?
f. Which country has the comparative advantage in the production of widgets?
g. What is the maximum price Sergovia is willing to accept or pay for 1 widget?
h. What is the maximum price Monrovia is willing to accept or pay for 1 gadget?