Homework 1-
1. For each of the following examples take the given information and write an equation in slope intercept form. Show all your work and NOT just your final answer.
a. The points (x, y) = (10,0) and (5, 15) both sit on the same line.
b. The points (x, y) = (0, 10) and (5, 15) both sit on the same line.
c. The slope of the line is -2 and the line contains the point (x, y) = (-20, -10).
d. The reciprocal of the slope for the line is 1/5 and the line contains the point (x, y) = (10, 5).
e. The point (x, y) = (5, 10) is on the line and furthermore you know that each time x increases by 2 units, y increases by 3 units.
f. The point (x, y) = (100, 200) is on the line and furthermore you know that each time x increases by 2 units, y decreases by 4 units.
2. Find the solution (x, y) for each set of equations. Show your work and NOT just your final answer.
a. y = 10 - x
y = 6
b. y = 10 - x
x = 4
c. y = 10 - x
x = y - 2
d. y = 10 - x
y = 20 - 3x
3. You are provided the following figure and given another equation, y = 2x + 1. Find the solution (x, y) given this information. (Hint: do NOT expect nice numbers! Do try to work this without a calculator though-it will be good practice.)
4. a. Suppose you are given a line described by the equation y = 100 - 2x and you are told that the x value has increased by 50 units at every y value. What is the equation for the new line? Show your work.
b. Suppose you are given a line described by the equation y = 100 - 2x and you are told that the x value has doubled at every y value. What is the equation for the new line? Show your work.
c. Suppose you are given a line described by the equation y = 100 - 2x and you are told that the y value has increased by 50 units at every x value. What is the equation for the new line? Show your work.
5. The average of 5 numbers is 52. Suppose five more numbers are included in the set of numbers and these five numbers equal 0, 100, 48, 90, and 50. What is the new average? Explain the steps you took to get your answer.
6. There are three midterms in the class Alice is taking. The first midterm counts as 20% of her grade, the second midterm counts as 30% of her grade, and the third midterm counts as 50% of her grade. Each exam has 100 points and Alice knows that her weighted average must be equal to 90 in order to earn an "A" in the class. Suppose Alice made an 85 on the first exam and a 92 on the second exam. What is the minimum score Alice must make on her third exam in order to get an "A" in the class? Fully explain your answer. Provide an answer two places past the decimal.
7. There are three midterms in the class Molly is taking. The first midterm counts as 20% of her grade, the second midterm counts as 30% of her grade, and the third midterm counts as 50% of her grade. The first midterm had 50 points and Molly made a 40 out of 50 points. The second exam had 60 points and Molly made a 50 out of 60 points on it. The third exam has a total of 75 points on it. To earn an "A" in the class Molly must have a weighted average of 90 on a 100 point scale from the three midterms. What is the minimum score Molly must make on her third midterm in order to get an "A" in the class? Fully explain your answer. Please provide an answer two places past the decimal.
8. Use the information in the table below to answer this set of questions. Suppose that each of the following points in the table is a point on the production possibility frontier for Econoland. Furthermore suppose that the PPF for Econoland is linear between each of these combinations-for example, the PPF is linear between points A and B, between points B and C, etc.
|
Combination
|
Pounds of Butter
|
Number of Guns
|
|
A
|
1000
|
0
|
|
B
|
800
|
110
|
|
C
|
600
|
150
|
|
D
|
400
|
175
|
|
E
|
0
|
200
|
a. Draw a graph of Econoland's PPF measuring guns on the vertical axis and butter on the horizontal axis. Label both axes as well as combinations A, B, C, D, and E.
b. Given the above information, what is the opportunity cost of producing 200 more pounds of butter if Econoland is currently producing at point C?
c. Given the above information, what is the opportunity cost of producing 200 more pounds of butter if Econoland is currently producing at point B?
d. Given the above information, what is the opportunity cost of producing 100 more pounds of butter if Econoland is currently producing at point D?
e. Given the above information, what is the opportunity cost of producing one additional gun if Econoland is currently producing at point B?
f. Given the above information, what is the opportunity cost of producing one additional gun if Econoland is currently producing at point D?
9. It takes Joe 5 hours to wash the family's clothes and 3 hours to cook the family dinner. It takes Sue 2 hours to cook the family dinner and 4 hours to wash the family's clothes. Both Joe and Sue have a total of sixty hours a month they can devote to these two tasks. (Assume that their PPFs are linear and that they can divide their time between these two tasks.) Use this information to help Joe and Sue answer these questions about their production within their family.
a. If Joe produces only laundry how many times can he wash clothes in an entire month?
b. If Joe produces only dinners how many family dinners can he produce in an entire month?
c. If Sue produces only laundry how many times can she wash clothes in an entire month?
d. If Sue produces only dinners how many family dinners can she produce in an entire month?
e. Who has the absolute advantage in doing laundry? Explain your answer.
f. Who has the absolute advantage in making family dinners? Explain your answer.
g. Who has the comparative advantage in doing laundry? Explain your answer.
h. Who has the comparative advantage in preparing family dinners? Explain your answer.
i. Construct the joint PPF for Joe and Sue measuring laundry on the vertical axis and family dinners on the horizontal axis.
j. What is the range of trading prices in terms of family dinners that both Joe and Sue will accept for 10 laundry times?