Homework
1. Math Review
Let the horizontal axis be the X variable and the vertical axis be the Y variable. There are two points. At point A, X has a value of 2 and Y has a value of 2 and at point B, X has a value of 4 and Y has a value of 6.
Draw a straight line passing through both points.
a. Give the equation of that line.
b. Indicate the slope of the line and the X and Y intercepts of that straight line.
c. Now consider another straight line: Y = 7 - X. Draw this second line in your graph. (The same graph that has the first line.)
d. Solve algebraically for the intersection of these two lines and compare the result with the graph you drew in question (c).
2. Calculating percentage changes
a. In 2015, Smileytown consumed 12,000 gallons of mouthwash. In 2016, mouthwash consumption rose to 17,000 gallons. Calculate the percentage change in mouthwash consumption.
b. If the price of gasoline was $3.25 a gallon and it is now $3.75 a gallon, what is the percentage change in price?
c. At a recent company meeting, Ravi Batra, sales manager of Life's a Beach, a surfboard producer announced, "We have increased our sales by 13 percent in just 9 months." Suppose 9 months ago, its sales amounted to $245,000, what is the value of its sales today?
3. Production Possibility Frontier and Opportunity Cost
A factory of 500 workers produces footballs and basketballs. Each worker could produce either 20 footballs or 10 basketballs per day.
a. Draw the PPF for this factory's production per day and label it PPF1. In your graph, place the number footballs on the x-axis and the number of basketballs on the y-axis. (Hint: It is a straight line.)
b. Find the equation of the PPF.
c. Find the opportunity cost of 1 basketball.
d. Find the opportunity cost of 1 football.
e. Is there a relationship between the opportunity cost and the slope of the PPF? If yes, what is the relationship?
f. Describe the differences between a linear PPF and a PPF that is bowed-outwards from the origin using the concept of opportunity cost.
g. Suppose the workers invent a new method to produce footballs. With the implementation of the new method, each worker can produce 30 footballs per day instead of 20. Draw the PPF and label it PPF2. Find its equation. What does this example suggest about the relationship between the PPF and technological improvements?
4. Comparative Advantage
Suppose Linda and Jack are doing Biology and Economics homework. In one hour, Linda can solve 10 Biology questions and 0 Economics questions, or 20 Economics questions and 0 Biology questions, or any other linear combination lying on the line between those two points. In the same amount of time, Jack can solve 20 Biology questions and 0 Economics questions, or 30 Economics questions and 0 Biology questions, or any other linear combination lying on the line between those two points.
a. What is the opportunity cost of solving 1 Economics question for Linda? What is the opportunity cost of solving 1 Economics question for Jack?
b. What is the opportunity cost of solving 1 Biology question for Linda? What is the opportunity cost of solving 1 Biology question for Jack?
c. Who has the absolute advantage in doing Biology homework? Who has the absolute advantage in doing Economics homework?
d. Suppose that Jack and Linda work together. Who will specialize in solving Biology problems and who will specialize in solving Economics problems?
e. If they were to trade with each other, what is the price range (in terms of the number of solved Economics problems) acceptable to both Linda and Jack for a solved Biology question?