Homework 1-
1. This set of questions will help you review some basic algebra, the slope-intercept form, finding a solution given two linear equations, and finding a new equation based upon an initial equation that has undergone a change. Each question below is independent of the other questions in the set.
a. You are given two pairs of coordinates that lie on a linear relationship. The two pairs of coordinates are (x, y) = (10, 15) and (5, 12). You are asked to find the equation for the line that these two points lie on.
b. You are given two pairs of coordinates that lie on a linear relationship. The two pairs of coordinates are (x, y) = (10, 15) and (12, 5). You are asked to find the equation for the line that these two points lie on.
c. You are given two equations:
Equation 1: y = 10 + 2x
Equation 2: y = 26 - 2x
Find the (x, y) solution that represents the intersection of these two lines.
d. You are given two equations:
Equation 1: y = 10 + 2x
Equation 2: y = 26 - 2x
But, you are also told that equation 1 has changed and now the x value is 10 units bigger at every y value than it was initially.
i. Write the equation that represents the new Equation1'.
ii. Given the new Equation 1' and Equation 2, find the (x,y) solution that represents the intersection of these two lines.
2. The price of money is called the interest rate. Suppose that when the interest rate is 5%, the demand for money is $1000 and when the interest rate is 10% the demand for money is $500. Assume the relationship between the quantity of money demanded (Q) and the interest rate (r) is linear.
a. Draw a graph representing the above information. In your graph measure Q on the horizontal axis and r on the vertical axis.
b. Write an equation for this relationship in slope-intercept form.
3. Josie's income in 2010 was $50,000 and her income in 2011 was $60,000. Her income in 2012 was $50,000. Use this information to answer this next set of questions. For this set of questions assume there was no inflation during this three year period of time.
a. What was the percentage change in Josie's income in 2011 relative to 2010?
b. What was the percentage change in Josie's income in 2012 relative to 2011?
c. Given that in both (a) and (b) you are measuring percentage changes and the numbers in both examples use $50,000 and $60,000, do you get the same answers? Explain your answer.
4. The following table provides data on the amount of labor Chin and Luis need in order to produce widgets (W) and gadgets (G). Assume that both Chin and Luis have linear production possibility frontiers and that the production of widgets and gadgets requires only labor as an input.
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Labor Needed to Produce One Gadget
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Labor Needed to Produce One Widget
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Chin
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2 Hours of Labor
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1 Hour of Labor
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Luis
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3 Hours of Labor
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4 Hours of Labor
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a. Assume that Chin and Luis each have 60 hours of labor they can devote to gadget and widget production. Fill in the following statements given this information. Assume both Chin and Luis produce at points on their PPFs.
i. When Chin produces 10 gadgets, his widget production must equal _________.
ii. When Chin produces 20 gadgets, his widget production must equal _________.
iii. When Luis produces 8 gadgets, his widget production must equal _________.
iv. When Luis produces 16 gadgets, his widget production must equal _________.
b. For Chin, the opportunity cost of producing 2 gadgets is equal to __________________.
c. For Luis, the opportunity cost of producing 4 gadgets is equal to __________________.
d. Chin has the comparative advantage in the production of ___________________ and Luis has the comparative advantage in the production of ________________. Explain your answer.
e. Construct Chin and Luis' joint PPF measuring gadgets (G) on the vertical axis and widgets (W) on the horizontal axis.
f. The acceptable range of trading prices for 10 gadgets is ________________________.