Homework 1-

1. For each of the following sets of information write an equation. Assume that each set of information describes a linear relationship. Assume Y is the variable measured on the vertical axis and X is the variable measured on the horizontal axis. Write all equations in slope-intercept form.

a. When X = 10, Y = 5 and when X = 7, Y = 2.

b. When X = 12, Y = 6 and the slope of the line is equal to -5.

c. When X = 20, Y = 40 and the slope of the line is equal to 1.

d. (X, Y) = (4,4) and the slope of the line is equal to -20.

e. (X, Y) = (14, -2) and the slope of the line is 2.

2. You are given the following information where each set of information describes two linear relationships. Use this information to determine what the (X, Y) values are that make both relationships simultaneously true. That is, use the information to solve for the answer (X, Y).

a. The first line contains the points (3,5) and (8, 10) while the second line has a slope of -2 and contains the point (20, 10).

b. The first line contains the point (20, 10) and has a slope of -1 while the second line has a y-intercept of 6 and a slope of 2.

c. The first line contains the point (10, 12) and has a slope of 5 while the second line has a x-intercept of 2 and a slope of 2.

d. The first line contains the point (10, 900) and has a slope of -10 while the second line has a y-intercept of 20 and contains the point (20,100).

3. You make a 70 out of a 100 possible points on your first midterm in your math class. On the second midterm you make an 80 out of a 100 possible points. If both exams are given equal weights in the calculation of your average, what must be true about your average score after the second midterm relative to your average score after the first midterm? Explain in words your answer. In your answer discuss what your average score is after the first midterm and what your average score is after the second midterm.

4. You make a 40 out of a possible 50 points on your first midterm in psychology.

a. On a 100 point scale what is your grade?

b. Suppose the second midterm is graded on a 40 point scale. In order for your average in the class to increase what is the lowest possible score you could make on this second midterm? Assume that both midterms are adjusted so that their weight in determining your final grade is the same.

5. Last year it snowed 80 inches in Snowtown, USA. This year it snowed 92 inches. What was the percentage increase in snow this year relative to last year?

6. This year the number of subscriptions to Snowtown's daily paper was 500,000. If the owners of the paper want to see a 25% increase in subscriptions during the coming year, what must be the increase in the number of subscriptions?

7. In the Cap Times section (pages 18-21) of the Wisconsin State Journal on January 5, 2011 it was reported that the number of "foreclosure court filings in Dane County for 2010 reached 1, 768, up from 282 in 2000". Calculate the percentage change in foreclosures between 2000 and 2010 in Dane County.

8. Italy can produce 40 pairs of shoes and 0 leather handbags or 0 pairs of shoes and 50 leather handbags or any combination that lies on the straight line between these two given combinations. Croatia can produce 20 pairs of shoes and 0 leather handbags or 0 pairs of shoes and 20 leather handbags. Assume that Italy and Croatia have the same level of resources to use in the production of shoes and handbags.

a. Which country has the absolute advantage in the production of leather handbags?

b. Which country has the absolute advantage in the production of shoes?

c. Which country has the comparative advantage in the production of leather handbags?

d. Which country has the comparative advantage in the production of shoes?

e. Suppose Italy is currently producing on its production possibility frontier and it is making 35 pairs of shoes. Suppose Croatia is currently producing on its production possibility frontier and it is making 15 leather handbags. Calculate the total number of pairs of shoes and leather handbags that these two countries are currently making.

f. Given the production in part (e), can you suggest how total production of these two goods can be increased? In your answer be sure to provide numerical values to support your position.

g. What is the range of prices in terms of leather handbags that 5 pairs of shoes will trade for?

h. What is the range of prices in terms of pairs of shoes that 2 handbags will trade for?

9. You are given the following information about the US and China's ability to produce widgets and gadgets. Assume that both countries have 300 hours of labor available that can be used to produce either widgets or gadgets.

a. From the above table and the information you have been given, what is the maximum amount of widgets that China can produce?

b. From the above table and the information you have been given, what is the maximum amount of widgets that the US can produce?

c. Write an equation for China's PPF assuming that widgets (W) are measured on the Y-axis and gadgets (G) are measured on the X-axis. Write your equation in slope intercept form.

d. Write an equation for the US's PPF assuming that widgets (W) are measured on the Y-axis and gadgets (G) are measured on the X-axis.

e. Which country has the comparative advantage in the production of widgets?

f. Which country has the comparative advantage in the production of gadgets?

g. What is the range of prices for one widget in terms of gadgets?

h. What is the range of prices for 10 gadgets in terms of widgets?