Problem 1. For each of the following statements identify whether the statement is positive or normative.
a. All birds in Wisconsin are red.
b. The state of Wisconsin should raise the minimum wage to $10 an hour for all workers.
c. If the state of Wisconsin raises the minimum wage this will result in individuals earning higher incomes.
d. If the state of Wisconsin increases its sales tax this will generate 25% more revenue for the state.
e. The state of Wisconsin should increase its expenditure on higher education.
Problem 2. Each of the scenarios below provide some type of mathematical review. Please read each scenario and then provide the relevant answer. Make sure you show all your work clearly and in an orderly manner in order to get full credit for this series of questions.
a. John weighs twice as much as Joe. Together they weigh 210 pounds. What is John’s weight (W) and Joe’s weight (J)?
b. When the price of spaghetti is $2 per pound people in Derby eat 10 pounds of spaghetti a week. When the price of spaghetti is $4 per pound people in Derby eat 5 pounds of spaghetti a week. Measuring spaghetti (S) on the x-axis of a graph and the price of spaghetti (P) on the y-axis of a graph, write an equation expressing the relationship between the quantity of spaghetti eaten in Derby and its price. Assume that this is a linear relationship.
c. You know that one linear equation contains the two points (10, 20) and (5, 20). You know that the other linear equation contains the point (30, 10) and has a slope of -1. What point (x, y) sits on both equations given this information?
d. You know that one linear equation contains the two points (10, 4) and (12, 2). You know that the other linear equation has a y –intercept of 2 and each time the x value increases by 2 units the y value also increases by 2 units. Write the two equations that are described in (x, y) space and then solve for the point (x, y) that sits on both equations.
Problem 3. Information about George’s production possibility frontier is given in the table below. George produces two goods: bicycles and mechanical pencils. Assume that George’s production possibility frontier is linear between each combination when answering this set of questions.
Combination Production of Bicycles Production of Mechanical Pencils
A 100 0
B 75 900
C 50 1500
D 25 1800
E 0 2000
a. What is the opportunity cost of producing 25 more bicycles if George is currently producing 50 bicycles?
b. What is the opportunity cost of producing 50 more bicycles if George is currently producing 25 bicycles?
c. What is the opportunity cost of producing 1 more bicycle if George is currently producing at combination D?
d. What is the opportunity cost of producing 1 more bicycle if George is currently producing at combination B?
Problem 4. Suppose that there are two individuals, Sam and Jill, who both produce books and hats. Sam and Jill currently do not trade with one another. You are told the following information about the amount of labor that Sam and Jill need to use in order to produce books and hats. Assume that labor is the only input needed for the production of either of these two goods.
Amount of Labor Amount of Labor Needed
Needed to Produce One Book to Produce One Hat
Sam 2 hours of labor 1 hour of labor
Jill 3 hours of labor 6 hours of labor
a. Measuring books on the horizontal axis and hats on the vertical axis draw two graphs. On the first graph depict Sam’s production possibility frontier assuming that he has 24 hours that he can spend making books or hats. On the second graph depict Jill’s production possibility frontier assuming that she has 24 hours that she can spend making books or hats.
b. What is Jill’s opportunity cost of making one more book?
c. What is Jill’s opportunity cost of making one more hat?
d. What is Sam’s opportunity cost of making one more book?
e. What is Sam’s opportunity cost of making one more hat?
f. Who can produce hats with the lower opportunity cost?
g. Who can produce books with the lower opportunity cost?
h. Measuring books on the horizontal axis and hats on the vertical axis draw a graph that depicts the combined production possibility frontier for Sam and Jill.
i. Who should specialize in producing hats?
j. Who should specialize in producing books?
k. What is the acceptable trading range for 1 hat measured in terms of books?
l. What is the acceptable trading range for 1 book measured in terms of hats?