Problem 1. Joe and Mary both produce carrots and turnips. They currently do not trade with one another. Joe’s linear production possibility frontier with carrots measured on the horizontal axis has a slope of -2. Mary’s linear production possibility frontier with turnips measured on the horizontal axis has a slope of -5.
a. What is Joe’s opportunity cost of producing one turnip given the above information?
b. What is Mary’s opportunity cost of producing one carrot given the above information?
c. Given this information, if these two individuals decide to trade, who should specialize in producing turnips?
d. Given this information, what is the range of trading prices in turnips that three carrots will trade for?
e. If Joe uses all his resources to produce turnips he can produce 40 turnips. If he were to use all of his resources and time to produce carrots, what would be the maximum amount of carrots he could produce?
f. Mary is currently producing on her production possibility frontier and she is producing 40 carrots and 20 turnips. What is the maximum amount of carrots she can produce if she only produces carrots?
Problem 2. The x-intercept of a straight line is 50 and the point (x, y) = (10, 40) sits on this line. Write an equation in slope intercept form for this line given this information.
Problem 3. You know that the points (10, 12) and (8, 14) sit on a straight line. What is the y-intercept of this line?
Problem 4. In (x, y) space there is a straight line described by the equation x = 10 + 2y. Suppose that there is a new line such that the x value is always three units larger than the initial x value. Write an equation in y-intercept form for this new line. Hint: you might find it helpful to draw a sketch of these two lines before you begin writing the new equation.
Problem 5. In (x, y) space there is a straight line described by the equation y = 100 – x. Suppose that there is a new line such that the y value is always five units smaller than the initial y value. Write an equation in y-intercept form for this new line. Hint: you might find it helpful to draw a sketch of these two lines before you begin writing the new equation.