Homework 1-
(1) Given the equations for two straight lines below, determine the point at which they intersect (Hint: solve the two equations for the values of x and y).
y = 8 - x
y = 2x + 1
(2) A straight line has a slope of 2/3 and crosses the y-axis at y = 6. Write the equation for this line in slope-intercept form. Graph this line.
(3) An experimental physicist is attempting to determine the relationship between the mass and kinetic energy of a particle in a laboratory setting. After two trials, she has observed the following data, written as an ordered pair (mass, kinetic energy): (2, 4) and (4, 10). As her lab assistant, what is the slope-intercept form of the straight line that expresses kinetic energy as a function of mass? Based on this estimate, what kinetic energy would we expect for a particle that has a mass of 8 units? Theoretically, a particle with zero mass should have zero kinetic energy. Is our experimental model consistent with this?
(4) Two TAs for Professor Kelly's class are in charge of writing exam questions and homework problems for the spring semester. The first TA, Steven, can write 3 homework problems and 0 exam questions per week or 3 exam questions and 0 homework problems per week. The second TA, Buzz, can write 2 homework problems and 0 exam questions per week or 1 exam question and 0 homework problems per week. Assume that both TAs have linear PPFs that include these two points and any other combination of homework problems and exam questions that lie on the line between these two points. There are 14 weeks in the semester.
a) Draw the PPF for each TA for the semester with exams on the y-axis and homework problems on the x-axis. Use two separate graphs for these two PPFs.
b) Which TA has the absolute advantage in writing exam questions? Which TA has the absolute advantage in writing homework problems?
c) What is Steven's opportunity cost (in terms of exam questions) of writing one homework problem? What is Steven's opportunity cost (in terms of homework problems) of writing one exam question?
d) What is Buzz's opportunity cost (in terms of exam questions) of writing one homework problem? What is Buzz's opportunity cost (in terms of homework problems) of writing one exam question?
e) Which TA has the comparative advantage in writing exam questions? Which TA has the comparative advantage in writing homework problems?
(5) Canada and the United States produce two goods: maple syrup and apple pie. The two countries have linear PPFs and each country can dedicate 100 hours to the production of the two goods. Canada can produce 20 bottles of maple syrup per hour and 0 apple pies per hour or 10 apple pies per hour and 0 bottles of maple syrup per hour, while the United States can produce 30 bottles of maple syrup per hour and 0 apple pies per hour or 40 apple pies per hour and 0 bottles of maple syrup per hour. Both Canada and the United States have linear PPFs that include the two points given for each country and any combination of the two goods that lie on the line connecting these two points.
a) Draw the PPF for each country with apple pies on the y-axis and maple syrup on the x-axis.
b) What is the opportunity cost of producing maple syrup (in terms of apple pies) in Canada? What is the opportunity cost (in terms of bottles of maple syrup) of producing apple pies in Canada?
c) What is the opportunity cost of producing maple syrup (in terms of apple pies) in the United States? What is the opportunity cost (in terms of bottles of maple syrup) of producing apple pies in the United States?
d) If Canada and the United States were to decide to trade, what would be the efficient distribution of production (ie: which good(s) should each country produce)? Why?
e) Assuming Canada and the United States decide to trade, what would be an acceptable price (in terms of apple pies) for a bottle of maple syrup? Hint: this price will be a range of prices that both countries would be willing to accept.