Discussion Section Suggested Answers for Problem Set #1Principles of Microeconomics Professor Scholz1) Portray the following hypothetical data on a two-variable diagram:Enrollment Data: Nowhere UAcademic Year Total Enrollment Enrollment in EconomicsCourses2000-01 3000 3002001-02 3100 3252002-03 3200 3502003-04 3300 3752004-05 3400 400Measure the slope of the resulting line, give an algebraic representation of the line, and explain whatthe slope means. Answer:Find the slope of the line (call it m). Let Y = enrollment in econ courses; Let X = total enrollments.The slope is the rise over run, or, in this case, 1/4.Find the equation of the line in slope-intercept form: take any point (we’ll take (3200, 350) and use theformula Y = mX + b; and you found the slope (1/4) in the previous part of the problem. Therefore,350=(1/4)*3200 + b, which implies b = -450. So the equation for the line is y = (1/4)*X - 450.The slope (1/4) means that enrollment in economics courses increase by 1 person every time totalenrollment increases by 4 people.2) Graph the following two equations on the same graph, X = 440 - 4Y and X = 40 + 4Y. Solve thesetwo equations for X and Y.Do the graphing. The solution, solving the two equations for the two unknowns, are X=240 and Y=50.3) Sam believe that the number of job offers he will get depends on the number of courses in which hisgrade is B+ or better. He concludes from observation that the following figures are typical:Number of grades of B+ or better 01234Number of job offers 13456Plot these numbers on a graph. Measure and interpret the slopes between adjacent dots.Plot the set of ordered pairs (with job offers on the vertical axis and grades B+ or better on thehorizontal axis). You’ll see that with Sam’s first B+ he gets a “big” jump in the number of job offers(2). Beyond the first B+, every additional B+ nets him one additional job offer.4) Graph the following two equations on the same graph, X = 8000 - 500P and X = 2000 + 1000P. Solve these two equations for X and Y.Again, plot the lines. Solving for X and Y you will find that Y=4 and X=6000.25) The following numbers measure the trade-off between grades and income for a hard workingstudent with 60 total hours available each week for both activities.Hours studying Hours working GPA Income60 0 4.0 $040 20 3.5 20030 30 3.0 30010 50 2.0 5000 60 1.0 600a) Calculate the opportunity cost of an increase in the number of hours spent studying in order to earn a3.0 GPA rather than a 2.0 GPA.The opportunity cost is 20 hours more studying, which implies 20 fewer hours of work, which lead to$200 less income.b) Is the opportunity cost the same for a move from a 3.0 GPA to a 3.5 GPA as it is for a move from a3.5 GPA to a 4.0 GPA? Why is this likely to be the case?The opportunity cost of going from a 3.0 to a 3.5 is 10 hours. The opportunity cost of going from a 3.5to a 4.0 is 20 hours. This is an example of increasing opportunity costs. The additional things thatneed to be learned to get a 4.0 are more difficult to acquire than the things needed to get from a 3.0 to a3.5.c) What is the opportunity cost of an increase in income from $200 to $300?The opportunity cost of the extra $100 of income (starting from $200) is 10 hours of study time, whichlowers the GPA half a grade point (going from a 3.5 to a 3.0). Working more, in this example, willlower your study time and GPA.6) Consider two equations, X=60-10Y and -3Y=15-3X. Graph the two equations on the same graphand solve them for X and Y.Solve the equations simultaneously and you will see that X=10 and Y=5.7. Let’s begin by establishing the opportunity cost of free throws for each player. If you allocate Kellyto the basketball team, the team gains a player with a 60 percent free throw average and the softballteam loses a player with a 70 percent (!) batting average. That is, the opportunity cost of allocatingKelly to the basketball team is 7/6. Similarly, Jackie’s opportunity cost of playing basketball is 1;Curt’s opportunity cost of playing basketball is 1/3, and Gerry’s opportunity cost of playing basketballis 8/7. Jackie and Curt have the lowest opportunity costs of playing basketball; that is, in a relativesense, theyr are better at playing basketball than they are playing softball. Therefore, the should beallocated to the basketball team. Kelly and Gerry are relatively better at playing softball than basketballand should therefore play on the softball team.You will read more about this logic when we cover Chapter 3 in class. The purpose of this question isto get you thinking about opportunities costs, and their implications for the allocation of economicactivity.It is likely that the basketball team will be unhappy with this arrangement. Both Jackie and Curt are, inan absolute sense, worse at basketball than the other two players. They are also worse than the othertwo at playing softball, but they are comparatively less bad at basketball than at softball. The softballteam is likely to be happy about this allocation because both Kelley and Gerry are the best softball3players. However, if you are concerned with the total number of wins for the dormitory (as aneconomist who would be concerned about efficiency), this allocation is the best one: it maximizes theoverall chances of the dormitory winning at any sport.8a: If the wage rate is greater than your opportunity cost of time, you will choose to work. So the wagerate is the independent variable and the number of hours worked is the dependent variable.8b: Your diagram illustrates the relationship between the hourly wage rate and the number of hoursworked. Since the hourly wage rate is the price paid for labor, economists place wages on the verticalaxis – just as in the case of other types of prices. So, plot the ordered pairs – your diagram will look(sort of) like a backwards “C”.8c. As the wage rate increases from $15 to $30, the number of hours worked increase by 5, Theaverage slope of the curve between the two points is therefore 15/5 = 3.8d. As the wage rate increases from $60 to $75, the number of hours worked decreases by 4 Theaverage slope of the curve between the two points is therefore 15/-4 = -3.75.9a: Annual salary is the independent variable and so is measured on the horizontal axis. Annualincome tax owed is the dependent variable and so is measured on the vertical axis. As salary increasesby $31,000 from Bill’s $63,000 to Mary’s
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