Sample Midterm Exam #1 Solutions. Economics 370 University of Victoria - Fall 2016

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1 Sample Midterm Exam #1 Solutions Economics 370 University of Victoria - Fall 2016 PART I: MULTIPLE CHOICE 1. D 2. E 3. B 4. A 5. D 6. B 7. A 8. A 9. D 10. A PART II: SHORT-ANSWER QUESTIONS 1. [15 marks] Curious George must decide how much to work. He has 60 hours per week available that he can spend either working or engaged in leisure (which for him is various kinds of mischief). He can work at a wage of $5 per hour. The Man with the Yellow Hat (who looks after George) also gives him an allowance of $100 per week, no matter how much George works. George s only source of income that he can use for consumption (mostly bananas) is this allowance plus his wage earnings. a) In a carefully labeled diagram, draw George s consumption-leisure budget constraint. Show an equilibrium where George chooses to work 40 hours per week. For the income-leisure choice diagram, refer to the figure below. The initial value of Yn is $100, and the coordinates of point A are (T=60, $100). The budget line has a slope of - 5. There is a solution at point E0, which in this case is the point (leisure=20,$300) Labour market income is 40*5 = $200. 1

2 b) In an effort to have George pay for other household expenses, The Man in the Yellow Hat decides to tax George 50 percent of his wage income. Using the same diagram you drew in part (a) (where George worked 40 hours), show what happens to his labour supply. To do this, show one possible outcome, and break it down into income and substitution effects. Explain the diagram below. As the effective wage is now cut in half, the budget line has a slope of - 2.5, but it still has the right endpoint (T=60, $100). There will be a tangency at an indifference curve which is lower than the original indifference curve. Call this final point of tangency E2. We do not know exactly what the resulting number of hours worked will be, but we do know that he will be worse off than before. Draw a hypothetical (dashed) budget line with slope -2.5 which is tangent to the higher, original indifference curve at point E1. The horizontal distance between the two points of tangency on the higher indifference curve gives the substitution effect, and its direction is left to right. The horizontal difference between the final tangency E2 and the hypothetical tangency E1 is the income effect, and its direction is right to left. The horizontal distance between the original and the final tangency points is the total effect of the wage cut on his labour supply, or the difference between the two equilibria that we observe. 2

3 c) Instead of the wage tax, the Man with the Yellow Hat could impose a poll tax, a lump-sum tax independent of George s wage earnings. This tax must raise the same revenue as the wage tax in part (b), and could be accomplished by reducing George s allowance. Draw the budget constraint with the poll tax and the wage tax, and compare the work incentive effects of the poll tax to the wage tax in part (b). As in part (b), assume that George was working 40 hours before any taxes were imposed. This event is depicted on the graph below. George will pay only one of these taxes at a time, so the problem asks us to compare their effects on his labour supply using the same diagram. The poll tax has the effect of shifting the original budget line down in parallel fashion. It is the equivalent of cutting George s allowance. Taking the original budget line with a slope of -5, shift it down by the amount of taxes that George was paying in part b). This is given by the net income level that he was earning in part b. (Recall that he kept half of his earnings and forked over the other half to his caretaker.) The equilibrium should lie to the left of the equilibrium in part b), with more hours worked and less leisure taken. George will be worse off than he was in part a). The idea is that the poll tax gives George greater incentives to work. It produces only an income effect, which will actually raise work effort if leisure is a normal good. There is no substitution effect in this case. 3

4 2. [15 marks] Consider two individuals with endowments of T=60 hours (per week) of leisure, non-labour income of YN, and facing a wage of $7.50 per hour. At this wage, assume that workers are constrained by their employers to work 20 hours per week, or not at all. a) On a carefully labelled diagram, show the equilibrium for a worker (Abby) for whom 20 hours is the optimum labour supply; and a second worker (Ally) who would like to work 40 hours, but still prefers the 20-hour week to not working. Compare the marginal rates of substitution for these individuals at 20 hours per week. Y($) Slope = -7.5 Ally A U Ally0 Abby U Ally1 B U Abby YN U Ally T=60 leisure Abby wishes to work 20 hours a week and is at an equilibrium at point B, receiving utility U Abby. Ally, however, would prefer to work 40 hours per week, and if allowed, would settle on the equilibrium shown at point A, receiving U Ally0. However, as she is constrained to only work 20 hours per week, she would receive utility U Ally1. Due to the shape of her indifference curve, she still prefers 20 hours a week over no hours, given by U Ally2. Since Abby is utility maximizing at 20 hours per week, her indifference curve is tangent there (point B), and so her MRS is the absolute value of the slope of the income constraint, which happens to be the wage. Thus, the MRS for Abby at 20 hours a week is 7.5. This is not the case for Ally, as her IC is not tangent to the income constraint at B. In this case, Ally s MRS at 20 hours is less than Abby s, so Ally s MRS <

5 b) Which of the two workers, Abby or Ally, could be made better off at a job that pays a lower wage but offers full-time hours? Explain making reference to your diagram above. Y($) Slope = -7.5 Ally U Ally0 Slope = -5 A U Ally1 B U Ally2 YN T=60 leisure Ally is made better off by receiving a lower wage while being allowed to work full time. Here, Ally chooses to work at point A if offered a lower wage (say, $5.00 per hour) and work full time (40 hours), receiving utility U Ally1. However, in the original case, if she was forced to work only 20 hours a week while receiving the original wage ($7.50 per hour) she would be at point B and receive utility U Ally2, which is lower than U Ally1. Therefore, Ally is better off with a lower wage and full time hours, relative to the original higher wage and constrained part-time hours. End of Exam 5