Question

Econ450 Instructor: Germán Izón Student full name: Nathaniel Clark Homework 2 Problems from the textbook Chapter 2: 2 (page 59), 13 (page 60). Problems not from the textbook 1) Suppose that a person has 2000 hours to allocate each year between leisure and work. a. Derive the equation of his budget constraint given an hourly wage of S10/hour. b. Graph his budget constraint line based on the equation you derived in part a. (Consumption (C) on the vertical axis and leisure (L) on the horizontal axis). Please make sure to include the value for the vertical and horizontal intercepts. C. Now suppose that the local government introduces an income guarantee program for single parents in which the income transfer is $5,000 per year if an individual does not work during that year (this dollar amount represents the benefit guarantee). If the individual decides to work, this transfer program imposes a 40% benefit reduction rate (e.g., each additional hourly wage earned is reduced by 40%). Derive the new budget constraint equation that corresponds to this scenario. d. Draw the budget line that corresponds to the new scenario on the graph you drew in part b.

Answer 1

Figure 1

Ak0000 Consumption -15000- 10000- 5000- 500 1000 1500 2000 2500 750 Leisure

a) Time intercept: 2000 nowis [OB] (to allocate between L and W) Budget constraint: C:10(2000-2) : 20000 - 10L . If L=0 or w= 2000 ; the highest c in $ 20,000: consumption intercept: 20000 (eson] by Budget constraint depicted in Figure! Initial budget line in AB . .( After income garantee C: 5000 for L = 2000 =10(2000-1) + 5000 -0.4 [10(2000-2) :6(2000-1)+5000 for 7506L 32000 =10(2000-) fw L6750 The 5000 benefit exhausted at; 10.4[10(2000-47] - 5000 a, 9(2000-2): 5000 or, 8000 - AL = 5000 ier, 3000 :4L il: 750 Then the budget line has kink at LE 750 (Point c) d) Aftere income gurantee the budget line is ACDB