Question

Problem #2: A subsidy on earnings This problem focuses on the labor supply eects of subsidies. Assume Ann gets utility from consumption c and leisure l. Ann chooses how many hours to supply to the labor market each day (h) but only has 16 hours per day for work and leisure (assuming 8 hours of sleep). For each hour she works, she earns an hourly wage w = 15. Assume Ann has no unearned income v = 0. Write down Ann's daily budget constraint in terms of c and l and graph it with leisure on the x-axis and consumption on the y-axis. What is the slope of the budget constraint and what does it tell you? Show how Ann might maximize utility with a tangency to a hypothetical indierence curve and how this determines her optimal leisure, consumption, and hours worked. When you draw a hypothetical indierence curve, make sure it is a legitimate indier- ence curve which satises all the rules we learned in the class. Now suppose the government subsidizes labor income by oering 30 cents on each dollar that Ann earns, i.e., s = 0:3 (30%). That is, Ann's net wage becomes w (1 + s). 1 What is the eect of this subsidy on Ann's budget constraint? Draw a graph showing both the new and old budget constraints. Discuss what could happen to Ann's labor supply (h) when the government implements the subsidy. Show how Ann's budget constraint will change if the government decides to apply the subsidy to only the part of labor income that is equal to or less than $60 (just like the way the Earned Income Tax Credit works).

Answer 1

a) Ann's daily budget constraint is as follows:

P*C = W(h-l) + v : assuming 0 tax

P : price of consumption goods

C : QTY OF CONSUMPTION GOOD

W : nominal WAGE RATE

h : working hour

l : leisure

v : unearned income

Rearranging, we get : C + wl = wh + v ; (W/P=w)

or, C = w(h-l)

Slope of constraint : dC/dl = w(0-1) + (h-l) (0) = -w i.e wage rate is the slope. It tells us that for one unit increase in labour hours, Consumption falls by a constant wage rate w.

Profit maximizing choice : MRS _{l,c =}  MU_l/MU_c = w. So, Ann maximizes her utility with a tangency to a hypothetical indiference curve and determines her optimal leisure, consumption, and hours worked.

Subsidy :$0.30 i.e her income is now increased by 0.30

Because of this, Ann can work less and still maintain same consumption levels. So, her Budget line now looks like this :

When government implements this labour subsidy, labour supply or working hours will go down.