Suppose a worker faces the wage w, has time endowment T, and has non-labor income Y.
a. Draw the budget constraint over leisure and money spent on consumption goods (M) for this worker, clearly labeling all points, slopes, etc.
b. Suppose the worker has utility function U(L,M) = 5L + M. Draw in some indifference curves for this worker.
c. What is the utility maximizing labor supply choice if w = 6?
d. Let non-labor income increase from Y to 2Y. Now what is the utility maximizing labor supply choice? Is there an income effect? Why or why not?
e. Go back to the case with non-labor income equal to Y, and continue to assume that w = 6. Now suppose the government introduces a guaranteed income program that provides everyone with income G whether they work or not, but reduces G by 50 cents for every dollar earned. Now Suppose that Y = 10, T = 16, and G = 18. Draw the new budget constraint, again labeling carefully.
f. With the values assumed in part e, and the guaranteed income program in place, what is the utility maximizing labor supply choice?