1. A worker has 24 hours per day to allocate between leisure and work. Use graphs to answer the following questions.
a. If leisure is a normal good, show how it is possible to derive a negatively-sloped labor supply curve. Explain how this is possible.
b. What happens to hours worked if a worker has an increase in non-wage income (that is, income that is received even when hours worked equals zero)? Assume that leisure is a normal good.
c. If leisure is an inferior good, then an increase in wage rate must increase hours worked per day. Do you agree? Explain.
d. Assume that an individual pays taxes but receives no benefit from them. How will an increase in the income tax rate affect this individual's supply of labor? Leisure is a normal good.
What if this same person receives enough non-wage income which leaves him just as well off as if he had paid no taxes. What will be the effect on his labor supply relative to the case where he pays no tax with no benefit?
2. Assume the following utility function: U=x0.5y0.5. Income = $100 and the initial prices for good X is $1 and the initial price for good Y is $1.
a. Using the uncompensated demand curve, find the quantity consumed for each good. What is utility at this bundle?
b. Suppose the price of x falls to $0.25. Holding REAL INCOME constant, what happens to the quantity of x consumed? Taking into account both the substitution and income effects, what happens to the quantity of x consumed?
c. Show the substitution and income effects on a graph. Use the numbers you calculated in the above sections.