16. A worker has 24 hours per day to allocate between leisure and work. Use graphs to answer the fol

16. 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?
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
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.

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