Question

John’s utility function is represented by the following: U(C,L) = (C-400)*(L-100), where C is
expenditure on consumption goods and L is hours of leisure time. Suppose that John receives
$150 per week in investment income regardless of how much he works. He earns a wage of $20
per hour. Assume that John has 110 non-sleeping hours a week that could be devoted to work.
a. Graph John’s budget constraint.
b. Find John’s optimal amount of consumption and leisure.
c. John inherits $300,000 from a relative which gives him $288 per week in additional
investment income. How does this change his hours of work decision? (Calculate C and
L). Is there an income and/or substitution effect? Explain.
d. Now suppose John’s wage increases to $50 per hour but he now still receives only $150
per week in investment income (no inheritance). Find his optimal amount of
consumption and leisure. Is there an income and/or substitution effect? Explain what
we can say about the relative magnitudes, if anything.

Answer 1