Suppose that a consumer can earn a higher wage rate for working overtime. That is, for the first q hours that the consumer works, she receives a real wage rate of W₁, and for hours worked more than q, the consumer receives a real wage of w₂, where w₂ > W₁. Suppose that the consumer pays no taxes and receives no nonwage income.
a) Write the consumer's budget constraint.
b) Draw the consumer's budget constraint and show graphically her optimal choice of consumption and leisure.
c) Show that the consumer would never work exactly q hours.
d) Determine what happens if the overtime wage rate w, increases to W₂₂, where W₂₂ > w₂. Determine the effects on working hours. Explain your results in terms of income and substitution effects.
(Hint: You should consider the case of a worker who initially works overtime, and a worker who initially does not work overtime.)
