# Question: Suppose that a consumer can earn a higher wage rate

Suppose that a consumer can earn a higher wage rate for working overtime. That is, for the first q hours the consumer works, he or she receives a real wage rate of w1, and for hours worked more than q he or she receives w2, where w2 > w1. Suppose that the consumer pays no taxes and receives no nonwage income, and he or she is free to choose hours of work.

(a) Draw the consumer’s budget constraint, and show his or her optimal choice of consumption and leisure.

(b) Show that the consumer would never work q hours, or anything very close to q hours. Explain the intuition behind this.

(c) Determine what happens if the overtime wage rate w2 increases. Explain your results in terms of income and substitution effects. You must consider the case of a worker who initially works overtime, and a worker who initially does not work overtime.

(a) Draw the consumer’s budget constraint, and show his or her optimal choice of consumption and leisure.

(b) Show that the consumer would never work q hours, or anything very close to q hours. Explain the intuition behind this.

(c) Determine what happens if the overtime wage rate w2 increases. Explain your results in terms of income and substitution effects. You must consider the case of a worker who initially works overtime, and a worker who initially does not work overtime.

## Answer to relevant Questions

Show that the consumer is better off with a lump-sum tax rather than a proportional tax on wage income (as in question) given that either tax yields the same revenue for the government. You must use a diagram to show this.Suppose that the firm has a minimum quantity of employment, N*, that is, the firm can produce no output unless the labor input is greater than or equal to N*. Otherwise, the firm produces output according to the same ...Suppose that there is a natural disaster that destroys part of the nation’s capital stock.(a) Determine the effects on aggregate output, consumption, employment, and the real wage, with reference to income and substitution ...Extend the model of public goods, in the last section of this chapter, as follows. Suppose that output is produced, as in the simplified model with proportional taxation, only with labor, and that z = 1. Here, however, there ...In the Solow growth model, suppose that the marginal product of capital increases for each quantity of the capital input, given the labor input.(a) Show the effects of this on the aggregate production function.(b) Using a ...Post your question