Question

** No need to answer (1) or (2), Please show explanation for (3), with specific calculation process if needed. Thank you. **

Dudley has a utility function U(C, R) = CR, where R is leisure and C is consumption per day. He has 16 hours per day to divide between work and leisure. Dudley has a non-labor income of $48 per day.

(a) If Dudley is paid a wage of $6 per hour, how many hours of leisure will he choose per day?

(b) As a result of a promotion, Dudley is now paid $ 8 per hour. How will his leisure time change?

(c) Analyze the changes in Dudley’s leisure time using the substitution effect and the income effect.

Answer 1

Solution:-

Given that

Dudley has a utility function U(C, R) = CR, where R is leisure and C is consumption per day. He has 16 hours per day to divide between work and leisure. Dudley has a non-labor income of $48 per day.

(c)

The higher wage increases the price of leisure. The substitution effect of a higher wage causes the consumer to substitute labor for leisure. Higher wage induces the individual to supply a greater quantity of labor.

But the higher wage also has an income effect. An increased wage means a higher income, and since leisure is a normal good, the quantity of leisure demanded will go up. And that means a reduction in the quantity of labor supplied.

The income effect of the wage change is negative; Substitution effect of wage change is positive.

As Dudley's leisure time decreases with an increase in his wage, the strength of the substitution effect of wage change is greater than the strength of income effect.

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