Alice’s preferences for consumption and leisure can be expressed as U(C, L) = ln(C) + ln (L). Where C is consumption and L represent the number of hours of leisure. There are 110 hours per week available to split between work and leisure. Alice earns $10 per hour and gets a non-labor income that is equal to $200 per week.
1. Graph Alice’s budget line.
2. Find Alice’s reservation wage.
3. Suppose Alice’s leisure marginal utility is 30 and her consumption marginal utility is 2. Given the wage of $10 per hour, should Alice give up one hour of leisure to get more consumption, give up consumption to get one more hour of leisure or be indifferent between both options? Explain why.
4. Find Alice’s optimal amount of consumption and leisure.
5. If the wage increases to $15 per hour, what will be the new equilibrium? Does the income effect dominate the substitution effect? Explain your answer using a graph.
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