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Takashi has non-labor income from his investments of I= $80 per day, and can earn an...

Takashi has non-labor income from his investments of I= $80 per day, and can earn an hourly wage at his job of $30 per hour.

Assume Takashi can work (or not work) as much as 24 hours in a day.

a. Write a formula for Takashi’s budget constraint as a function of L (leisure hours) and C (consumption spending per day).Draw a diagram showing this budget constraint.

b. Suppose Takashi’s utility function is given by U = 2lnL+ lnC, where ln is the natural log. Calculate Takeshi’s optimal number of leisure hours L*, laborhours H*, and consumption C*. Hint: equal MRS to the absolute value of the slope of the budget constraint!

c. Is Takeshi’s labor supply curve upward or downward sloping as a function of the wage? Explain. Hint: Use calculus and resolve for the optimal L given a generic W rather than $30.

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