Takashi has non-labor income from his investments of I = $60 per day, and can earn an hourly wage at his job of $20 per hour. 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*, labor hours H*, and consumption C*. Hint: equal slopes and on 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 $20.