Hunter has utility over consumption c and leisure & given by the following equation: U(e, c) = ce Note that this is a form of Cobb-Douglas utility, which we have covered in class. He has the following budget constraint describing his trade-off between leisure and consumption: w(T-e)=pc The slope of the indifference curves represents the marginal rate of substitution between consumption and leisure. The marginal rate of substitution of leisure for consumption is MRS 2c (MRS) a. Solve for optimal consumption c and leisure & using a system of two equations: 1) Equation 1) is derived from setting the slope of the indifference curves equal to the slope of the budget constraint. 2) Equation 2) is the budget constraint. Hint: In your answer, you should express optimal leisure and consumption (l*, c*) as a function of the parameters (w, p, T). (5 pts) b. What are Hunter's optimal hours of labor, h? (1 pt) c. Suppose Hunter's wage w increases. Will his optimal hours of labor h* increase, decrease, or stay the same? Explain the economic intuition behind your answer. (4 pts) d. Suppose the price of consumption p decreases. Will Richard's optimal hours of labor h* increase, decrease, or stay the same? Explain the economic intuition behind your answer. (4 pts) e. Suppose the price of consumption rises. Will Hunter's optimal consumption c* increase, decrease, or stay the same? Explain the economic intuition behind your answer. (4 pts) f. Suppose that T = 24, w = 10, and p = 8. What is Hunter's optimal consumption c*, leisure *, and hours of work h*? Use your answers from part a. (2 pts)