An individual's utility function is given by = , where is consumption and is leisure. and are constants. The individual's non-labor income is zero. She has 16 hours per day, and her wage rate is $10 per hour

a. Assume = 1 and = 2. Compute the marginal rate of substitution between leisure and consumption. How many hours of leisure does this individual consume, and how many hours does she work? Also, find her consumption.

b. Using the parameters in part a, compute the share of the individual's consumption spending in her total income. Compare this ratio to + .

c. Now, instead of the parameters in part a, assume = 1 and = 3. Find the number of hours of leisure the individual consumes and the amount of her consumption spending. Compute the share of this individual's consumption spending in her total income. Compare this ratio to + . d. Given your analysis in parts a-c, what do and in = represent in general?