III: Constructed Response (40 points) Tara divides up her day between working H hours at her job, for which she is paid a wage of w per hour, and spending time at home pursuing N hours worth of leisurely activities. Tara's other source of income / comes from lottery payments of v per day (e.g. non-labor income). Tara uses her income I to buy goods from which she draws utility she also derives utility from leisurely pursuits. Formally speaking, Tara's labor-leisure choice is modelled according to: max aIN IN subject to wH tu = I N + H = 24 where a > 0 is a scalar. Based on the problem setup: 10. (a) Derive Tara's optimal choice of leisure (N*) working hours (#*), and her total optimal level of income (e.g. I* = wH* + v) in terms of w, v, and a. 10 points (b) Draw a graph representing Tara's labor-leisure choice. Your graph should include her: optimal working/leisure choice and her corresponding level of income; budget constraint; and, indifference curve. Everything (including intercepts) must be labeled. 6 points (c) Suppose Tara's initial wage is w = 1 and her lottery payments are set to v = 4. How long does Tara work and what is her total income? Now suppose that Tara's wage doubles: how long does she work now and what is her new income? |4 points (d) Construct a graph that shows the income and substitution effects of Tara's wage in- crease. Please label your substitution effect bundle (there's no need to compute the substitution effect bundle). Demonstrate/mark out how the income/substitution effects influence Tara's change in working hours. Everything must be labeled. |10 points (e) Draw out Tara's labor supply function, e.g. w vs H * (w), assuming: (i) no labor income (set v = 0 in your answer for #*); and (ii) some labor income (e.g. v > 0). Find and label Tara's reservation wage w (e.g. set H*(w) = 0 and find the wage rate): how does Tara's reservation wage change as her lottery payments increase (e.g. what is the sign on "w )? 10 points