4. Jeff, Alan, and Katie all work for the same employer at an hourly wage rate of wo=$24. All three of them have T=100 hours of weekly time endowment and non-labor income of IN=$O. Their preferences over consumption and leisure are as follows: a) b) Jeff: U023!) = CF Alan: U(c, i) = min {324.13 Katie: U(c, l) = c + 22:! (3 points) Based on the consumption-leisure model, solve for Jeff, Alan, and Katie's optimal consumption and leisure choices: (cf, if), (a; 2), and (4.1;), respectively. For each worker, graphically illustrate their optimal consumption and leisure choices by drawing the indifference curve and budget constraint and labeling their respective optimal bundle (use separate graphs for each worker). What are the optimal working hours for each worker? (3 points) Now suppose that due to the economic downturn, the market wage of all three workers dropped to wl=$20 per week. Recalculate the optimal choice of consumption and leisure for each worker. Compared to the initial setup in Part a), graphically illustrate how the decrease in wage rate affects each worker's indifference curve, budget constraint, and optimum. How does each individual's working hours change compared to that in Part a)