Shelly purchases milk and cookies at the local supermarket. She has regular-shaped strictly convex indifference curves and a given income $100. After observing the prices for milk and cookies, P$4 and P$4 respectively, she ends up purchasing some milk and some cookies. Assume that cookies are a normal good. a) α β 2 γ δ 2 normal good (b) Keeping milk on the horizontal axis, provides a diagrammatic representation of Shelly’s optimal bundle using a suitable graph with necessary details and briefly explain your work. (c) Suppose now that the price of milk in the local supermarket changes from Pto P2(α − 1.5), while the price of cookies and Shelly’s income remain unchanged. Calculate the new price of milk using the information above by substituting for the values of α and pm. Reproduce your graph for part (b) and do further work on it to show how Shelly’s optimal bundle might adjust due to this price change. While creating your graph, make sure to illustrate any substitution effect and/or income effect as applicable and also the total effect of the price change. Explain your work. (d) Suppose now that S's income changes from to 100(γ − 1.5), while the prices of milk and cookies are still at their original levels (i.e., PP$4). Calculate the new level of income using the information above by substituting the values of γ and Y. Reproduce your graph for part (b) and do further work on it to show how Shelly’s optimal bundle might adjust due to this income change. While creating your graph, make sure to illustrate any substitution effect and/or income effect as applicable and also the total effect of the income change. Explain your work.