Suppose a consumer's preferences over bundles of bread (2:1) and butter ((82) can be represented by the following utility function: 1 2 U(:n1, m2) = Elna-1) + 51710112) Let p1 = 6 and p2 = 3. The agent's income I = 72. Q1: Graph the consumer's budget set. Q2: Derive the optimal consumption bundle for the consumer and label it on your graph from Q1. Sketch the indifference curve that corresponds to the optimal consumption bundle. Q3: Suppose the price of bread decreases from p1 = 6 to 131 = 4. Draw the new budget line on the same graph as before. Derive the new optimal consumption bundle and label it on the graph. Sketch the indifference curve corresponding to the new optimal consumption bundle. Q4: Calculate the magnitude of the substitution effect for both bread and butter. Label the substitution effect on your original graph. Q5: Calculate the magnitude of the income effect for both bread and butter. Label the income effect on your original graph. Indicate whether the magnitude of the income effect is greater than, less than, or equal to the magnitude of the substitution effect for each good