Mordecai consumes only coffee (C) and video games (G), and his utility function is U(C,G)=C1/2G1/2. The price of coffee is p, and the price of video games is 10. Mordecai's income is m. In this problem, you will find Mordecai's utility maximizing combination of coffee and video games. a. Write down Mordecai's budget constraint and find its slope. (1 points) b. Find Mordecai's marginal utility of each good and his marginal rate of substitution. (2 points) c. For Mordecai to be maximizing utility, what relationship must hold between his MRS and the slope of his budget constraint? Write down this relationship in the form of an equation, using your answers from parts (a) and (b). (3 points) d. Using the equation from part (c) and and the budget constraint from part (a), find Mordecai's utility maximizing combination of coffee and video games. (4 points) e. Suppose m=100 and p=10. How much of each good does Mordecai consume? Draw a graph showing his budget constraint and indifference curve passing through the chosen bundle. (2 points) f. Suppose m=100 and p=5. How much of each good does Mordecai consume? On the same graph from part (e), draw Mordecai's budget constraint and indifference curve passing through the chosen bundle. (2 points) g. On the same graph, show the (hypothetical) budget constraint that is tangent to the indifference curve from part (e) but parallel to the budget constraint in part (f). (3 points) h. On the same graph, show the income and substitution effects of the decrease in p from 10 to 5 on Mordecai's consumption of coffee. Is coffee a normal or inferior good? Explain your answer. (3 points) i. Find the equation representing the (hypothetical) budget constraint drawn in part (g). Hint: you know this budget constraint has the same prices as in part (f), so you need to find the income level m that makes the budget constraint just tangent to the indifference curve passing through Mordecai's chosen consumption bundle in part (e). (4 points) j. Find the amount of each good that Mordecai would consume if is his budget were the one found in part (i). What are the numerical values of the income and substitution effects shown graphically in part (h)? (2 points)