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3. Paul derives utility only from CDs and DVDs. His utility function is U =

i) Sketch Paul's indifference curves for U = 5, U = 10, and U = 15.

ii) Suppose Paul has $200 to spend and that CDs cost $5 and DVDs cost $20. Draw Paul's budget constraint on the same graph as his indifference curves.

iii) Suppose Paul spends all of his income on DVDs. How many can he buy?

iv) What is Paul's utility? iv) Show that Paul's income will not permit him to reach the U = 20 indifference curve.

v) If Paul buys 5 DVDs, how many CDs can he buy? What is his utility?

vi) Use a carefully drawn graph to show that the utility calculated in part (v) is the highest Paul can achieve with his $200.

vii) Assume Paul's income increased by $100 while price of both the items remained unchanged. How many of each of the goods would he buy to maximise his utility?