3. Consider the pair of indifference curves given in Figure 1 on the last page of this problem set. (a) Draw a budget constraint that is tangent to the grey indifference curve at 6 apples and 3 pears. (b) If income is 12, what is the price of each of apples and pears if it is optimal to consume 6 apples and 3 pears? (c) Now suppose the price of pears decreases such that the new optimum is at 6 apples and 6 pears on the black indifference curve. Draw the budget constraint that is tangent to the black indifference curve at this point. What is the price of pears that gives this as an optimum? (d) With the help of the graph, decompose the change in demand for pears into a substitution effect and an income effect (you might want to use a different color for the new budget constraint or draw a dashed line) (e) Are pears normal or inferior? Justify your answer.