Problem
Jack consumes only Bread (good x) and Cheese (good y). His utility function is given by
U(x, y) = ln(x) + ln(y)
1. Find Jack's marginal rate of substitution (MRS) at bundle (x, y).
2. The price of good x is $6 and the price of good y is $3. Jack has an income of $120. Find his utility maximising consumption bundle.
3. Calculate Jack's utility from the bundle you have solved in part (2). (You can leave your answer expressed in logarithm.).
4. In a graph with the quantity of x on the x-axis and the quantity of y on the y-axis, draw Jack's budget line, clearly marking the intercepts and the utility maximising bundle you have solved in part (2) (call it bundle A). Also sketch an indifference curve passing through bundle A.
5. Now the price of good y increases to $6 while the price of good x remains at $6. Jack's income remains at $120. Calculate his new utility maximising consumption bundle.
6. On the diagram you have drawn for part (4), draw Jack's new budget line, clearly marking the intercepts and the new optimal bundle you have solved in part (5) (call it bundle B). Also sketch an indifference curve passing through bundle B.
7. Find the minimal expenditure required for Jack to achieve his original utility level (i.e., your answer to part (3)) under the new prices. As you are finding this minimal expenditure, solve for the expenditure minimising bundle that achieves the original utility level under the new prices.
8. On the diagram you have drawn for parts (4) and (6), draw the budget line associated with the minimal expenditure you have solved in part (7), clearly marking the intercepts and the expenditure minimising bundle you have solved in part (5) (call this bundle H).
9. Using your answers above, compute the changes in the quantities of good x and good y due to the substitution effect, and the changes in quantities due to the income effect, both associated with the increase in the price of good y from $3 to $6.