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Suppose that Mr. Chauncey Gardener consumes two goods, X1 and X2 .His preferences can be described by the following utility function:
U = X10.5X20.5
He faces the following prices in the market: P1 = $5.00 and P2 = $10.00. His income is $1,000. Assume that he spends all his income.
A. How much will he buy of commodities 1 and 2? Explain your answer.
B. Suppose that the price of commodity 2 rises by $2.50 (from $10.00 to $12.50); what will be the change in the quantities consumed of goods 1 and 2? Explain.
C. In the previous question (part B), take the change in the quantity consumed of commodity 2 and decompose it into an amount associated with the substitution effect and another one connected to the income effect (use the Slutsky decomposition discussed in class).
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