Suppose that Mr. Chauncey Gardener consumes two goods, X_{1} and X_{2} .His preferences can be described by the following utility function:
U = X_{1}^{0.5}X_{2}^{0.5}
He faces the following prices in the market: P_{1} = $5.00 and P_{2} = $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).
In answering these questions, remember to provide numerical answers and to explain where your answers come from.