2. (12 points) Consider a consumer who buys only two goods. Her utility function is u(X1, X2) =X1x2 . The prices of the two goods are P1=$2 and P2=$4 . The consumer has income m=$60 . a. Does the utility function v(x1, X2)=4 In x1 + In x2 also represent the consumer's preferences? Why or why not? b. Derive the consumer's demand function. What is the optimal consumption bundle? c. Suppose the government provides a $1 subsidy on X1 . Write down the new budget constraint. What is the consumer's optimal consumption bundle after the policy change