Q3. Assume that there are only two goods purchasable in the economy. Consumer choice problem is formulated as follows: max u(q1, q2) 91.42 S. t. P191 + P292 - Y where p1, P2, and Y are prices of goods and the consumer's budget. Let (qi, q2 ) denote the optimal solution for this problem. Also, let u denote the maximized utility, that is, u = u(qi, q2) Assume that the utility function is strictly increasing and concave. (1) Consider an expenditure minimization problem with the above-mentioned u that is formulated as follows: min p191 + P292 ( = E) 41/42 s. t. u(q1, 92) 2 u Let (q1*, q2*) denote the optimal solution for this minimization problem. Also, let E** denote the minimized expenditure, that is,E =P1qi +P292 Show that these two optimization problems have a same solution, that is, (91, 92) = (91",92") and moreover E** = Y holds true. (2) Suppose hereafter that the consumer's utility function is a CES form, that is, u (91, 92) = {(aq,)P + (bq2)?)p where a, b, and pare parameters. Note that p