Problem Set Four (Constrained Maximization, Demand) 1. Consumer's preferences are represented by the utility function U(:r1,:1:2) = :rfacg. At the optimal consumption bundle, what is the ratio 2:? What does this ratio represent? If the utility function is U (331, 332) = cx'facg, what is the ratio 2:; at the optimal bundle? 2. Find the consumer's demand functions if his utility is U (3:1, 322) = $1 + 111.932. 3. What are the demand functions for the consumer with the utility function U(:c1, $2, $3) = 331:1:2 + m3. 4. The economics department implemented a new grading policy in ECONlOOb, where the student's overall score is the minimum of the number of correct answers the student gets on two examinations. The student's utility function is U (S, M) = S %M2, where S is the student's overall score for the course, M is the number of minutes Spend studying, and A is a variable that reects how much the student dislikes studying. For the rst exam, each correct answer costs the student 10 minutes of study time. For the second exam, each correct answer costs the student 20 minutes of study time. We know that the student studied for 1,200 minutes. What is the value of A in this student's utility function? 5. Consumer's utility function is min(4:r:, 2:1: + y), where the price of :1: is $10. The consumer is consuming 15 units of a: and 10 units of 3;. What is the consumer's income