Question

1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min . If P. = $1. P. = $1. and I = $100. find the value of xı* (Hint: This is Leontief utility, the kind with right-angled indifference curves) 2. (10 points) If P, = $4, P2 = $2, and I = $20, and my utility is given by u(x1, x2) = 4x1 + 3x2, find x* (Note: I'm asking for optimal consumption of Good 2). (Hint: This is linear utility). 3. (20 points) Jack's utility is given by u(x1, x2) = x, x. If I = $160. P = $20 and P2 = $4, how many units of x; will Jack consume to maximize his utility? (Hint: This is Cobb- Douglas utility. You can use the 5 step method to solve this problem, or the appropriate demand function derived in class). 4. (10 points) Carl's utility is given by u(x1, x2) = xx2. If I = $90 and P, = $30 and the price of good 2 is unknown, can you determine how much of good 1 Carl will consume to maximize his utility? If your answer is 'yes," enter the utility maximizing consumption of good 1. If your answer is "no" enter 99 for your answer.

Answer 1

1)

Junu = (zzº tan

the Budget Constraint can be written as by the given information:

P1=P2=$1 and Income = 100

21 + 12 = 100

the consumer will try to be indifferent between x1 and x2 and will choose,

=> 3.11 = 2.12

Plug the values: in the budget line:

12

x1 + x1 = 100

2.01 +3.21 = 100

5.01 = 100

100 11 =

01 = 20

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