Question

Suppose the price of good A is \$2 and price of good B is \$3. You...

Suppose the price of good A is \$2 and price of good B is \$3. You have \$90 to spend and your preferences over A and B are defined as: a^2/3*b^1/3 = U(a,b).

If income changes from \$100 to \$84, Pa = \$2, Pb = \$3 calculate and show work on how the optimal choice of A and B change and what the total utility achieved is given the Utility Function.

U(a,b) = a2/3 b1/3

MUa / MUb = [2/3* a-1/3 b1/3 ] / [1/3*a2/3 b-2/3] = 2b / a

optimal choice when

price of good A is \$2 and price of good B is \$3 and Income = 90

MUa /Mub = Pa / Pb

2b/a = 2/3

a = 3b

put this in budget constraint

90 = 2*3b + 3*(b)

90 = 6b + 3b

90 =9b

b = 10

a =10*3 = 30

optimal choice (a,b) = 30,10

now if income change from 90 to 84, then

a = 3b -- put this is new budget constraint

84 = 9b

b = 9.33

a = 28

optimal choice (a, b) = (28, 9.33)

If income fall from 90 to 84, quantity of both the goods a and b falls.

Total utility when income= 90

U =302/3 101/3 = 20.8

Total utility when income= 84

U =282/3 9.331/3 = 19.4

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