Question

Scenario 5

Charlie has the utility function U ( X A , x B ) = X^1/2_A X^1/2_B

where X_A stands for the number of apples and X_B stands for the number of bananas consumed.

Refer to Scenario 5.

- Putting apples on the x-axis, and bananas on the y-axis, what is the equation for the Marginal Rate of Substitution (MRS)?

Refer to Scenario 5.

- His indifference curve passing through 36 apples and 4 bananas will also pass through the point where he consumes 4 apples and how many bananas? (you may leave your answer as a fraction if necessary)

Refer to Scenario 5.

- His indifference curve passing through 81 apples and 36 bananas will also pass through the point where he consumes 16 apples and how many bananas? (you may leave your answer as a fraction if necessary)

Answer 1

Given Charlie's utilitt function, U = Xa^1/2.Xb^1/2

a) His MRS = MUx/MUy = Xb/Xa.

b) Given that his indufference curve passes through (36,4), his total utility at this point = (37)^1/2.(4)^1/2 = 12. Thus, his indifference curve will also pass through the point (4,36) in order to give him the same utilitt along an indiffrence curve.

c) Similarly, an indifference curve passing through the point (81,36), giving him a utility of (81)^1/2.(36)^1/2 = 54 will also pass through (16,182.25) to give him the same utility.