Tim consumes only apples and bananas.He prefers more apples to fewer, but he gets tired of bananas.If he consumes fewer than 29 bananas per week, he thinks that 1 banana is a perfect substitute for 1 apple.But you would have to pay him 1 apple for each banana beyond 29 that he consumes.The indifference curve that passes through the consumption bundle with 30 apples and 39 bananas also passes through the bundle with A apples and 21 bananas, where A equals
A)25.
B)28.
C)34.
D)36.
E)None of the above.

Question

Quizplus · Accepted Answer

To find the value of A, we need to establish the equation for the indifference curve passing through the given bundles. Let x represent the number of apples and y represent the number of bananas. The indifference curve passing through (30,39) and (A,21) can be represented by the equation: U(x,y) = k Where k is a constant representing the level of satisfaction Tim derives from consuming the bundles. We can set up a system of equations: U(30,39) = k U(A,21) = k Substituting in the conditions given in the problem: For Tim, 1 banana is a perfect substitute for 1 apple if he consumes fewer than 29 bananas per week. Beyond that, he requires 1 apple for each additional banana consumed. This means that the marginal rate of substitution (MRS) between bananas and apples changes at y = 29: MRS = -Δy / Δx = -1 for y < 29 (1 banana is a perfect substitute for 1 apple) MRS = -Δy / Δx = -1/29 for y > 29 (1 apple is required for each additional banana) Using the definition of MRS: MRS = MUx / MUy Where MUx is the marginal utility of apples and MUy is the marginal utility of bananas. Since Tim prefers more apples to fewer, we know that MUx > 0. However, he gets tired of bananas, so the marginal utility of bananas is diminishing. This means that MUy is decreasing as y increases. Let's assume for simplicity that the marginal utility of apples is constant. Then we can derive an equation for MUy as follows: For y < 29: MRS = MUx / MUy = -1 MUy = -MUx For y > 29: MRS = MUx / MUy = -1/29 MUy = -MUx / 29 Now we can set up the equations for the two indifference curves: U(30,39) = MUx(30) - MUy(39) = k U(A,21) = MUx(A) - MUy(21) = k Substituting in the expressions we derived for MUy: U(30,39) = MUx(30) + MUx(39) = k U(A,21) = MUx(A) + MUx(21) / 29 = k Now we can equate the two expressions for k: MUx(30) + MUx(39) = MUx(A) + MUx(21) / 29 Since we assumed that MUx is constant, we can simplify: 30MUx + 39MUx = AMUx + 21MUx / 29 Solving for A: 30MUx + 39MUx - 21MUx / 29 = AMUx A = (30MUx + 39MUx - 21MUx / 29) / MUx Simplifying: A = 28.6 Rounding up, we get: A = 29 Therefore, the indifference curve passing through the bundle with 30 apples and 39 bananas also passes through the bundle with 29 apples and 21 bananas.

Tim Consumes Only Apples and Bananas