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

Hadassah Thompson · Accepted Answer

Final Answer : B, Explanation : 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) = kWhere 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) = kU(A,21) = kSubstituting 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 / MUyWhere 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 = -1MUy = -MUxFor y > 29:MRS = MUx / MUy = -1/29MUy = -MUx / 29Now we can set up the equations for the two indifference curves:U(30,39) = MUx(30) - MUy(39) = kU(A,21) = MUx(A) - MUy(21) = kSubstituting in the expressions we derived for MUy:U(30,39) = MUx(30) + MUx(39) = kU(A,21) = MUx(A) + MUx(21) / 29 = kNow we can equate the two expressions for k:MUx(30) + MUx(39) = MUx(A) + MUx(21) / 29Since we assumed that MUx is constant, we can simplify:30MUx + 39MUx = AMUx + 21MUx / 29Solving for A:30MUx + 39MUx - 21MUx / 29 = AMUxA = (30MUx + 39MUx - 21MUx / 29) / MUxSimplifying:A = 28.6Rounding up, we get:A = 29Therefore, the indifference curve passing through the bundle with 30 apples and 39 bananas also passes through the bundle with 29 apples and 21 bananas.

Definitions

Learning Objectives

Learning Objectives

Related questions