Question #70595

Your budget constraint for the two goods A and B is 12A + 4B = I, where I is your income. You are currently consuming more than 27 units of B. In order to get 3 more units of A, how many units of B would you have to give up?

Expert's answer

at first, let's express A in terms of I and B:

A = I / 12 - B / 3

now, given the same income (that is, I is constant) suppose we decrease the level of consumption of good B from B1 to B2. How many additional units of A (dA = A2-A1) can we get within the same budget constraint?

dA = A2 - A1 = [I / 12 - B2 / 3] - [I / 12 - B1 / 3] = (B1 - B2) / 3

from the formula above we see that in order to consume one additional unit of A (dA = 1), we have to give up three unit of B. Or, to get three more units of A, we have to give up 9 units of B.

A = I / 12 - B / 3

now, given the same income (that is, I is constant) suppose we decrease the level of consumption of good B from B1 to B2. How many additional units of A (dA = A2-A1) can we get within the same budget constraint?

dA = A2 - A1 = [I / 12 - B2 / 3] - [I / 12 - B1 / 3] = (B1 - B2) / 3

from the formula above we see that in order to consume one additional unit of A (dA = 1), we have to give up three unit of B. Or, to get three more units of A, we have to give up 9 units of B.

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