Question #53189

Tom has an income of £400 which he spends as follows:
40% goes on good X and 60% on good Y. The price of good Y is 80 per cent of the price of good X which is £5. The price of good Y rises by 25 per cent and Tom’s nominal income rises by 15 per cent. Which of the following new consumption patterns would indicate inconsistent preferences by Tom.
A He consumes 32 of X and 60 of Y
B He consumes 40 of X and 52 of Y
C He consumes 25 of X and 67 of Y
D None of the above

Expert's answer

I = £400, 40% goes on good X and 60% on good Y, PY = 0.8*5 = £4, PX = £5. The price of good Y rises by 25 per cent and Tom’s nominal income rises by 15 per cent. The new consumption patterns would indicate next inconsistent preferences by Tom:

PY1 = 4*1.25 = £5, PX1 = £5, I1 = 400*1.15 = £460, so as now the prices are the same, then Tom will consume less of good Y and the same amount of good X (Qx = 400*0.4/5 = 32), so he will consume 32 of X and 60 of Y.

That's why the right answer is:

A He consumes 32 of X and 60 of Y

PY1 = 4*1.25 = £5, PX1 = £5, I1 = 400*1.15 = £460, so as now the prices are the same, then Tom will consume less of good Y and the same amount of good X (Qx = 400*0.4/5 = 32), so he will consume 32 of X and 60 of Y.

That's why the right answer is:

A He consumes 32 of X and 60 of Y

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