Imagine that you had £10 per month to allocate between two goods, A and B. Imagine that good A cost £2 per unit and good B cost £1 per unit. Imagine a
Imagine that you had £10 per month to allocate between two goods, A and B. Imagine that good A cost £2 per unit and good B cost £1 per unit. Imagine also that the utilities of the two goods are those set out in the table. (Note that the two goods are not substitutes for each other, so that the consumption of one does not affect the utility gained from the other.)
\r\nThe utility gained by a person from various quantities of two goods: A and B
\r\n| \r\n \r\n | \r\n\r\nGood A\r\n | \r\n\r\n \r\n | \r\n\r\n \r\n | \r\n\r\n Good B \r\n | \r\n\r\n \r\n | \r\n
| \r\n Units per \r\nmonth \r\n | \r\n\r\n MU \r\n(utils) \r\n | \r\n\r\n TU \r\n(utils) \r\n | \r\n\r\n Units per \r\nmonth \r\n | \r\n\r\n MU \r\n(utils) \r\n | \r\n\r\n TU \r\n(utils) \r\n | \r\n
| \r\n 0 \r\n | \r\n\r\n – \r\n | \r\n\r\n 0.0 \r\n | \r\n\r\n 0 \r\n | \r\n\r\n – \r\n | \r\n\r\n 0.0 \r\n | \r\n
| \r\n 1 \r\n | \r\n\r\n 11.0 \r\n | \r\n\r\n 11.0 \r\n | \r\n\r\n 1 \r\n | \r\n\r\n 8.0 \r\n | \r\n\r\n 8.0 \r\n | \r\n
| \r\n 2 \r\n | \r\n\r\n 8.0 \r\n | \r\n\r\n 19.0 \r\n | \r\n\r\n 2 \r\n | \r\n\r\n 7.0 \r\n | \r\n\r\n 15.0 \r\n | \r\n
| \r\n 3 \r\n | \r\n\r\n 6.0 \r\n | \r\n\r\n 25.0 \r\n | \r\n\r\n 3 \r\n | \r\n\r\n 6.5 \r\n | \r\n\r\n 21.5 \r\n | \r\n
| \r\n 4 \r\n | \r\n\r\n 4.5 \r\n | \r\n\r\n 29.5 \r\n | \r\n\r\n 4 \r\n | \r\n\r\n 5.0 \r\n | \r\n\r\n 26.5 \r\n | \r\n
| \r\n 5 \r\n | \r\n\r\n 3.0 \r\n | \r\n\r\n 32.5 \r\n | \r\n\r\n 5 \r\n | \r\n\r\n 4.5 \r\n | \r\n\r\n 31.0 \r\n | \r\n
| \r\n \r\n | \r\n\r\n \r\n | \r\n\r\n \r\n | \r\n\r\n 6 \r\n | \r\n\r\n 4.0 \r\n | \r\n\r\n 35.0 \r\n | \r\n
| \r\n \r\n | \r\n\r\n \r\n | \r\n\r\n \r\n | \r\n\r\n 7 \r\n | \r\n\r\n 3.5 \r\n | \r\n\r\n 38.5 \r\n | \r\n
| \r\n \r\n | \r\n\r\n \r\n | \r\n\r\n \r\n | \r\n\r\n 8 \r\n | \r\n\r\n 3.0 \r\n | \r\n\r\n 41.5 \r\n | \r\n
| \r\n \r\n | \r\n\r\n \r\n | \r\n\r\n \r\n | \r\n\r\n 9 \r\n | \r\n\r\n 2.6 \r\n | \r\n\r\n 44.1 \r\n | \r\n
| \r\n \r\n | \r\n\r\n \r\n | \r\n\r\n \r\n | \r\n\r\n 10 \r\n | \r\n\r\n 2.3 \r\n | \r\n\r\n 46.4 \r\n | \r\n
\r\n
(a) What would be the marginal utility ratio (MUa/MUb) for the following combinations of the two goods: (i) 1A, 8B; (ii) 2A, 6B; (iii) 3A, 4B; (iv) 4A, 2B? (Each combination would cost £10.)
\r\n(b) Show that where the marginal utility ratio (MUA/MUB) equals the price ratio (PA/PB) total utility is maximised.
\r\n(c) If the two goods were substitutes for each other why would it not be possible to construct a table like the one given here?
