Question

On the basis of the following Marginal utility data for products X and Y Assume that the prices of X and Y are $2 and $4 respectively and that the consumer's income is $16.

Units of X	MUx	MUx/ Px	MUy	MUy/Py
1	20		48
2	18		40
3	16		36
4	14		32
5	12		24
6	10		12

Refer to the above data. How many units of the two products will the consumer purchase to achieve the equilibrium?

Answer 1

Answer :

Given = Px = $2 and Py = $4

Units	MUx	MUx / Px (where Px = $2)	MUy	MUy / Py (where Py = $4)
1	20	10	48	12
2	18	9	40	10
3	16	8	36	9
4	14	7	32	8
5	12	6	24	6
6	10	5	12	3

As per the law of equi marginal utility a consumer maximizes his total utility when he allocates his money income in such a manner that the utility derived from the last unit of money spent on them is equal, that is

MUx / Px = MUy / Py

We see from the table that this happens in four occasions

Those are :

1) 1 X and 1 Y (shown in black bold)

2) 2 X and 3 Y (shown in red)

3) 3 X and 4Y (shown in green)

4) 5 X and 5Y (shown in yellow)

Now the task is to check out of these options which one exhausts the money income and thus can be attainable

Given income level = $16

1) 1 X and 1 Y = $2 + $4 = $6 (not the best since income is not exhausted)

2) 2 X and 3 Y = 2 * $2 + 3 * $4 = $16 (exactly exhausts the income)

3) 3 X and 4Y = 3 * $2 + 4 * $4 = $22 (exceeds the given income level and thus is not attainable)

4) 5 X and 5Y = 5 * $2 + 5 * $4 = $30 (exceeds the given income level and thus is not attainable)

We see that from the given options 2nd option (2 X and 3 Y) is the best since it exactly exhausts the income and it satisfies the condition of MUx / Px = MUy / Py (which is 9 in this case)

Answer : The consumer should purchase 2 units of X and 3 units of Y to achieve equilibrium.