Question

If a consumer purchases a combination of commodities x and y such that mux/px = 30 and muy/py = 40, to maximize utility, the consumers should buy.

Answer 1

If $MU_{x}/P_{x}$=30 and $MU_{y} /P_{y}$=40 then the consumer should buy the commodity y to maximise utility.

Given that $MU_{x}/P_{x}$=30 and $MU_{y} /P_{y}$=40 of commodities x and y.

Marginal utility is the additional utility that a consumer gets from consuming additional units of commodity. For maximising the utility of the consumer,the ratio of marginal utilities must be equal to the ratio of the products.

There can be two situations in our case:

Because $MU_{x}/P_{x}$<$MU_{y} /P_{y}$

So to equalise the ratio we need to reduce $MU_{y} /P_{y}$. To reduce the utility of y the consumer needs to increase the consumption of y because as the consumption of commodity y increase it decreases the utility of commodity y.

Hence if $MU_{x}/P_{x}$=30 and $MU_{y} /P_{y}$=40 then the consumer should buy the commodity y to maximise utility.

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