Question

If MUx MUy > Px Py for a consumer, then she must purchases more x

True or false?

Answer 1

Ans. True

Let total utility be TU

=> Marginal utility of x, MUx = dTU/dx
and Marginal utility of y, MUy = dTU/dy

=> Marginal rate of substitution = dy/dx

=> Marginal rate of substitution = (dTU/dx) / (dTU/dy) = MUx/MUy

At the level of maximization of utility,

MRS = Px/Py

=> MUx/MUy = Px/Py

But if, MUx/MUy > Px/Py

Then MUx must be reduced or MUy must be increased or both to reach at utility maximizing level.

So, from law of diminishing marginal utility, more consumption of x will lead to decrease in MUx and because income is a constraint, so, consumption of y must be decreased which will lead to increase in MUy. Thus, increase in x will lead to utility maximizing level.

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