Question

Assume that Monica is spending all her income on purchasing a combination of two products: cookies (C) and tea (T). The marginal utility of cookies (MUC) is 12 and the price of a cookie (PC) is $3. The marginal utility of tea (MUT) is 10 and the price of tea (PT) is $5. Is Monica maximizing utility? If not, what should she do to maximize utility? Explain

Answer 1

A utility maximising consumer will be in equilibrium when the consumer spends his entire income on purchase of various commodities in such a way that marginal utility per dollar spent on each good is proportional to its price. Monica will maximize total utility and will be in equilibrium when Marginal utility per dollar spent on cookie is equal to the Marginal utility per dollar spent on tea.

MU _{​​​​​​C}/ P_{​​​​​​C}= MU_​T / P_{​​​​​T}

( where C is cookies and T is tea).

So, marginal utility per dollar spent on cookie-

Marginal utility= 12, price of cookie= $3

Marginal utility per dollar spent on cookie= 12/3= 4

Marginal utility per dollar spent on cookie= 4

Now, Marginal utility per dollar spent on tea-

Marginal utility= 10, price of tea= $5

Marginal utility per dollar spent on tea= 10/5= 2

Marginal utility per dollar spent on tea= 2

We can see that MU/P of cookies is not equal to MU/P of tea. Hence, Monica is not in equilibrium and is not maximising utility.

As we can see that marginal utility per dollar spent on cookie is more than marginal utility per dollar spent on tea, Monica should switch her expenditure from tea to cookie. As Monica will switch from consumption of tea to cookie, the quantity consumed of tea will reduce and, given the law of diminishing marginal utility, a decrease in the consumption of tea will increase the Marginal utility of tea. At the same time, the quantity consumed of cookies will increase. As per the law of diminishing marginal utility, as more of cookies will be consumed, the Marginal utility of cookies will fall. This process of reallocation of expenditure will ultimately result in equalisation of marginal utility per dollar spent on cookie and tea(MU/P of cookie= MU/P of tea). At this point, Monica will be in equilibrium.

Hence, to maximize utility, Monica should consume more of cookies and less of tea.