Quasi-Linear Preferences

5.4.1 of The Economy 1.0 & The Economy #3

What does a quasi-linear function look like mathematically?

-Let free time = t, and bushels of grain = c

-Such that v is an increasing function, because Angela prefers more free time to less.

Generally speaking, what does a utility function like this produce in terms of its indifference curve? Why?

-The rate at which Angela will exchange grain for free time will remain constant, as consumption of grain increases. Meaning, MRS depends only on the free time, not on the grain

-Hence, for any given amount of free time: t_0, we see that the slope of the indifference curves are the same.

Given this utility function, what is the MRS mathematically?

-Using the generic formula of dividing the marginal utilities, we can find that:

∂U/∂t = v’(t) and ∂U/∂c = 1, thus making the MRS:

-Which proves that the MRS only depends on free time.

What is the use of quasi-linear preferences?

-Utility being in the form of ‘c + something’, it is measured in the same units as consumption.

-Angela values t hours of free time as much as v(t) bushels of grain.

-Thus, utility is simply measured in consumption, but quasi-linear preferences usually use ‘c’ as money income so that you measure gains and losses of utility in terms of money.