Suppose an individual has the following utility function, where U denotes total utility and Q the quantity of a good or service consumed in a given period of time:

U(Q) = aQ +

(a) Obtain the individual’s marginal utility function.

Assume a = 10 and b = −1/2, and that the individual’s consumption rises from Q1 to Q2, where Q1 = 2 and Q2 = 4.

(b) What is the individual’s marginal utility at Q1 and Q2?

(c) Show that total utility can be interpreted as an area under an appropriate marginal utility function, and use this result to obtain the increase in total utility when consumption rises from Q1 to Q2.