Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

CHAP. 4] CONSUMER DEMAND THEORY 75
4.5 (a) Using the values in Table 4.8, give a real-world case where the MU curve for a good might first
rise and then fall. (b) Explain the shape of the MU y curve in Fig. 4-11 in terms of the slope of the
TU y curve.
(a) Suppose a mother has two candy bars to give to her two little boys. If the two candy bars are different, an
argument may arise between the children if both prefer the same candy bar. Suppose that the older boy
(who cries the loudest) gets the preferred candy bar and refuses to share it with his little brother. The
utility that the older boy receives from getting his preferred candy bar is only 4 utils (the argument and
crying look away a great deal of his satisfaction in consuming the candy bar). Subsequently, the mother
buys only the preferred type of candy bar so that now each child gets the same (preferred) candy bar. It is
possible that the second unit of the preferred candy bar gives the older boy more utility (say, 10 utils) than
the first since there is no arguing or crying now (see Table 4.8). Subsequently, additional units of the preferred
candy bar give the older boy less and less additional utility.
Another example might be given by the first, the second, and subsequent martinis.
(b) The MU y in Fig. 4-11 is equal to the average slope of the TU y curve. For example, in going from 0 to 1 unit of
Y consumed, the TU y increases from 0 to 4 utils. Thus, the change in total utility resulting from increasing the
consumption of Y by 1 unit is 4 utils. This is the MU y and is equal to the slope of segment OA of the TU y
function in Fig. 4-11. Similarly, when the quantity of Y consumed per time period increases from 1 to 2
units, the total utility increases from 4 to 14 utils or by 10 utils. Thus the MU y is 10 and is equal to
the slope of the TU y function between points A and B. Between points E and F, the TU is horizontal.
Thus its slope, or the MU y , is zero. To the right of point F, the TU y is negatively sloped and so the MU y
is negative.
4.6 (a) Derive the MU curve geometrically from the TU curve of Fig. 4-12. (b) Explain the shape of the
MU curve of part (a) in terms of the shape of the TU curve. (c) What is the relevant portion of the TU
curve?
Fig. 4-12