This document contains answers to problem set #7 in an economics class. It addresses concepts related to marginal utility, demand curves, consumer surplus, rational consumption of multiple goods, and how changes in relative prices can impact an individual's consumption bundle and satisfaction. For question 1, the document explains how to determine rational consumption levels for a single good based on the marginal utility schedule and price. For question 4, it uses indifference curves and budget constraints to illustrate the impact of a change in relative prices on an individual's optimal consumption bundle.

1. Mark Evers
Economics 1030
University of Denver
Spring 2011
ANSWERS TO PROBLEM SET #7
1.a. In general, the marginal utility derived from the consumption of any good is:
MU = ΔTU / ΔQ
So for this example:
GLASSES OF WHISKY TU($) MU($)
0 $0 --
1 6 6
2 11 5
3 15 4
4 18 3
5 20 2
6 21 1
7 21 0
b,c,d. Following the rule of rational behavior for the single good case, the consumer should consume to the
point where MU=P, that is to the point where the marginal benefits of consumption just equals the marginal
cost of consumption. If the price per glass is $5, the consumer should rationally consume 2 glasses of
whisky since at that point, MU=P. If the price fell to $3 per glass the consumer should rationally consume 4
glasses. Note that the marginal utility schedule is just a representation of the amount of additional
satisfaction that a consumer receives from additional consumption of a good. If we include market prices,
the marginal utility schedule is a representation of the consumer’s willingness to consume specific quanti-
ties of a good at different possible market prices or the ordinary demand curve.
e,f. If the price falls to $2, the rational consumer would consume 5 glasses of whisky. To determine how
much the consumer will have to pay, in total to consume 5 glasses of whisky, just multiply the number of
glasses (5) times the market price ($2) to get $10. The maximum amount the consumer is willing to pay is
represented by the demand curve itself. The difference between the amount the consumer is willing to pay
and what the consumer actually pays is consumer surplus. An alternative way of measuring the amount con-
sumers are willing to pay to consume each glass of whisky, is to sum the MU's up to the optimal consump-
tion point. For five glasses of whisky this is 6+5+4+3+2=$20. Newt has to pay a market price of $2 for
each glass or $10 in total. Consumer surplus is then $20-$10 or $10.
2. Remember that the rule of rational behavior for the multi-good case tells us that the consumer should
consume multiple goods in their consumption bundle to the point where the marginal utility for the last
dollar spent on all goods is equal to each other.
That is to the point where:

2. MUx / Px = MUy / Py
However, for this example:
5/3 ≠ 3/1
Since the marginal utility for the last dollar spent on Pepsi is greater than the marginal utility for the last
dollar spent on pizza, the consumer can increase their satisfaction from the consumption of both goods by
consuming more of the good that gives her greater satisfaction per dollar spent. That is, she should consume
more Pepsi.
3. The family that receives the direct cash would be better off if the family values other goods in their
consumption bundle higher than they value food. Generally, consumers prefer variety in their consumption
bundle, and would maximize their total utility from the consumption of all goods (food and others) by
following the rule of rational behavior for the multi-good case.
4.
a) Px/Py = PCD/PRB = 10/5 = 2
b) See the Graph below.
c) Optimum quantities of consumption are found where the slope of the Indifference Curve equals the slope
of the Budget Constraint or where the Indifference Curve and the Budget Constraint are just tangent to each
other. That is where the MRSCD,RB = PCD/PRB. So, Joe buys 2 Root Beer @ $5 each and 1CD @ $10 and
spends all his income of $20.
d) Since the MRSCD,RB is 2 from above, Joe is willing to trade 2 Root Beer for 1 CD at prevailing market
prices..
e) See the graph below.
f) Since the price of CD’s has decreased to $5, Joe’s budget constraint rotates outward (changing the
relative price of CD’s compared to Root Beer) increasing his choice set for CD’s relative to Root Beer. As
a result of the fall in the price of CD’s: Px/Py = PCD/PRB = 5/5 = 1 and Joe is able to move to a higher
Indifference Curve (I1) increasing his satisfaction from consumption by consuming more of the good whose
price has fallen. That is, Joe now buys 3CD’s @ $5 each and 1 Root Beer @ $5 and still spends all his
income of $20.