MACROECONOMICS 2007 Week 3 Seminar Questions: Consumer and Firm Behaviour: The Work-Leisure Decision and Profit Maximization

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Oct 28, 2013 (3 years and 10 months ago)

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MACROECONOMICS







2007



Week 3 Seminar
Questions
:
Consumer and Firm Behaviour: The Work
-
Leisure
Decision and Profit

Maximization



Questions for Review

1.

How are a consumer’s preferences over goods represented?

2.

What three properties do the preferen
ces of the representative consumer have? Explain
the importance of each.

3.

What two properties do indifference curves have? How are these properties associated
with the properties of the consumer’s preferences?

4.

Why is the marginal product of labour d
iminishing?



Problems


1
.

Last week
, we showed an example where the consumer has preferences for consumption
with the perfect complements property. Suppose, alternatively, that leisure and
consumption goods are
perfect substitutes
. In this case, an indi
fference curve is
described by the equation




u

=
al

+
b
C,


where
a

and
b

are positive constants, and
u

is the level of utility. That is, a given
indifference curve has a particular value for
u
, with higher indifference curves having
higher values for
u
.

a.

Show what the consumer’s indifference curves look like when consumption and
leisure are perfect substitutes, and determine graphically and algebraically what
consumption bundle the consumer will choose. Show that the consumption
bundle the consumer ch
ooses depends on the relationship between

and
w
, and
explain why.

b.

Do you think it likely that any consumer would treat consumption goods and
leisure as perfect substitutes?

c.

Given perfect substitutes, is more preferred to l
ess? Do preferences satisfy the
diminishing marginal rate of substitution property?


2
.

Suppose that a consumer can earn a higher wage rate for working “overtime.” That is,
for the first
q

hours the consumer works, he or she receives a real wage rate of
w
1
, and for
hours worked more than
q

he or she receives
w
2
, where
w
2

>
w
1
. Suppose that the
consumer pays no taxes and receives no non
-
wage income, and he or she is free to choose
hours of work.

a.

Draw the consumer’s budget constraint, and show his or he
r optimal choice of
consumption and leisure.

b.

Show that the consumer would never work
q

hours, or anything very close to
q

hours. Explain the intuition behind this.

c.

Determine what happens if the overtime wage rate
w
2

increases. Explain your
results
in terms of income and substitution effects. You will need to consider the
case of a worker who initially works overtime, and a worker who initially does
not work overtime.


3.

Suppose a firm has a production function given by Y=zK
0.3
N
0.7
.

a.

If z=1 and K=1, gr
aph the production function. Is the marginal product
of labour is positive and diminishing?

b.

Now graph the production function when z=2 and K=1. Explain how
the production function changed from part (a).

c.

Given this production function graph the marginal pro
duct of labour
for (z,K)=(1,1), (2,1), (1,2) and explain what you get.