CHAPTER 2
2-1. How many hours will a person allocate to leisure activities if her indifference
curves between consumption and goods are concave to the origin?
A worker will either work all available time or will not work at all. As drawn in Figure A,
point B is preferred to points A and C. Thus, the worker chooses not to enter the labor
market. As drawn in Figure B, point C is preferred to both points A and B. Thus, the worker
chooses not to consume any leisure and to work all available time.
Figure A Figure B
Goods Goods
C
C
U1
U1
A A
U0 U0
B B
Hours of Leisure Hours of Leisure
2-2. What is the effect of an increase in the price of market goods on a worker’s
reservation wage, probability of entering the labor force, and hours of work?
Suppose the price of market goods increases from p to p and the person’s non-labor income
is V. If she chooses not to work, she can purchase V/p units of consumption after the price
change, whereas she could have consumed V/p units of consumption prior to the price
,increase. Thus, her endowment point has moved from E to E in Figure A (on the next page).
Under normal conditions, including that leisure is a normal good, the indifference curve is
steeper as we move up a vertical line, indicating that the slope of the indifference curve is
steeper at E than at E. Thus, an increase in the price of goods lowers the reservation wage
and makes the person more likely to work.
[Figure A is on the next page.]
, Figure A.
To simplify the illustration of the effect on hours of work, assume for simplicity that V = 0.
The increase in the price of goods shifts the budget line from FE to GE in Figure B below,
moving the worker from P to point R. This shift induces both an income effect and a
substitution effect. The price increase lowers the person’s real wage rate, increasing the
demand for leisure and leading to fewer hours of work (the substitution effect). This
substitution effect is illustrated by the move from point P to point Q in Figure B. The price
increase also reduces the worker’s wealth, lowering the demand for leisure and leading to
more hours of work (the income effect). This income effect is illustrated by the move from Q
to R. As drawn the income effect dominates the substitution effect and the price increase
lowers the demand for leisure and increases hours of work. It is, of course, possible for the
substitution effect to dominate the income effect (not pictured), so that hours of work
, decreases. Thus, without further restrictions on preferences, an increase in the price of
market goods has an ambiguous effect on hours worked.
Figure B.
2-1. How many hours will a person allocate to leisure activities if her indifference
curves between consumption and goods are concave to the origin?
A worker will either work all available time or will not work at all. As drawn in Figure A,
point B is preferred to points A and C. Thus, the worker chooses not to enter the labor
market. As drawn in Figure B, point C is preferred to both points A and B. Thus, the worker
chooses not to consume any leisure and to work all available time.
Figure A Figure B
Goods Goods
C
C
U1
U1
A A
U0 U0
B B
Hours of Leisure Hours of Leisure
2-2. What is the effect of an increase in the price of market goods on a worker’s
reservation wage, probability of entering the labor force, and hours of work?
Suppose the price of market goods increases from p to p and the person’s non-labor income
is V. If she chooses not to work, she can purchase V/p units of consumption after the price
change, whereas she could have consumed V/p units of consumption prior to the price
,increase. Thus, her endowment point has moved from E to E in Figure A (on the next page).
Under normal conditions, including that leisure is a normal good, the indifference curve is
steeper as we move up a vertical line, indicating that the slope of the indifference curve is
steeper at E than at E. Thus, an increase in the price of goods lowers the reservation wage
and makes the person more likely to work.
[Figure A is on the next page.]
, Figure A.
To simplify the illustration of the effect on hours of work, assume for simplicity that V = 0.
The increase in the price of goods shifts the budget line from FE to GE in Figure B below,
moving the worker from P to point R. This shift induces both an income effect and a
substitution effect. The price increase lowers the person’s real wage rate, increasing the
demand for leisure and leading to fewer hours of work (the substitution effect). This
substitution effect is illustrated by the move from point P to point Q in Figure B. The price
increase also reduces the worker’s wealth, lowering the demand for leisure and leading to
more hours of work (the income effect). This income effect is illustrated by the move from Q
to R. As drawn the income effect dominates the substitution effect and the price increase
lowers the demand for leisure and increases hours of work. It is, of course, possible for the
substitution effect to dominate the income effect (not pictured), so that hours of work
, decreases. Thus, without further restrictions on preferences, an increase in the price of
market goods has an ambiguous effect on hours worked.
Figure B.
