Chapter 4 – Exercises and suggested
solutions
1.Consider a low-wage labor market. Workers in this market are not presently
covered by the minimum wage, but the government is considering implementing
such legislation. If implemented, this law would require employers in the market
to pay workers a $5 hourly wage. Suppose all workers in the market are equally
productive, the current market clearing wage rate is $4 per hour, and that at this
market clearing wage there are 600 employed workers. Further suppose that under
the minimum wage legislation, only 500 workers would be employed and 300
workers would be unemployed. Finally, assume that the market demand and
supply schedules are linear and that the market reservation wage, the lowest wage
at which any worker in the market would be willing to work, is $1.
Compute the dollar value of the impact of the policy on employers, workers, and
society as a whole.
, Chapter 4 – Exercises and suggested
solutions
1. As a consequence of the increase in the wage they must pay, employers lose surplus that
corresponds to the area of a trapezoid resulting from the reduction in the size of the surplus
triangle under the demand curve for labor. The trapezoid, in turn, can be thought of as a
rectangle with sides equal to the wage increase ($5-$4 = $1) and the new employment level (500)
and a triangle with a height equal to the wage increase ($1) and a base equal to the reduction in the
number of workers demanded (600-500=100). Adding these two areas together, we have (1)(500)
+ (1)(100)/2 = $550.
The 500 workers who remain employed in the market each gain surplus equal to the $1 increase in the
wage that they receive. Hence, their total increase in surplus is ($1)(500) = $500).
The 100 workers who lose their jobs as a result of the minimum wage obviously lose surplus. If these
workers are assumed to be equally distributed along the market supply curve between the market
reservation wage of $1 and the market equilibrium wage of $4, their average loss of surplus can be
computed as (.5)($4-$1) = $1.50. Hence, their total loss of surplus is ($1.50)(100) = $150.
Alternatively, they can be viewed as losing $4 of earnings for each hour they are unemployed, but
gaining leisure that has an average hourly value to them of $2.50 [= (.5)($1 + $4)]. Thus, their total
loss in surplus is ($4.00-$2.50)(100) = $150, the same amount as computed above.
Finally, 200 workers are induced by the higher wage to enter the market. However, since jobs are not
available for these persons, they do not work either before or after the minimum wage is introduced.
Hence, they neither gain nor lose surplus.
Therefore, the total impact of the minimum wage on society as a whole equals:
$500 - $150 - $550 = -$200.
solutions
1.Consider a low-wage labor market. Workers in this market are not presently
covered by the minimum wage, but the government is considering implementing
such legislation. If implemented, this law would require employers in the market
to pay workers a $5 hourly wage. Suppose all workers in the market are equally
productive, the current market clearing wage rate is $4 per hour, and that at this
market clearing wage there are 600 employed workers. Further suppose that under
the minimum wage legislation, only 500 workers would be employed and 300
workers would be unemployed. Finally, assume that the market demand and
supply schedules are linear and that the market reservation wage, the lowest wage
at which any worker in the market would be willing to work, is $1.
Compute the dollar value of the impact of the policy on employers, workers, and
society as a whole.
, Chapter 4 – Exercises and suggested
solutions
1. As a consequence of the increase in the wage they must pay, employers lose surplus that
corresponds to the area of a trapezoid resulting from the reduction in the size of the surplus
triangle under the demand curve for labor. The trapezoid, in turn, can be thought of as a
rectangle with sides equal to the wage increase ($5-$4 = $1) and the new employment level (500)
and a triangle with a height equal to the wage increase ($1) and a base equal to the reduction in the
number of workers demanded (600-500=100). Adding these two areas together, we have (1)(500)
+ (1)(100)/2 = $550.
The 500 workers who remain employed in the market each gain surplus equal to the $1 increase in the
wage that they receive. Hence, their total increase in surplus is ($1)(500) = $500).
The 100 workers who lose their jobs as a result of the minimum wage obviously lose surplus. If these
workers are assumed to be equally distributed along the market supply curve between the market
reservation wage of $1 and the market equilibrium wage of $4, their average loss of surplus can be
computed as (.5)($4-$1) = $1.50. Hence, their total loss of surplus is ($1.50)(100) = $150.
Alternatively, they can be viewed as losing $4 of earnings for each hour they are unemployed, but
gaining leisure that has an average hourly value to them of $2.50 [= (.5)($1 + $4)]. Thus, their total
loss in surplus is ($4.00-$2.50)(100) = $150, the same amount as computed above.
Finally, 200 workers are induced by the higher wage to enter the market. However, since jobs are not
available for these persons, they do not work either before or after the minimum wage is introduced.
Hence, they neither gain nor lose surplus.
Therefore, the total impact of the minimum wage on society as a whole equals:
$500 - $150 - $550 = -$200.
