Answers to Selected Questions in Chapters 22 and 23
Chapter 22
Taxation and Efficiency
4
Craig is willing to work 100 hours for $40 per hour but will receive only $24 per hour after tax.
The percentage change in labour is (
∆
L / L) =
η
(
∆
W / W) where W represents wage and
η
is the
ordinary labour supply elasticity. If
η
= 0.5 and the tax rate is 40%, Craig reduces his labour by
20 hours: (20/100 = 0.5
×
16/40). Craig now works 80 hours and pays income tax of $1280 (80
hours
×
$16).
The total deadweight loss (DWL) is the area between the market wage of $40 and the
compensated labour supply curve (ignoring income effects). Assuming a linear compensated
labour supply curve and a perfectly elastic labour demand, the deadweight loss (DWL) of a tax on
a labour is given by:
DWL = 0.5 (Q
1
– Q
2
)(W
1
–W
2
)
As shown in the text, this is equivalent to
DWL = 0.5 Q
1
W
1
η
cs
t
2
where
η
cs
is the compensated labour supply elasticity and
t
is the tax rate. Given a compensated
labour supply elasticity of 0.7 (which ignores income effects), Craig would reduce his labour by
28 hours.
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 Three '09
 a
 Supply And Demand, DWL

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