End of Chapter Exercises: Solutions
Chapter 5
1. Draw an upward sloping supply curve and a downward sloping demand curve for
labour. Label the axes. Assuming that the labour market is distorted by a
minimum wage (which is a binding constraint), draw in the level of the minimum
wage, labelled wm, and identify the quantity of labour demanded, labelled Q. On
the supply curve of labour, identify the level of the wage corresponding to Q units
of labour supplied, and label it wa.
(i)
state what the efficiency benefit-cost analysis rule tells us about valuing
labour input in a benefit-cost analysis;
(ii)
suppose that a project will use a small amount of labour drawn from the
above market. Under what circumstances should the labour be costed in
the efficiency benefit-cost analysis at:
(a) wm per unit;
(b) wa per unit?
Answer:
(i) value the labour input at opportunity cost
(i)
(a) when the labour is diverted from alternative employment and cannot be
replaced in that employment from the ranks of the unemployed;
(b) when the labour would otherwise be unemployed
2. Suppose that the elasticity of demand for a monopolist's product is 1.5. Calculate
the ratio of the value of the marginal product of labour to the marginal revenue
product of labour. What is the opportunity cost of labour expressed as a multiple
of the wage? What is the appropriate shadow-price of labour diverted from the
monopoly's production process?
Answer:
Since MR=P(1-1/e), where e is demand elasticity expressed as a positive number,
the ratio of VMP/MRP=1/(1-1/e)=3. Since MRP=w the opportunity cost of labour,
measured by its VMP, is 3w.
3.
For each of the sixteen cases indicated in the following diagram, state
whether you would use the demand curve or the supply curve to determine the
appropriate price for valuation purposes in an efficiency benefit-cost analysis,
and state whether the appropriate price is gross or net of the tax or subsidy. In
each case briefly justify your answer.
Item to be valued
Project Output
- Satisfies additional demand
- Satisfies existing demand
from alternative source
Project Input
- From additional supply
- Diverted from alternative use
Indirect Tax
Distorting
Corrective
Subsidy
Distorting Corrective
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(xiii)
(x)
(xiv)
(xi)
(xv)
(xii)
(xvi)
Answer:
(i) output is valued at a point on the consumer demand curve – inclusive (gross) of
tax
(ii) output is valued at a point on the consumer demand curve less the external cost,
which is measured by the tax. Hence net value of output per unit is price exclusive
(net of) tax.
(iii) output is valued at a point on the consumer demand curve which is the
subsidized price – the supply price less the subsidy.
(iv) output is valued at a point on the consumer demand curve plus the external
benefit, which is measured by the tax. Hence gross value of output is the
unsubsidized price.
(v) output is valued at a point on the supply curve which is the price net of tax.
(vi) same as (v) above. The reason is that the level of the total external cost does not
change because the total quantity consumed does not change.
(vii) output is valued at a point on the supply curve which is the unsubsidized price.
(viii) same as (vii) above. The reason is that the level of the total external benefit
does not change because the total quantity consumed does not change.
(ix) input is costed at a point on the supply curve which is the price net of tax.
(x) input is costed at a point on the supply curve plus the marginal external cost,
which is measured by the tax. Hence use the gross of tax price.
(xi) input is costed at a point on the supply curve which is the unsubsidized price.
(xii) input is costed at a point on the supply curve less the marginal external benefit,
which is measured by the subsidy. Hence use the subsidized price.
(xiii) input is costed at a point on the demand curve which is the price gross of tax.
(xiv) same as (xiii) above. The reason is that the level of the total external cost does
not change because the total quantity used does not change.
(xv) input is costed at a point on the demand curve which is the subsidized price.
(xvi) same as (xv) above. The reason is that the level of the total external benefit
does not change because the total quantity used does not change.