Public Finance, 2nd Edition

prevents an analysis of the eVect of rationing the X

i

among diVerent con-

sumers. Removing any one of these assumptions would require signiWcant

modiWcations in the government production-tax model of Chapter 22. None-

theless, the model as it stands remains a fairly general description of govern-

ment policy in a second-best environment. It would appear to be applicable

to government hydroelectric projects in which some of the beneWts are sold

(electricity) while others (recreational facilities) are given away even though

they are routinely marketed in other contexts.

We leave it to the reader to derive and interpret the Wrst-order conditions

for this model. The normative policy rules yield a number of interesting

conclusions. The existence of goods (factors) given away (drafted) does not

change either the optimal tax rules or the result that with optimal taxation

(and CRS in private production) the government should discount all

marketed inputs and outputs at their marginal rate of transformation (the

producer price). A diVerent discount rate does apply to all free goods and

drafted factors, however.

THE USE OF SHADOW PRICES FOR GOVERNMENT PROJECTS

The preceding sections discussed three problems commonly associated with

government projectsÐintangibles, lumpiness, and nonmarketed beneWts

(costs)Ðthat are unlikely to arise in private sector analysis. These problems

need not always occur, however. In many instances government projects

might be virtually identical to their private sector counterparts in the sense

that they represent marginal additions to capacity and all inputs and outputs

are bought and sold at competitive private sector prices.

22

Even when this

occurs, however, there are still substantial diVerences between the evalu-

ations of private and public sector costs and beneWts, as a general rule.

As noted above, competitive producer prices are the proper values to

attach to each unit of private inputs or outputs under these conditions, from

society's point of view. pDX is an appropriate gross beneWt measure for a

private project in either a Wrst- or second-best environment.

In contrast, Eq. (22.46), reproduced here as Eq. (26.16) (with a negative

sign, since B dL),

dB t

0

M

ij



E

1

p

ij

dt p

1

g

Z

 p

0

 t

0

M

ij

E

1



dZ (26:16)

gives the proper shadow prices for government inputs and outputs in the one-

consumer-equivalent, second-best economy of Chapter 22. The assumptions

about government producers that underly Eq. (26.16) are the same as for

private producers: The government buys and sells at competitive private

22

One may wonder why the government is involved in the production of these services, but

this is beside the point for cost±beneWt analysis.

800 THE USE OF SHADOW PRICES FOR GOVERNMENT PROJECTS