Ceris-Cnr, W.P. N° 3 /2008

D0 = Marginal Social Benefit

D1= Private Social Benefit
S0
M0

R1

C0

R0

M1

S1

R2

R3

C1

R

D2 = Marginal Social Benefit after the subsidy
D0 = D1

S1

C1

M2

R3

R4

S2

R5

C2

R

FIGURE 4. THE EFFECT OF PUBLIC GRANTS ON THE OPTIMAL ALLOCATION OF BUSINESS
R&D IN PRESENCE OF SPILLOVERS

Here, the new equilibrium (the long-run equilibrium) is in M2 which is, in turn, a sub-optimal
point since subsidy spillovers have in the meantime created a new curve of marginal social benefits
(D2) determining the social optimum in the point S2 where the cost is C2. In other words, any attempt
to correct market failure by injecting subsidies could fail in presence of significant spillover effects
since dynamic structural change (cost reductions) activated by the subsidy through the spillovers
modify the expected allocation. The subsidy, nevertheless, will produce a substantial technical
change and production growth (as long as directed towards sectors with higher spillovers).
According to the analysis of Klette, Møen and Griliches (2000, p. 483), a full cost-benefit analysis
of an R&D support would take into account the estimation of the following expression:
[4]

w( s ) =

∑ Δπ (s ; s ) + ∑
i

i∈Sub

i

j∈ NSub

Δπ j ( s ) +

∑

k ∈Rest

Δπ k ( s ) +

∑ Δ(CS ) − d (s)
l

l ∈C

where Sub is the set of subsidized firms, NSub that of non-subsidized, Rest that of the rest of the
economy, CS the consumer surplus and d(s) the loss associated to the subsidy. The first term on the
right-hand-side of the [4] represents the change in profits of subsidized firms, that depends on the
subsidy received (i.e., the direct effect of si) and the effect of the change in profits of the other
supported firms (i.e., the indirect effect labeled s ); the second term is the change in profits of nonsubsidized firms (belonging to the same industry) that are a mixture of rent and knowledge

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