Variables

Consider a government that levies a lump-sum tax T on households and uses these tax resources to hire a fraction δ ∈ [0, 1] of the total workforce as policemen, LP, to enforce the rule of law. Hence, under a balanced budget we have for all t

T = wLP = wδL. (3.18)

We stipulate that the strength of the rule of law, q, depends on the share of the policemen in the total workforce, δ = LP/L, according to

q = F (δ) with F : [0, 1] → [0, 1]. (3.19) F is C² with F (0) = q0 ∈ (0, qmin), F (1) = 1, F⁰ > 0 > F⁰⁰, and lim

δ→0F⁰ = ∞.

3.4.2.1 Dynamic General Equilibrium

The representative household’s flow budget constraint is now ˙Ω = wL + Ω + M − pcc − T . This modification leaves the Euler and the transversality condition of the household’s problem unaffected. Since workers are also used as policemen, the labor market equilib-rium condition is now Lx(t)+LA(t) = (1−δ)L. Then, given δ, the equilibrium consists of an allocation {y(t), c(t), Ω(t), M (t), x(j, t), l(j, t), Lx(t), LA(t), LP(t), A(t), T (t)}^t=∞_t=0 and a price system {r(t), pc(t), w(t), p(j, t), v(j, t)}^t=∞_t=0 such that (3.18), (3.19), the new labor market equilibrium condition and the remaining conditions of the DGE of Section 3.3.1 hold.

Then, following the same steps that led to the steady-state growth rates in Section 3.4.1.1 we obtain the steady-state growth rates as

g^∗_A = max



0,(1 − α)(1 − δ)F (δ)L − aαρ a [F (δ)(1 − α) + α]



≡ g_A^∗(δ) (3.20) and

g_c^∗ = σ

 − 1g_A^∗. (3.21)

In contrast to Section 3.4.1.1, government activity as captured by δ has two opposing effects on the steady-state growth rates of A and c. On the one hand, government spending on the rule of law positively affects the equilibrium growth rates through its effect on q. On the other hand, government activity reduces the labor supply available for research and intermediate-good production to (1 − δ)L. The following proposition establishes the growth-maximizing government policy.

Proposition 3.4. It holds that

1. if ˆδ = arg max

δ∈[0,1]

(1 − δ)F (δ) is such that (1 − ˆδ)F (ˆδ) ≤ qmin, then g^∗_A = 0 for all δ ∈ [0, 1].

2. if (1 − ˆδ)F (ˆδ) > qmin, then there are δmin and δmax with 0 < δmin < δmax < 1 such thatg^∗_A> 0 for all δ ∈ (δmin, δmax). In this case, there is a unique δ^∗ ∈ (δmin, δmax) that maximizes g_A^∗ and g_c^∗.

The first statement of Proposition 3.4 reveals that the government’s ability to move the economy to an equilibrium with strictly positive growth rates depends on the environ-ment, in which the economy operates, i. e., qmin, and on the effectiveness of the police as specified by the function F .⁸ If qmin is large and/or the police not very effective, then the reduction of the workforce due to public employment of policemen outweighs its benefits and the steady-state growth rate is zero, independent of the choice of δ. If government intervention can trigger positive growth rates, then according to the second statement of Proposition 3.4, there is a growth-maximizing share of government activity, δ^∗, which balances the two opposing effects of government activity.

3.4.2.2 Welfare Analysis

In this section, we derive the welfare-maximizing policy of the government and compare it to the growth-maximizing policy. Following the same steps as in Section 3.4.1.2, we obtain the following piecewise-defined welfare function:

U =

The following proposition establishes the share of government employment that maxi-mizes U and compares it to the growth-maximizing share discussed in Proposition 3.4.

Proposition 3.5. The following statements are true.

1. If Statement 1 of Proposition 3.4 holds, then U is maximized at δ = 0.

8As before, we assume that the environment of our economy is such that there would be positive growth if the rule of law were perfect without any government intervention, i. e., qmin = aαρ/(1−α)L <

1.

2. If Statement 2 of Proposition 3.4 holds, then

Similarly to Proposition 3.3 , Proposition 3.5 reveals that in terms of welfare no growth can be better than some growth. Moreover, if a positive welfare-maximizing public employment share exists it will be strictly smaller than the growth-maximizing one, i. e., δ^∗∗< δ^∗. To grasp the intuition for this, consider that

The second term, i. e., the consumption growth rate is maximized at δ^∗. By contrast, the first term, which corresponds to the static welfare effect, is always negative because a rise in δ reduces the resources available for final-good production. Thus, the public employment share that maximizes U has to be smaller than the one that maximizes g^∗_c. Hence, we conclude that our qualitative results regarding the welfare-maximizing gov-ernment policy do not depend on whether the govgov-ernment uses final output or part of the labor force to enforce the rule of law.

3.5 Concluding Remarks

This chapter studied the interdependence between innovation, economic growth, and the rule of law in an economy where growth results from an expanding set of product varieties. The strength of the rule of law determines the profit that firms expect from an innovation investment. The results may be summarized as follows.

9In the non-generic case where U (0) = U (δ^∗∗), the solution of max

δ∈[0,1]U is not unique.

First, on the positive side, we find that a weak rule of law may be the reason why an economy is caught in a “no-growth trap”. In other words, a minimum strength of the rule of law is a prerequisite for sustained growth. Second, on the normative side we establish that a weaker rule of law may be Pareto-improving. This is the case when the equilibrium growth rate exceeds the Pareto-efficient one. Then, the mafia acts like a government charging a tax on monopoly profits, which reduces the incentive to innovate in a desirable way.

Third, when government investment determines the rule of law endogenously, such an in-vestment may shift the economy from a no-growth equilibrium onto a welfare-improving equilibrium with strictly positive growth rates. This is always possible if the government invests final output in the enforcement of the rule of law. By contrast, if policemen are necessary to enforce the rule of law, this possibility arises only if the economic envi-ronment is sufficiently favorable to research and/or policemen are sufficiently effective.

Finally, even if the government is ready to intervene, the price of fighting the mafia may be too high. In this case, in terms of welfare no growth may be better than some growth.

Overall, however, the more favorable the economic environment is towards innovation and growth, the more likely it is that the welfare-maximizing strength of the rule of law requires taxes and government intervention.