## Volltext: Very small countries: economic success against all odds

```where C is the consumption of a bundle of private goods and θ(< 1) is the elasticity of substitution. The budget constraint is: (2) with Y as the exogenous level of individual income. It can easily be shown that the maximization of (1) subject to (2) yields the following optimal supply of the public good: (3) What we are interested in is the ratio of public expenditure to GDP, G/YN. If the first derivative of G/YN with respect to N, (4) is negative, then the ratio of public expenditure to GDP declines with a growing number of tax payers or inhabitants, respectively. Needless to say, the actual sign of equation (4) depends on the range of θ. The less substitutable C and G (the smaller θ), the greater the effect of population on government size. At the limit (where θ= – ∞) one can easily see, though, that an increase of N runs in the opposite direc- tion, but the right-hand side of equation (4) remains negative in any case, with the notable exception of θ= – ∞and N = ∞, where there is no in- fluence of country size (population) on government size (public expen- diture to GDP ratio). It is also fairly easy to show that there are no size effects by using a Cobb-Douglas utility function, which is approached by a unit elasticity of substitution here (θ= 0). For the interval θ= [0;1[ we obtain a positive sign for the right-hand side of equation (4), which would be contrary to the conjecture developed above. If θ= 1, the uti - lity function is linear, but equation (4) is not defined in that case. According to Alesina and Wacziarg (1998) the resemblance to two well-known effects in economics provides a proper intuition. First, an increase in N of course reduces the per capita costs of provision of G and allows more income to be allocated to private consumption. This may be 40Does
country size matter for public sector size? C = Y –GN Y N G =N+ 1
θ θ-1 Y N
Gθ θ-1
∂NN1
θ-1 + 1)
θ θ-1 (N2
= ∂
```

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