THE IMPACT OF INFRASTRUCTURE SPENDING IN SUB-SAHARAN AFRICA The demand function of households is derived from a utility-maximization process (Cobb-Douglas utility function), which leads to demand functions that are fixed-value shares for each good. Investment demand is broken down into private investment made by households, the rest of the world, and firm and public investment from government savings. Investment demand is also specified with a fixed-value share function; we already described the demand for intermediate goods, which are fixed volume shares based in input-output matrix shares.

The price equations are standard. We used the GDP deflator as a price index, and as stated earlier, international prices (imports and exports) are exogenous; accordingly, the country has no control over the prices applied to the world market.

The key assumptions of this model are based on infrastructure spending, positive externalities, infrastructure, and budget constraints. Hence, it is important to look at the series of equations directly related to these elements. Other equations of the model also play important indirect roles but these effects are generated via the general equilibrium effects of the simulated policies. We first examine government income sources (equation 1.1). The government draws its revenues from indirect taxes on output ( _Ti_ ), direct taxes on household ( _Td_ ) and firms ( _Tde_ ) and import duties ( _Tim_ ).

The other sources of income are transfers from other agents; these transfers can be negative or positive depending on the country. Three other agents provide transfers from other agents: households ( _Tgm_ ), firms ( _Teg_ ), and the rest of the world ( _Trg_ ). Generally, the _Tgm_ is a negative value, reflecting the fact that the government pays the transfers to households. In countries where public firms are still important, transfers to government are positive if the aggregate public firms make profits; if they run deficits, they are negative. The rest of the world transfers are made up mainly of foreign aid to Africa, a likely funding source for infrastructure investments.

This first equation (1.1) does not provide a complete picture because investment will also be linked to government expenditure on public services. The next equation (1.2) is the budget constraint for government, which will spend part of its income ( _Yg_ ) on public services or expenditure ( _G_ ) and the other part on government savings ( _Sg_ ), which will be used entirely for public investment.

> 1.2 _Sg_  _Yg - G_

At this point, the closure rule<sup>1</sup> used to balance this budget constraint is key to our analysis. We introduce an additional assumption that percentage increases in public infrastructure investment will generate higher operation and maintenance costs. Hence, the level of government expenditure will be a function of its original expenditure ( _Go_ ) plus the operation and maintenance of new infrastructure. This is because empirical studies have shown that new public infrastructure generates higher operation and maintenance costs, which varies by region and type of infrastructure investment. We compute imposed increases in expenditure by computing the increase in public investment ( _Itp - Itpo_ ) and premultiplying _ω,_

> 1 The closure rule consists in determining the variable of adjustment to reach an investment objective and hence the government savings will be exogenous.

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