in the model by creating an additional good, _investment_ ( _I_ ). In the model consumers derive utility by purchasing savings/investment. We set preferences as Cobb-Douglas over investment and all other goods, meaning that consumers devote a constant proportion of their incomes to savings/investment. On the production side of the economy, firms receive funds from sales of their production and from investment. These funds are spent on factors of production. Thus the production sectors are modelled as using factor inputs, to produce jointly a final good ( _untaxed_ , _domestic_ or _export_ ) together with _investment_ . Sector output is divided between the good and investment according to a constant elasticity of transformation function. By setting this elasticity equal to one (Cobb-Douglas), a constant proportion of each production sector’s total income is derived from investment.<sup>8</sup> The production goods use four factors of production: _formal capital_ ( _K_<sup>_f_</sup> ), _informal capital_ ( _K_<sup>_i_</sup> ), _formal labor_ ( _L_<sup>_f_</sup> ) and _informal labor_ ( _L_<sup>_i_</sup> ).<sup>9</sup> One consequence of including informal factors is that capital taxation results in a deadweight loss, even though the total supply of capital is fixed. Labor taxation also induces a deadweight loss as a result of substitution between formal and informal labor, in addition to the deadweight loss arising from substitution between labor and leisure.

Constant elasticity of substitution (CES) functions are used in all production and utility functions. The structure of these functions is set out in Figure 2. The first panel is the utility function, where utility ( _W_ ) is a CES function of _leisure_ , _investment_ , and a consumption good _C_ , and _C_ is a composite good produced by a CES function of _untaxed_ , _domestic_ , and _imports_ . The remaining panels are the production functions for _domestic_ , _export_ and _untaxed_ . The bottom parts of these diagrams represent the nested CES functions over the factors of production, with the top levels representing capital/labor substitution, and the bottom levels representing formal/informal substitution. The top parts of the diagrams represent the CET functions between the final good and investment. The relevant elasticities, used in robustness testing of the model, are labelled by sigma and tau and appropriate sub- and super-scripts.

Taxes are imposed on _domestic_ , _exports_ , _imports_ , _formal capital_ , and _formal labor_ . There are no untaxed traded exports or imports. This is not meant to imply that no smuggling occurs in African countries. Rather, the official figures for trade are based on customs data, which typically reflects taxed goods. An implication is

> 8The modelling differs from the standard 1-2-3 model. The standard model starts with the definition that _GDP_ = _C_ + _G_ + _I_ +( _E − M_ ) (see section 3.2), and combines _C_ + _G_ + _I_ into a single domestic good, giving _GDP_ = _D_ + _E − M_ . In the IMF figures used in this study government spending is already allocated to consumption or investment, so the original data are represented as _GDP_ = _C_ + _I_ + ( _E − M_ ). It would be simple to make the figures for investment disappear (since investment serves no role in a static model) by simply following the standard model. But it seems wrong to suppose that all investment goes toward domestic consumption goods, and that no investment goes into the production of export goods. We have thus included an explicit investment good, ensuring that the full value of GDP is reflected our model.

9 The _informal_ good uses only _informal capital_ and _informal labor_ .

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