## COUNTRIES SUBSIDIZE INVESTMENT: A Model to Explain the Investment Subsidy Puzzle

Consider now the second stage. In a competitive labour market, each firm chooses labour input to maximize net revenue Y+z^-wL if production is taken up. This simply yields the marginal productivity condition YL=w. The equilibrium wage rate obviously satisfies w\$c. The wage rate may exceed c if L=N in the equilibrium, i.e. no voluntary unemployment exists. For the following analysis, it is useful to concentrate on the case of an interior solution, where the labour market clears with L
We finally turn to the first stage where the firms choose K. For the analysis of investment behaviour, suppose for the sake of the argument that all firms decide to take up production, that is |ic=0. We show below that this conjecture is indeed correct. Expected profits of a firm i are thus given by

## COUNTRIES SUBSIDIZE INVESTMENT: The Investment Subsidy Puzzle 3

At the third stage, is finally revealed. Given ц;, each firm has to decide whether to take up production or to close down. If the firm produces, the entrepreneur earns Y(L;K)+z |irwL. If the firm is closed down, the workers become unemployed and the capital goods are sold. The liquidation of the firm yields (1+r0)K. We assume r>r0>-1, such that, while the liquidation value of the firm is strictly positive, the return from selling the firm’s assets is less than the market rate of interest. A firm i therefore chooses to produce if and only if

Given that firms may be liquidated, it is natural to ask whether labour contracts chosen before the revelation of can be renegotiated at this final stage. To keep the analysis simple, we rule

out this possibility here. In section 4.4., however, we will show that none of our results is affected if renegotiation is allowed for.

While the entrepreneurs in our economy take investment decisions and manage the firms, there is a second group of agents, the workers. The overall number of workers is N and each worker inelastically supplies one unit of labour such that L denotes the number of workers employed in each firm. Workers have no initial endowment with capital. A worker of a firm which is not liquidated earns the wage rate w while a worker who finds no job or is employed by a firm which is closed down has an income c, which may also be interpreted as the value of leisure. The workers are assumed to be risk neutral, i.e. they only care about their expected income. comments
In the following section, we first analyse the benchmark case where no trade union exists, i.e. the case of a competitive labour market. In section 4.3., we then assume that the workers form trade unions, such that labour contracts are subject to bargaining between unions and firms.

Equilibrium with Competitive Labour Markets

We determine the competitive equilibrium by solving the model recursively, beginning with the third stage. We first note that, for given values of K, w, and L, (2) determines the critical shock level |ic. All firms where the productivity shock turns out to be lower than the critical level |ic are liquidated because the operating profits (the l.h.s. of (2)) is lower than the liquidation value (the r.h.s. of (2)). As all firms in the economy are assumed to be distributed in the interval ц 0 [0;1], a corner solution where no firms are liquidated with |ic=0 may arise. Note that |ic is also the ex ante probability that a firm will be closed down at the third stage. Finally, as we have normalised the overall number of firms in the economy to unity, |ic may also be interpreted as the number of firms which will be liquidated at stage three; hence, the number of producing firms will be 1-^c.

## COUNTRIES SUBSIDIZE INVESTMENT: The Investment Subsidy Puzzle 2

Investment subsidies, in contrast, are paid immediately and therefore serve as a substitute for employment subsidies. This argument, however, has the weakness that it does not explain why the government should not pay out labour subsidies immediately as well, based on future employment as announced by the firms, and raise taxes later in case the firm does not fulfill its employment obligations.
In what follows, we develop a model which gives a different explanation. In this model, union-firm bargaining distorts both employment and investment decisions and leads to an inefficiently low number of active firms. To correct these distortions, the government may use investment and employment subsidies. Our key result is that investment subsidies strictly dominate employment subsidies in this framework.