Notes

EQUILIBRIUM AND AGGREGATE VARIABLES

A stationary competitive equilibrium in the model consists of (1) consumption, firm entry in each sector, and saving decisions of the household [c, a, Me1, Me2, M1, M2]; (2) labor demands and prices for each variety, and innovation and exit decisions of formal firms [l1 (ω), p1 (ω), l2 (ω), p2 (ω), qt (ω), ιt (ω)]; (3) demand functions for intermediate inputs and final output [y1 (ω), Y1, y2 (ω), Y2]; (4) the age distributions of informal firms, the productivity distribution of formal firms, schedules of idiosyncratic distortions, and the entry barrier: [Mt (ω), f2 (a), [1 − τω], τ E]; and (5) interest rate and wages such that: (1) solves households’ optimization problem, subject to the budget constraint, the law of motion for the number of firms, and taking as given the interest rate, the wage rate, aggregate demand, and the profile of idiosyncratic distortions; (2) solves each producer’s intermediate goods static profit maximization problem; taking as given wages, the demand functions for individual varieties, and the laws of motion for idiosyncratic productivity; (3) solves the final good’s static profit maximization problem, taking as given the price of intermediate varieties; and the labor market clears, net asset demand is equal to zero, and the free-entry conditions are satisfied.

This chapter was commissioned by the World Bank’s Chief Economist Office for South

Asia, in support of a flagship report on informality in South Asia. The views presented here are solely the author’s and do not represent the World Bank Group’s or any of its member countries. 1. OECD-World Bank Group Product Market Regulation database, 2013–18. 2. Examples of idiosyncratic distortions are: financial frictions, size dependent labor regulations, and size-dependent tax enforcement, among others. 3. One could have directly defined Q to be the aggregate consumption, where the aggregation is done at the level of the household. This is isomorphic to our specification of Q as a good produced by a final good aggregator. 4. To fix ideas, consider the effect of a particular type of financial friction, a collateral constraint whereby firms can only borrow up to a proportion λ of their assets in order to pay for the wage bill. In this case, there would not be a (1 −τω) in the profit function, but would rather be a constraint l(ω) <λa affecting the demand for labor. If the constraint binds, then, the first order condition with respect to labor would take the form (1 − multiplier) * MRPL = w, where multiplier is the multiplier of the financial friction. This shows that the modeling of the distortion, in this case a collateral constraint, as a revenue tax is in many cases equivalent in terms of their implication for optimality conditions. 5. Since the assumption of the theory is that firms confront the same wage rate, we think that this is most likely to be the case in reality across firms within a narrow industry, but it is less likely across firms in very different industrial categories. Accordingly, it is to maximize the plausibility of the assumption that we assess the degree of dispersion in marginal revenue products across firms within a narrow industry classification.