While the major argument for a progressive tax system is often framed in terms of equity or fairness, a flat tax is often promoted on grounds of efficiency (greater total wealth). My hypothesis is that a progressive tax system is actually more efficient than a flat tax, arguments of fairness aside. The scope of my proposed experiment cannot make that conclusion, but it begins an evaluation of wealth redistribution that does not involve ethics.
The economy consists of N households and F firms. Each firm has a productivity of random variable P. The experiment lasts from t(0) to t(T). At t(0), the economy has K(0) total assets and each household has a portion k(i,0). At the beginning of every time period, each household invests all its capital in a single firm. The investment decision is made according to the household’s skill, S—its probability of picking the firm with the highest expected value, E(P). A household’s skill is determined at t(0) by sampling the random variable Ð, representing the economy’s skill distribution. After the investments, the firms increase or decrease their capital stocks according to P, then return all capital to their investor-households, in proportion to the investment made. A household’s return on investment is r(i,t). ∑r(i,t) = R(t). At the end of each time period, each household’s income is taxed X%, which is determined by the wealth redistribution function, X = Þ(r).
The key assumption for this model is that the households have a constant and positive desire to increase their assets through investment. The model also treats firms as “black boxes” that simply take in investment and return a dividend.
The two independent variables I would like to focus on are Ð and Þ. Holding all else constant, I believe we can discover a relationship between the two explanatory variables and the growth of K.
If the idea of redistributing wealth rubs you the wrong way, then imagine the model in the context of a venture capital firm. Every year, each associate of the firm is given a portion of the firm’s capital with which to buy a stake in a start-up. The firm sells all its assets at the end of every year. As the owner of the firm, how do you apportion your capital to your employees? Do you let your star investor make all the choices, or do you let some of those with a worse track record (but solid resume) try again?