# Local Economy Model, v1.0

I've been working with a toy model for a couple of months as a way of exploring the consequences of "buy local" campaigns, and I'm pretty much done with this iteration, so I thought I'd share. I've got all of the messy mathematics sequestered elsewhere on this site, but here are the guts of the model. It's based around three sectors: households (H), locally-owned firms (L), and national chains (N). I use Y to represent Gross Municipal Product, the overall size of the local economy, and I use the subscripts *i* and *e* to represent Income received by and Expenditures made by H,L and N. We'll define the economy thusly:
{${:(H_i = alpha_0L_e + alpha_1N_e),
(L_i = beta_0L_e + beta_1N_e + beta_2H_e),
(N_i = (1-alpha_0-beta_0)L_e + (1-alpha_1-beta_1-r)N_e + (1-beta_2)H_e),
(Y = H_i + L_i + N_i)
:}$}
All of the coefficients on H_{e}, L_{e} and N_{e} (the *α*_{n} and *β*_{n} terms and the sums involving them) represent fractions of the whole, and thus are restricted to between 0 and 1. Also, the coefficients on the household and local expenditures terms add up to 1: household expenditures get split between local firms and national chains, and local firm expenditures are split between households, other local firms, and national chains. However, take note of the *r* in the expression for national expenditures. Unlike households and local firms, the national chains direct some of their expenditures out of the local economy in the form of licensing fees, profits, and so forth, which is represented by the fraction *r* ; it basically acts as a "leak" out of an otherwise sealed system.

Again, the math is hidden elsewhere, but in a nutshell I was able to find how various the different coefficients affect the sectors of the economy, with my main interest being how things affected H. I found the following consequences of this model:

- Spending at national chains tends to have a negative effect on the local economy when compared to the effects of spending at locally owned businesses.
- The household sector can increase its income by redirecting spending away from national chains and toward locally-owned businesses.
- Rational national chains will tend to export a larger fraction of their earnings the less they depend upon the local economy for resources and the larger the fraction of local consumption they absorb.

Again, these conclusions fall immediately out of the model and its assumptions, which are clearly quite simplified (no larger regional economy, no investment, no government, etc.), but as a first step it's reasonably satisfying, at least to me. My next steps are adding a government sector and taxation to the model (which will begin in a moment), and interfacing the current model with the contents of the Andersonville study which undergirds a lot of the rhetoric of the 3/50 Project and similar buy local campaigns.

Categories: Blog, Bootstrapping, EconomicTheory