# Model

## Agent Behavior

Consider N firms selling goods to M households. Households are free to choose from which firm they purchase a product, but their demand for the product is inelastic—they must buy from one firm—and constant over time (one unit per period). Firms sell two products that are exact physical substitutes: a lower value product 1 (representing the standard mix of conventional electricity) and a higher valued product 2 (representing purely renewably generated power). Households weigh the choice of purchasing product 1 or product 2 against other aspects of their preferences in deciding for a firm to be their supplier.

Let all N firms and all M households be distributed on a two-dimensional plane. Firms and households do not change their position throughout the simulation. Each firm i sells only one type of product (t = gray or green) in each period and does not change products throughout the simulation. We refer to firms selling gray electricity as gray firms and to firms selling green electricity as green firms. Households that are densely placed on the map are explicitly labeled as either belonging to a given regional cluster or not. Household j has a preference for the green electricity product defined by the parameter gj > 0 which weights a household’s utility of consuming renewable electricity instead of the standard mix.

Each household *j* also considers regionality to be a factor in choosing a supplier. This is reflected in their preferences by the factor ф which weights physical distance from the household to the supplier. Household *j*’s utility is thus a function of price (p_{i}), the type of product (gray or green) and the distance to the selling firm (dj). Households’ utilities take the following functional form:

where p is the price paid for power, d is the distance to the selling firm, ф is a parameter weighting distance in the household’s decision, and *U _{0}* is the intercept of the utility function. T

_{eco}is equal to one if the firm sells renewable power, and is equal to zero otherwise.

*i*indexes firms and

*j*indexes households.

Households thus choose the firm *i* from which they purchase according to:

**Fig. 5 ****Wholesale and retail market structure (conventional mix and RES electricity)**

Firms set prices equal to their costs plus a markup:

where c_{;} denotes the wholesale costs of supplying the product and *в _{;}* the markup. c

_{; }is given by exogenously set, constant wholesale prices for the two types of power. These prices are equally available to all firms on an open wholesale exchange (see Fig. 5).

Letting *x _{;}* denote the total demand of household customers of firm i, we model the price setting decision of the firm such that firm i adjusts its markup up or down by a fixed incremental amount such that the firm’s expected profit increases the most. There are three possible outcomes for each firm: (1) raise markup, (2) keep markup constant, or (3) lower markup. If the firm adjusts price downward, and expects (ceteris paribus) to capture no household demand in the next period, then it continues to adjust its markup downward until some household customers are expected to be acquired. Firms assume in forecasting next period sales that the prices of all other firms remain unchanged. Furthermore, we assume that households’ preferences are known to the firms for the purposes of forecasting sales.