Inspired by Cheung (2005),1 each day, each potential rideshare driver first chooses whether or not to drive. Revenue for each hour driven that day, determined by the number choosing to drive, is announced. Faced with an upward-sloping marginal cost schedule, each driver then chooses how many hours to drive. Each day, each driver is free to enter whether or not she previously entered.
In the short-run, a firm can choose its variable costs but not its fixed costs. In the long-run, a firm chooses both its variable and fixed costs (i.e., fixed costs are only fixed in the short run).
Short-run profit maximization involves thinking at the margin and choosing all units where the benefit is at least as large as its marginal cost.
In the long-run equilibrium of a competitive market, all firms in the market earn non-negative profits. Any firm that has not entered the market would earn negative profits if it had instead chosen to enter.
After choosing the number of potential firms in each market (Group Size), all you need to do is set the equilibrium number of entrants (Equilibrium Entrants) N*. Entry will generally converge to this equilibrium by round 5, especially with Fixed Costs set to Heterogeneous.
In particular, the market price on a given day is determined by the number of entrants N, P(N) = 2 (8N* + 16)/(2+N). When making the production decision, each producer faces a per-period cost function of C(qi)=Fi+qi2 where Fi and qirepresent the Fixed Costs and Variable Costs of driving. As an example, with N* entrants equal to 6 (default setting), the market price is P=16, and each entrant earns a producer surplus of $64.
With Fixed Costs set to Homogenous, fixed costs are $64 for all firms. Therefore, in the long-run equilibrium N* players enter, and every player earns $0. Of course, the equilibrium does not specify which N* enter.
Consistent with the textbook model, price is determined by a market supply curve that assumes each active firm chooses the profit maximizing quantity (even though, in the game, price is announced before output is chosen).
A profit calculator is consistent across player screens. Prior to the entry decision, a player can vary the number of predicted entrants, and thus, the resulting market price. She can then adjust output to see profits under different scenarios. After all have chosen whether to enter, all players see this same calculator, but with both number of entrants and price fixed. Entrants use this calculator to select output, while a non-entrant can explore whether he would profited had he been one of the entrants.
The aggregate market demand is Q(P)=8N*+16-P, where N* is the equilibrium number of entrants. Solving this game backward, we have each entrant's profit-maximizing production function qi = P/2, where P is the market price on the given day. With the market clearing condition, qi * N = Q(P), we have the market price as a function of the number of entrants N, P(N) = 2 (8N* + 16)/(2+N).
Setting Fixed Costs to Heterogeneous facilitates convergence to the equilibrium number of firms. N* players will have fixed costs drawn randomly between $54 and $64, while the remainder are drawn randomly between $65 and $74. In the unique equilibrium, all of the former, and none of the latter, enter.
The results we present focus on the question of whether groups find the long-run equilibrium number of firms.
Choose Aggregate Results from the dropdown menu at top to see results for each round across all groups (Figure 1). In the table, the second column presents the fraction of entrants choosing the profit maximizing output for each round. The remaining columns show average entry and resulting profits. Use the radio button to select a particular round, and the graph shows the distribution of number of firms entering across all groups.
Choose Individual Markets from the dropdown menu to follow a particular market. The table presents the number of firms entering in each round for each market. Use the radio button in the first column of the table to select a particular market and have its per-round entry shown graphically in the figure under the table. Use the checkbox next to Equilibrium Prediction to control whether it is displayed in the graph.
Our robot (i.e., an automated player) will act in the following way: