Inspired by Cheung (2005),1 each day, each potential rideshare driver first chooses whether or not to drive. The number choosing to drive determines hourly revenue for those driving. Upon learning the day's hourly revenue—and faced with an upward-sloping marginal cost schedule—those driving that day choose 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, 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: choosing all those 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). Entry will generally converge to this equilibrium by round 5.
In particular, each producer faces a per-period cost function of C(qi)=Fi+qi2. With N* equal to equilibrium entrants, players face market demand Q(P)=8N*+16-P. With N* entrants, market price is P=16, and each entrant earns a producer surplus of 64.
With Fixed Costs set to Homogeneous, 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 have profited had he been one of the entrants.
The default setting of Fixed Costs equal to Homogeneous matches the standard textbook model and highlights the “magic” of equilibrium entry when all firms are identical. Setting Fixed Costs to Heterogeneous facilitates convergence to the equilibrium number of firms. N* players will have fixed costs drawn randomly between 54 and 63, 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 (group). 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.