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Oligopoly / Government Firm | Differentiated Oligopoly | Monopolistic Competition
Oligopoly / Public Firm / Mixed Oligopoly Model
Elmer G. Wiens
The Public Firm (Government Enterprise) with Managerial Incentives
A. Go to the Oligopoly / Public Firm Model. Click here to set the parameters and run the model. The results are displayed graphically. Key words: microeconomics, industrial organization, oligopoly, imperfect competition, government (public) enterprise (firm), managerial bonus systems for public and private companies, production function, cost function, managerial incentives.
My programs let you model an industry that is:
1. a monopoly (private or public),
2. an oligopoly,
3. an oligopoly with one firm a government (public) firm,
4. and, specify the managerial incentives for the government (public) enterprise.
(These managerial incentives can also be used in "private firms" with profit centers.)
The demand function and cost functions (long run and short run) are the standard functions that one can find in any undergraduate microeconomics textbook, with the industry's long run cost curve the 'envelope' of the firms' short run cost curves. I don't let you specify the parameters of these functions (other than shifting them up or down). This does not really limit the model very much. You can specify the number of firms (1-6) in the industry, and how the oligopoly firms interact with each other. Are they price-takers (competitive), Cournot (set the firm's marginal cost equal to the firm's marginal revenue), or are they a cartel (setting each firm's marginal cost equal to the cartel's marginal revenue)?
Public (Private) Managerial Incentives
If one chooses to have a government firm in the model, one needs to specify its behaviour. Is it a price-taker (produce where its marginal cost equals price), or does the government control the firm with some system of bonuses for the managers of the government firm? I permit you to specify bonus weights on the government firm's profit and industry's output. Other schemes are also feasible in a real world situation, like bonus weights on the government firm's profit and (own) output if the firm is large enough (problems can occur when government firm losses are very large), or weights on own profit and the value of industry output if you are sure that demand will remain elastic, i.e. industry marginal revenue is positive).
An alert reader might say: How about bonus rates on profit, output, and industry's revenues? Right! So I've included this option in my model. If the industry's marginal revenue is positive, the model uses profit and revenue bonuses, otherwise it switches to profit and output bonuses.
The one I like the best is: bonus rates on profit, industry output, and the government firm's own revenue (my invention, I think). This seems to yield the largest bonus rate on profit (incentive to minimize costs), yet it still yields bonus rates on the government firm's profit and revenue only. That is, a bonus rate on the industry's output only kicks in when the industry's marginal revenue gets 'really negative' (try my model with 5 competitive private firms). The model for these managerial incentives is contained on the derivation of the model web page. This page is bit technical, but well worth a look.
If the public firm is the only firm, the industry's revenue and firm's revenue are identical.
Computing Managerial Bonus Rates
I just permit you to set the overall bonus amount. My program uses linear programming to calculate the bonus weights on profit, output and revenue (industry or public firm) so that the government firm behaves as a price-taker (mc = price). Furthermore, the total bonus will equal whatever you specify. I use an iterative process to arrive at the correct bonus rates: the information the government needs is surprisingly limited. The derivation of the model illustrates this process with a diagram. The iterative process can be extended — when private firms exhibit Cournot behaviour or form a cartel — to obtain levels of output for the government firm where mc > price.
My 1978 version (rough draft) of this model is available as a pdf download: UCLA Economics: Working Paper #134: "A Positive Theory of Government Firm Regulation" by Elmer G. Wiens.
One can also have the government achieve a target total output for the industry through bonus weights. A version of this mode of regulating the industry is sometimes called 'Harris-Wiens' regulation.
Harris, Richard G. and Wiens, Elmer G. 1980
"Government Enterprise: An Instrument for the Internal Regulation of Industry." Canadian Journal of Economics, 13: 125-31.
1. The government firm is 'firm 0', if present.
2. The scheme with bonus rates on the government firm's profit and own revenue is the most practical — in my opinion — because you can think of the 'quantity' of the product produced by the industry or firm as a vector q = (v1,...,vr) of outputs, and the 'price' as a vector p = (u1,...,ur) of prices. It works (usually) even if the industry's marginal revenue is negative. Furthermore, the public firm does not need any special information about the private firms in the industry.
3. The managerial bonus system with weights on profit and own revenue and/or own output can control the decisions of managers of any profit-center, public or private, with a view to the 'larger' objectives of the parent entity. The events of the last decade show that shareholders' interests and managers' interests cannot be aligned with share options for managers (CEOs and executives). With share options, myopic managers have an incentive to inflate share prices. The managerial bonus system, however, pays on the basis of performance, with managers getting the (fixed) maximum bonus if they behave optimally for the parent entity or shareholders. (Perhaps — to lessen misrepresentation of revenue and cost data, and to place the onus of planning on managers — the managers themselves could have some say about the weights on profit and own revenue and/or own output that would yield a given bonus dollar value.)
4. With 'Harris-Wiens' regulation, I limit you to only 4 firms in the industry. The government firm in the model must be large relative to the industry. Otherwise, the loss (profits) to the government firm could be ridiculously large.
5. With 'Harris-Wiens' regulation my model, aka the government, 'cheats' by computing the target industry output as the 'output that would be achieved if all firms behaved competitively.' The government would need a fantastic amount of information to compute this — the level of industry output that maximizes consumer plus producer surplus. Of course, it would want to revise the target when cost and demand conditions changed, requiring ongoing information collection.
6. The information the government needs can be 'reduced' through iteration.
The derivation of the model web page describes iterative processes with which the government can induce the g.f. to produce a level of output so that its marginal cost = price (or mc > price). The government just needs to know g.f. profits and output, product price, and industry output.
7. A government could use other criteria to maximize its prospects for re-election. For example, a political party backed by labour might place a weight on the total wage bill for the government firm.
8. See my internet essay on
government enterprises and democracy.
9. Remember: It's just a model
10. Use my model to examine the effect of a firm's entry and/or exit on the profits, outputs, etc. of the oligopoly firms.
11. Notice how the bonus rate on g.f. profits gets smaller as the private firms's behavior switches from competitive to Cournot to Cartel. Relate this to the empirical literature on the efficiency of government enterprises.
12. Managerial incentives that place a weight on the profits and the growth of a (private) firm (i.e. revenues) contribute to the firm's productivity. In their Bank of Canada review of technical research on productivity, Richard Dion and Robert Fay state that strong management performance matters "a lot for productivity and other performance indicators at the firm level."
Dion, Richard and Robert Fay. " Understanding Productivity: A Review of Recent Technical Research." Bank of Canada Discussion Paper 2008-3.
B. Oligopoly / Government Firm Model:
Run the Oligopoly / Public Firm Model
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