Determination of price and quantity supplied by firm in the short run

From Market

This article describes the general process by which a firm selling a good, service, or commodity in a market determines the price and quantity to supply to the market in the short run. The significance of short run here is that the firm cannot alter its fixed costs, so its total production depends only on its variable costs.

Extreme cases

General principles

  • The firm has its own marginal cost curve. The analysis and construction of the marginal cost curve is (largely) independent of the market structure or of specific data on the demand side (in small oligopolistic structures, advertising expenses can play a significant role).
  • The firm receives data from the market that allow it to construct a marginal revenue curve. This marginal revenue curve depends both on the market demand curve and on the rest of the firms in the market. Two extreme cases:
    • Perfect competition: The firm receives a single price value, and the marginal revenue curve is a flat curve with constant value equal to that price.
    • Monopoly: The marginal revenue curve has a marginal-to-average relationship with the market demand curve.

The calculation problem: first step: determine price in terms of quantity

  1. The firm first constructs its price curve (price to charge as a function of quantity): this is a curve that plots, for each quantity the firm produces, the maximum price it can charge at which it can sell off the entire quantity. In the case of perfect competition, the price curve is the market price curve (i.e., the price function is constant at the market price). In the case of monopoly, the price curve is the market demand curve.
  2. The firm can then construct its revenue curve: The revenue is plotted as a function of quantity. It is the product of the price function with quantity. Explicitly, if the price function of quantity is , then the revenue as a function of quantity is .
  3. The firm can then construct its marginal revenue curve: The marginal revenue function is the derivative of the revenue function. It has a marginal-to-average relationship with the price function.

Determination of the price function

The key challenge for the firm is to determine the maximum price it can charge for a given choice of quantity it produces. Two extreme cases are easy:

  • Perfect competition: The price is constant at the market price, regardless of how much the firm produces.
  • Monopoly: The graph of the price function coincides with the market demand curve (note that the roles of dependent and independent variable are switched: the market demand curve viewed quantity as a function of price, whereas the price function views price as a function of quantity).

Complications arise in intermediate situations. The key difference in intermediate situations is that competing sellers can respond to one's pricing decisions. In oligopolistic situations, this is studied using paradigms of game theory. Similar tools may be needed in the case of monopolistic competition, where a seller has a monopoly of sorts but there are sufficiently close substitutes that respond to the seller's pricing decisions.

The calculation problem: second step: determining quantity

Upshot: The analysis is similar to that for monopoly, and is mathematically identical, only the marginal revenue curve now need not come from the market demand curve but could be constructed another way.

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