The demand curve that an individual firm faces is called the residual demand curve: the market demand that is not met by other sellers at any given price. The firm's residual demand function, Dr(p), shows the quantity demanded from the firm at price p. A firm sells only to people who have not already purchased the good from another seller. We can determine how much demand is left for a particular firm at each possible price using the market demand curve and the supply curve for all other firms in the market. The quantity the market demands is a function of the price: Q = D(p). The supply curve of other firms: So(p). The residual demand function equals the market demand function, D(p), minus the supply of all other firms: Dr(p) = D(p) – So(p).
At prices so high that So(p) is greater than D(p), the residual demand, Dr(p), is zero. ________________________________________
Residual Demand Curve. The residual demand curve, Dr(p), a single office furniture manufacturing firm faces is the market demand, D(p), minus the supply of the other firms in the market, So(p). The residual demand curve is much flatter than the market demand curve. ________________________________________
In the figure, we derive the residual demand for a Canadian manufacturing firm that produces metal chairs. Panel b shows the market demand curve, D, and the supply of all but one manufacturing firm, So.1 At p = $66 per chair, the supply of other firms, 500 units (one unit being 1,000 metal chairs) per year, exactly equals the market demand (panel b), so the residual quantity demanded of the remaining firm (panel a) is zero. At prices below $66, the other chair firms are not willing to supply as much as the market demands. At p = $63, for example, the market demand is 527 units, but other firms want to supply only 434 units. As a result, the residual quantity demanded from the individual firm at p = $63 is 93 (= 527 - 434) units. Thus, the residual demand curve at any given price is the horizontal difference between the market demand curve and the supply of the other firms. The residual demand curve the firm faces, panel a, is much flatter than the market demand curve, panel b. As a result, the elasticity of the residual demand curve is much higher than the market elasticity. If there are n identical firms in the market, the elasticity of demand, i, facing Firm i is i = n – (n – 1) o,
where is the market elasticity of demand (a negative number), o is the elasticity of supply of each of the other firms (typically a positive number), and n – 1 is the number of other firms. There are n = 78 firms manufacturing metal chairs in Canada. If they are identical, the elasticity of demand facing a single firm is i = n – (n – 1) o = [78 x (–1.1)] – (77 x 3.1)
i = –85.8 – 238.7 = –324.5.
So even though the market demand elasticity is only –1.1, a typical firm faces a residual demand elasticity of –324.5. If a firm raises its price by one-tenth of a percent, the quantity it could sell would fall by nearly one-third. Therefore, the competitive model assumption that this firm faces a horizontal demand curve with an infinite price elasticity is not much of an exaggeration. As Equation 2 shows, the residual demand curve a single firm faces is more elastic the more firms, n, in the market, the more elastic the market demand, , and the larger the elasticity of supply of the other firms, o. ________________________________________
1 The figure uses constant elasticity demand and supply curves. The elasticity of supply, 3.1, is based on the estimated cost function from Robidoux and Lester (1988) for Canadian office furniture manufacturers. I estimate that the elasticity of demand is –1.1, using data from Statistics Canada, Office Furniture Manufacturers.
Market Demand Curve:
The market demand curve for a good, service, or commodity is defined with the following backdrop: •
The specific good, service, or commodity.
A unit for...
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