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ajaz_eco_204_2012_2013_chapter_15_Competition

From the market demand function we can derive the

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Unformatted text preview: sentative consumer” with a Cobb-Douglas utility function and income level ∑ (isn’t it nice that the income of this representative consumer is the sum of the individual consumers’ incomes)3. From the market demand function we can derive the marker demand curve by re-arranging and : ∑ ⏟ ∑ ⏟ More succinctly, letting ∑: ∑ 3 Note to self: in next version, discuss Gorman forms. 5 ECO 204 Chapter 15: Competitive Firms and Markets (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Notice that this aggregate demand curve is non-linear and in fact is a constant elasticity demand model with price elasticity always equal to -1 (can you show this?). _________________________________________________________________________________________________ Example: Let’s try a different example, this time with numbers. Suppose “good 1” is the commodity being analyzed and “Good 2” is “all other goods”. Suppose there are two price taking consumers “A” and “B”, each with the following quasilinear utility function: By the way, this is a special case of where . Assuming an interior solution to their UMPs, you can show that each individual’s demand function for good 1 is: In turn, the aggregate demand function is: From this we have the aggregate market demand curve: __________________________________________________________________________________________________ In summary, to derive the market demand curve we assume all consumers are price takers solve each consumer’s UMP and derive her demand function for the good in question sum the demand functions for all consumers to get the market demand function re-arrange to get market demand curve. 3. The Competitive Firm’s Demand Curve To derive the competitive market supply curve, we need to derive each firm’s supply curve, but for that we need to derive each firm’s demand curve. This is because the firm takes price as given and the only decision it makes is how much to produce and for this we need to derive the firm’s “demand curve”. Suppose the market price and quantity has been determined and let’s denote these by (see graph below): The “Market” A Price Taking Firm Assuming static rivals Market Supply This firm’s capacity Market Demand For convenience, linear demand and supply curves shown.In practice these are often non-linear 6 ECO 204 Chapter 15: Competitive Firms and Markets (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Consider the following scenarios in which a particular firm’s price is greater than the market price, equal to the market price, or less than the market price. Assuming dormant, static rivals and that the firm’s capacity is greater than the maximum market size we have: { Putting these together gives us the firm’s demand curve (the “kinked” orange line below): The “Market” A Price Taking Firm Assuming static rivals Market Supply Market Demand Firm Demand This firm’s capacity Market Demand For convenience, linear demand and supply curves shown.In practice these are often non-linear For simplicity, we will always work with the horizontal portion of the firm’s demand curve so that the firm’s demand curve is a constant and equal to the market price (for simplicity let’s denote the market price by ). With a flat demand curve equal to we see that the firm’s revenue from producing output is: ⏟ Because a competitive firm’s price is always constant and invariant to the firm’s output, we do not write its demand curve as a function of output: (that would be the case for a firm with market power since its price depends on its quantity). For a competitive firm: Whereas for a firm with market power (a downward sloping demand curve and ): 7 ECO 204 Chapter 15: Competitive Firms and Markets (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Notice that demand curve slope. In fact, we can derive a competitive firm’s marginal revenue from the above equation by noting that it’s demand curve is flat so that and therefore A Firm with “Market” Power (“Monopoly”) ⏟ . A Price Taking Firm Competitive Firm Demand and Curve Market Demand Curve For convenience, shown here is a linear demand curve for firm with market power Next, we derive a competitive firm’s supply curve. 4. The Competitive Firm’s and Market Supply Curve Consider a “good” (product/service) sold in a competitive market with price taking firms, where “price taking” behavior may arise with a “few” firms. Start by assuming that the “market” consists of “price taking” rational firms with exogenously given input prices. Denote: Given price Given price quantity supplied by an individual price taking firm this is total “market” quantity supplied by all firms in the market ∑ To obtain the market supply curve we need to derive individual firms’ supply curve – a supply curve is supposed to tell us how much output a price ta...
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