Unformatted text preview: sentative consumer” with a CobbDouglas 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 rearranging 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 20122013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. Notice that this aggregate demand curve is nonlinear and in fact is a constant elasticity demand model with price
elasticity always equal to 1 (can you show this?).
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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 rearrange 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 nonlinear 6
ECO 204 Chapter 15: Competitive Firms and Markets (this version 20122013) 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 nonlinear 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 20122013) 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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 Fall '14

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