Intermediate Microeconomics Ch22 notes

Intermediate Microeconomics Ch22 notes - Ch 22-23. Firm and...

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1 Ch 22-23. Firm and Industry Supply In these two chapters, we will study how a competitive firm chooses its level of output based on its cost function to maximize its profits, how the firm’s supply curve can be derived from its cost function, and how the supply curves of all firms in an industry can be aggregated to obtain the market supply curve of the industry’s output. We will also distinguish between the LR and the SR curves in order to have a good understanding of a firm’s and an industry’s supply behavior. Some of the material presented in this note is quite different from that in the text. You should closely follow the logic to be developed as follows. These two chapters are the most difficult of production theory, and you will have to read this note very carefully to avoid confusion. 1. Market Environment We will deal with a purely competitive market with an identical product and many small firms so that each firm is just a price taker and worries only about how much to produce. The market price is outside the control of any individual firm (whose action y has no influence on the price p ). We need to distinguish between the market demand curve and the demand curve facing a firm . The former measures the relation between the market price and the total amount of output sold by the industry, whereas the latter curve measures the relation between the market price and the output of that particular firm . The firm can sell nothing above the market price since consumers buy the cheapest good. Also, the firm has no reason to sell below the market price since to do so would reduce its profits and could trigger over-competition with other firms. Thus, the demand curve a firm faces for its output is a horizontal line at the market price. 2. The Firm’s Supply Curve As mentioned before, a firm’s profit maximization can be broken into two stages. First, we obtain its cost function C(y) by choosing inputs to minimize costs for any given y . Next, we can model how the firm chooses output y to maximize its profit by taking output price p as given: ) ( ) ( max y C py y y = π As usual, the optimality condition is MR = MC . In the competitive case, MR = p and MC = C’ (y) . So, solving p = MC(y) yields the firm’s optimal choice of output : y* = y(p),
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2 which can be roughly viewed as the firm supply curve as price p changes, and we will elaborate on this point shortly. Note that p = MC(y) is the firm’s inverse supply curve. The proof of p = MC as the optimality condition: By definition, y* is the profit- maximization output such that p = MC (y*) {= y C at y * }. Suppose that this was not the case, e.g., y* might be such p > MC(y * ). Then, 0 > y C p at y* , where * ' y y y = and () *) ( * y C y y C C + = . Let 0 > y . So, 0 0 > > π C y p , indicating that raising output by y can increase profit (in this case, the increased revenue from higher output can outweigh the increased cost). That implies that
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Intermediate Microeconomics Ch22 notes - Ch 22-23. Firm and...

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