ECON 212 Lecture Notes - Lecture 9: Inverse Demand Function, Marginal Revenue, Demand Curve
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Recall: competitive firms (4) find price (5) find revenue (6) find cost. Have the ability to affect the price and therefore p is now p(y) a function of quantity. A competitive firm"s supply curve, or its inverse supply curve ((cid:1842)=(cid:1858)(cid:4666)(cid:1843)(cid:4667)) is the same as its marginal cost curve, so long as. Every firm wants to maximize profits ( (cid:1870)(cid:1857)(cid:1874)(cid:1857)(cid:1866)(cid:1873)(cid:1857) (cid:1855)(cid:1867)(cid:1871)(cid:1872)) and for competitive firms, price is fixed. The profit maximizing quantity and price is down dependent on (cid:1844)= (which is the first order condition) (cid:1844)= (cid:883)(cid:884) (cid:884) (1) rearrange the demand curve with respect to q : (2) find mr : (3) set mr = mc: Example: cost curve (cid:4666)(cid:4667)=(cid:2870) faces a demand curve =(cid:883)(cid:884) (cid:1842) (cid:1844)(cid:1857)(cid:1874)(cid:1857)(cid:1866)(cid:1873)(cid:1857)=(cid:4666)(cid:883)(cid:884) (cid:4667)=(cid:883)(cid:884) (cid:2870) (cid:883)(cid:884) (cid:884)=(cid:884) (cid:883)(cid:884)=(cid:886) =(cid:885) (cid:1842)=(cid:883)(cid:884) (cid:1842)=(cid:891) (cid:1844)(cid:1857)(cid:1874)(cid:1857)(cid:1866)(cid:1873)(cid:1857)=(cid:4666)(cid:883)(cid:884) (cid:885)(cid:4667)(cid:885)=(cid:884)(cid:889) (cid:2870)=(cid:891) (7) find profit (cid:1842)(cid:1870)(cid:1867)(cid:1858)(cid:1872)=(cid:884)(cid:889) (cid:891)=(cid:883)(cid:890) (cid:1842)=(cid:883)(cid:884) you lose money because you had to reduce the price on all units in order to increase your sales by one unit.