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# C 8 define and derive the market equilibrium e e p q

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c) (8) Define and derive the market equilibrium ( , ) e e p Q , and the optimal output choice for each firm ( ) e q . Market equilibrium: price and quantity such that each firm is max'g profits, and each consumer is max'g utility at given price, and quantity supplied = quantity demanded. Can solve for easily by 1. sub'g market supply curve into inverse market demand curve: p= 400-0.02Q = 400 - 0.02[25p-2500] or p = 450/1.5 = 300. 2. sub. price into market supply to get eq'm quantity: Q = 25p-2500 = 7500-2500 = 5000 3. Each firm supplies 1/500 of market, so q = 5000/500 = 10. 2 for definition (only one if just say D=S); 2 each for price, market quantity, firm's quantity d) (4) Illustrate the equilibrium of the market, and a representative firm, on the following page. Be sure to label your axes, and clearly identify the equilibrium. 2 each In an attempt to decrease the commercial use of silver, the government introduces legislation committing to tax each firm \$10 for each silver teapot it produces.

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Name___________________________________________________________ Student number _________________________________ Lab LF0__________ 203 (F01), 2005; midterm 2 Page 3 of 3 e) (2) After this legislation passes, what is the relationship between the price a consumer pays for a teapot and the price the producing firm receives? Producer price = consumer price - 10, or 10 d s p p = + Use this page for your diagram. f) (8) Solve for the short run equilibrium in this market with the tax, and illustrate it in your diagram for (c) above. SR equilibrium: 1. market supply is Q = 25p s -2500 = 25(p d -10)-2500 2. sub'g this into inverse market demand gives consumer price, p d , as solution to p d = 400-0.02Q = 400 - 0.02[25(p d --10)-2500] or p d = 455/1.5 3. producer price is then 10 s d p p = = 440/1.5 4 Market quantity is Q = 25p s -2500 2 for picture, 6 for new market equilibrium g) (3) Will this tax increase or decrease the total surplus produced in this market?
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