ARE 100 PS1-10ANS

ARE 100 PS1-10ANS - University of California, Davis...

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University of California, Davis Department of Agricultural and Resource Economics ARE 100B Winter 2010 Dr. Larson Problem Set 1 Answers 1. The market for tortillas is perfectly competitive, with market demand for packages of tortillas given by P 1 .00002Q, with price in dollars per package and Q in thousands of packages. The long-run œ marginal cost curve for a typical tortilla factory is MC .05 .0005q, with MC in dollars per œ package and q in thousands of packages. (a) If there are 100 identical factories, determine the long-run industry supply function. The long-run supply comes from adding together the quantities supplied by all factories at a given price. The graphical illustration is in the graph below. Algebraically, to sum the quantities, you must solve for q as a function of MC. Doing this for a typical tortilla factory, one gets q (MC .05)/.0005. Adding two of these together, for factories 1 and 2, one gets q (MC .05)/.0005 " q (MC .05)/.0005 # œ Q q q 2(MC .05)/.0005. œœ "# Note that q and q have subscripts, to keep track of which factory's quantity we're adding to the total, but MC does not have a subscript. This is because, by definition, the aggregate supply is the sum of quantities supplied by individual firms for a given price that is the same for all. By extension, doing the sum for 100 identical factories gives Q 100(MC .05)/.0005. Solving back for MC as a function of Q, the aggregate supply curve is MC .05 .000005Q. (b) What is the market equilibrium quantity of tortillas, and what is the equilibrium price? The market equilibrium quantity of tortillas comes from equating the aggregate supply with the market demand curve: MC .05 .000005 1 .00002 P, where denotes the market œ œ QQ Q -- - equilibrium quantity. Solving, this is (1 .05)/(.000005 .00002) .95/.000025 38,000, or Q - œ œ 38 million packages (since q is defined in thousands of packages).
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This note was uploaded on 10/04/2011 for the course ARE 100B 100B taught by Professor Larson during the Spring '10 term at UC Davis.

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ARE 100 PS1-10ANS - University of California, Davis...

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