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Econ1-Fall2010-PS7-sols - Econ 1 PS#7 Solutions Fall 2010 1...

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Econ 1 PS #7 Solutions Fall 2010 1. Suppose that the supply curve for wheat is given by Q S = 10 P – 10 and suppose that the demand curve for wheat is given by Q D = 200 – 20 P . a. Find the equilibrium price and quantity of wheat.     In equilibrium, the quantity supplied will equal the quantity demanded. 10 10 200 20 30 210 * 7 We can substitute this price into either Supply or Demand to get quantity. * 10 7 10 60 or * 200 20 7 S D Q Q P P P P Q Q 60 b. Sketch a picture of the supply curve and the demand curve. Be sure to label i) both axes, ii) the y-intercept both curves, iii) the slope of both curves, and iv) the equilibrium price and quantity. For the graph it’s helpful to convert the supply and demand equations to ones where price (on our y-axis) is a function of quantity (on our x-axis). Supply: P = Q S /10 + 1; Demand: P = – Q D /20 + 10 c. Concerned about rising food prices, suppose that the government introduces a price ceiling of $5. What will be the new equilibrium quantity of wheat bought and sold on the market? Q P S D Slope=1/10 Slope=-1/20 60 40 5 7
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The short side of the market will win (supply in this case). Q * = 40. d. Is this new quantity economically efficient? Explain. No. Assuming that the demand curve equals the marginal social benefit curve and assuming that the supply curve equals the marginal social cost curve, then we know the efficient quantity is 60. The total surplus of producing 40 is less than the total surplus of producing 60.
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