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EEP 101 Homework #1 Answer Key 1) Let the market for SUVs be characterized by an Aggregate Utility Function equal to US S S () =- 100 2 2 , and a Cost of Production function equal to CS S = 2 4 (where both U and C are in \$). a) Imagine that you are in charge of this economy, how many SUVs should be produced and consumed? What is the net utility to society from this allocation? If I were in charge of this economy, I would choose a quantity of SUVs to maximize the net benefits of SUVs. That is, I would maximize U(S)-C(S). max 100 24 22 S SS -- so, take the first derivative, and set it equal to zero, 100 2 06 6 2 3 -- =f= S S S . The net utility can be found by putting 66 2/3 back into U(S)-C(S), 100 200 3 200 3 2 200 3 4 10000 3 3333 1 3 * - Ê Ë Á ˆ ¯ ˜ - Ê Ë Á ˆ ¯ ˜ == Now imagine that the market for SUVs is competitive. b) Derive the Demand Curve for SUVs. The Demand Curve is equivalent to the Marginal Benefit/Utility Curve, so simply take the first derivative of the Utility Function to find that PS 100 c) Derive the Supply Curve for SUVs. The Supply Curve is equivalent to the Marginal Cost Curve, so simply take the first derivative of the Production Cost Function to find that P S = 2 d) What is the Competitive Equilibrium price and quantity sold?

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We find the competitive equilibrium by setting the demand equal to supply, which yields 100 2 66 2 3 -= f= S S S , to find the price, we put this quantity back into either the supply or the demand curve, to get P=\$ 33 1 3 .
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