Solution 1 - FRE/ECON374 Problem set 1 SOLUTIONS 1 A little...

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FRE/ECON374 Problem set 1 SOLUTIONS 1. A little village wants to invest in an aqueduct system. The aggregate inverse demand from the villagers is p = 17 – 2Q. The total cost of the system is defined by the following equation: TC = 5Q + 1/2Q 2 . a) Show graphically the equilibrium price and quantity. Identify the consumer and producer surpluses. b) Compute the consumer and producer surpluses. What is the social surplus generated by the new system? 24 1. Supply = MC = 5 + Q 2. Equilibrium price and quantity: 17 – 2Q* = 5 + Q* Q*=4; p*=9 3. Consumer surplus: CS = (17-9)(4)/2 = 16 4. Producer surplus: p Q 17 CS PS 5 MC = 5 + Q Demand p*=9 Q*=4
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PS = (9-5)(4)/2 = 8 5. Social surplus: SS = CS + PS = 16 + 8 = 24 Suppose the villagers do not directly pay for the aqueduct service. c) What will be the quantity consumed? 8.5 Replacing p by 0 in the demand equation: 0 = 17 – 2Q. The demand meets the price of 0 at a quantity of 8.5. d) In that case, is it optimal for the village to build the new system? Hint: What is the social surplus under this circumstance? No 1. Total Benefits = 17*8.5/2 = 72.25 2. Total Costs = 5*8.5 + ½(8.5) 2 = 78.625 3. Net benefits = TB – TC = 72.25 – 78.625 = -6.375 4. In this case, the net benefits (social surplus) from the new system are negative; it is not optimal to invest in it.
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