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Homework1_4_Problem_Set

# Homework1_4_Problem_Set - AEM 250 Environmental and...

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AEM 250: Environmental and Resource Economics Homework 2 Solution Key 1. a. & b. Create individual and aggregate demand schedules. P C1 C2 C1+C2 0 20 10 30 0.5 18 9 27 1 16 8 24 1.5 14 7 21 2 12 6 18 2.5 10 5 15 3 8 4 12 3.5 6 3 9 4 4 2 6 4.5 2 1 3 5 0 0 0 c. The algebraic equation for the aggregate demand could be obtained by using the intercept and slope approach used in answering Q1 from HW 1. Or, one could add the two equations, using the logic that if price is held constant, the sum of Q C1 and Q C2 will yield aggregate demand. Q C1 = 20 – 4*P Q C2 = 10 - 2*P Q Aggregate = 30 – 6*P Remember that it is always good to cross check your answer, e.g. 30 – 6*(4) = 6, which corresponds to the demand scheduled above. d. To obtain the marginal benefits equation, simply invert the aggregate demand equation to get: P = MB = ((- 1/6) * Q) + 5 2. a. & b. Create individual producer and aggregate supply schedules. P S1 S2 S1+S2 0 0 0 0 0.5 0.5 1.5 2 1 1 3 4 1.5 1.5 4.5 6 2 2 6 8 2.5 2.5 7.5 10 3 3 9 12 3.5 3.5 10.5 14 4 4 12 16 4.5 4.5 13.5 18 5 5 15 20 c. The algebraic equation for the aggregate supply could be obtained by using the intercept and slope approach used in answering Q1 above. Or, one could add the two equations, using the logic that if price is held constant, the sum of Q C1 and Q C2 will yield aggregate supply. Q S1 = P Q S2 = 3*P Q Aggregate = 4*P Remember that it is always good to cross check your answer, e.g. 4*4 = 16, which

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corresponds to the aggregate supply schedule above. d. To obtain the marginal costs equation, simply invert the aggregate supply equation to get: P = MC = ¼ * Q 3. a. To calculate market equilibrium, first set MB = MC and solve for Q*: 10 – (1/3) * Q = ½ * Q 30 – Q = 3/2 Q 60 – 2Q = 3Q 60 = 5Q Q* = 12 Next plug Q* into MB or MC to find P: MB = 10 – (1/3 * 12) = 10 – 4 = 6 P* = 6 MC = ½ * 12 = 6 P* = 6 It’s always a good idea to check both equations to be sure you get the same answer. b. To answer b and c it is perhaps easier to derive the supply and demand curves. To calculate the supply curve, simply resolve the MC function in terms of Q as a function of P MC = ½ * Q Q S = 2P And similarly for the demand curve simply resolve the MB function in terms of Q as a function of P. MB = 10 – (1/3 * Q) Q B = 30 – 3P If you plug in the prices of \$5 and \$7 for both supply and demand equations, you can find the exact quantities supplied and demanded at the specific prices. If the price was \$1.00 below the equilibrium price, the quantity demanded would be greater than the quantity supplied, resulting in a shortage, or excess demand in the market. Some consumers would be willing to pay more to obtain the units they want, and the price would eventually be pushed upwards until MB = MC. P = 5 P SM C DM B Q Q* = 12 P* = 6 excess demand
c. If the price was \$1.00 greater than the equilibrium price, the quantity supplied would be greater than the quantity demanded, resulting in a surplus, or excess supply in the market.

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