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section2_brian_solutions

section2_brian_solutions - 1 Section Notes Week 2 Outline...

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1 Section Notes Week 2 Outline Key Concepts Announcements Externality Numerical Example Over- or Under- Production Welfare Graphing Regulation Discussion Internalization Calculating Outcomes Competition Monopoly Monopsony Middleman Social Planner M. Benefit MPB MR MPB MR MSB=MPB+MEB M. Cost MPC MPC MO MO MSC=MPC+MEC Solution MPB=MPC MR=MPC MPB=MO MR=MO MSB=MSC Recall that: MR = d d Q Revenue = d d Q (Q · MPB(Q)) = MPB(Q) + Q · d d Q MPB(Q) MO = d d Q Outlay = d d Q (Q · MPC(Q)) = MPC(Q) + Q · d d Q MPC(Q) Putting numbers to it Let marginal private benefit of output Q be given by P = 12 - Q , marginal private cost by P = 2 Q . Suppose that production generates a negative externality, with marginal cost as a function of output given by MEC = 1 . 5 + 0 . 5 Q . Let’s assume there are no positive externalities. Find the equations for: MR: Revenue = (12 - Q ) · Q = 12 Q - Q 2 . MR = d d Q (12 Q - Q 2 ) = 12 - 2 Q MO: Outlay = (2 Q ) · Q = 2 Q 2 . MO = d d Q (2 Q 2 ) = 4 Q MSB: MSB = MPB + MEB. MEB is zero, so MSB = MPB = 12 - Q MSC: MSC = MPC + MEC = (2 Q ) + (1 . 5 + 0 . 5 Q ) = 1 . 5 + 2 . 5 Q Now we’re going to go through the case of (perfect) competition. Solve out the competitive case quantity and price ( Q C , P C ). Q C : Set MPB=MPC, so 12 - Q = 2 Q , which can be arranged to find Q = 12 / 3 = 4 . P C : This quantity is then plugged into demand to find price: P = 12 - 4 = 8 .
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2 Next find the socially optimal quantity and price ( Q * , P * ). Try solving out the other outcomes if you have time. Q * : Set MSB=MSC, so 12 - Q = 1 . 5 + 2 . 5 Q , which results in Q = 10 . 5 / 3 . 5 = 3 . P * : This quantity is then plugged into demand to find price: P = 12 - 3 = 9 . Q M : Set MR=MPC, so 12 - 2 Q = 2 Q , which can be arranged to find Q = 12 / 4 = 3 . P M : This quantity is then plugged into demand to find price: P = 12 - 3 = 9 . Q N : Set MPB=MO, so 12 - Q = 4 Q , which can be arranged to find Q = 12 / 5 = 2.4 . P N : This quantity is then plugged into supply to find price: P = 2 · (2 . 4) = 4.8 . Q MM : Set MR=MO, so 12 - 2 Q = 4 Q , which can be arranged to find Q = 12 / 6 = 2 . Middleman has two prices, one to consumers, P C MM , and one to producers, P P MM ...
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