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Lecture 7

Economics 2151B - Lecture 7.docx

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Western University
Economics 2150A/B
Kristin Denniston

Economics 2151B Monday January 27 Lecture 7 Homework 2 • Will be posted on Tuesday • Covers chapters 11 and part of 12 • Due next Wed. Feb. 5 Midterm • Will cover chapters 9, 10, 11 and 12 • No math problems from chapter 9 • Will be in class on Monday Feb. 10 Monopoly – Chapter 11 part 1 Marginal Revenue Curve of a Monopolist • The monopolist chooses Q to maximize profits o Maximum profits occurs for all firms where MR = MC • Under perfect competition, the firm sees a horizontal demand at the given market price (P*) o This means that the marginal revenue per unit sold for a perfectly competitive firm is the price of the unit itself o The change in total revenue that the firm received as a result of selling one more unit was the price they would receive in the market for that unit • In a monopoly, firms will see a downward-sloping demand curve. o In order to sell another unit, we must lower the price. • The downward-sloping marginal revenue curve lies below the demand curve. o It is downward-sloping because in order to sell another unit, the monopolist must lower the price from P 1o P 2 o You must lower the price on all of your units to sell additional units. • TR = P x Q • Example: o Initially a1 P = $10  Q 1 2 million  TR =1area I + II o To increase Q sold to 5 million…  We must decrease P to 27  Q 2 5 million  TR =2II + III ΔTR o MR = ΔQ o Change in TR = TR –2TR = 1rea(III + II) – area(II + I) = area III – I o Area II = increase in TR from marginal units  You can gain revenue from selling additional units at the lower price, but you lose revenue on the previously sold units at the higher price (known as inframarginal units) o The monopolist can only sell at one price in this market. • Mathematical proof of why MR lies below demand: o TR = P(Q) x Q dTR dP o MR = = P(Q) + Q( ) dQ dQ dP  Note that dQ is negative because to decrease quantity, we have to decrease price  Your book doesn’t use derivatives, it uses: ΔP o MR = P + Q( ΔQ )  P is the increase in TR from selling the marginal units  Q is the quantity you sold previously  This expression tells you it is the decrease in TR from the sale of existing units (inframarginal units) at a lower price Linear Market Demand Curve • It is easy to find the MR when we have a linear market demand curve • Formula for a linear demand curve (demand): P = a – bQ o This is the inverse form of the demand curve that we would graph o y-intercept = a o slope = -b 2 • TR = P x Q = (a-bQ)Q = aQ-bQ dTR • MR = dQ = a – 2bQ o The only difference between the MR curve and the demand curve is that the slope is twice as steep. • Properties of MR when Demand is Linear: 1. Slope of the MR curve is 2x the slope of the demand curve 2. MR curve bisects the x-axis a 3. MR is decreasing but positive until Q = 2b 4. MR = 0 where MR crosses the x-axis and TR is maximized (note that maximizing TR is not the same as maximizing profit) 5. The monopolist always produces on the elastic portion of the demand curve (and never produces on the inelastic portion) [Figure 11.4] • If you decrease price, Q and TR increases 6. Figure 11.5 – Shows profit and DWL for a monopolist 1) The monopolist produces Q where MR = MC  The price we should set to maximize our profits should be P  In this example, P = $8 2) The profit rectangle for the monopolist: a. Profit π = TR – TC = PxQ - QxAC b. Profit π = Qx(P-AC) o This is a good equation to use for graphs o π = 4 x (8-2) = 24 (positive in the LR) 3) Monopoly creates a DWL (decreases the TS to society)  The DWL is caused by the lost transactions that never took place because the monopolist reduces quantity below the optimal level, and increases price above the optimal level.  The reduction in Q means that beneficial trades that would benefit society do not occur because the price is too high Note: Make sure you don’t confuse the MC and AC curves.  Profit is based on the average cost curve  Economic efficiency is based on the marginal cost curve 4) Monopoly markup:  At the monopoly price and quantity(P , Q ), P > MC  The markup is the difference between the market price and marginal costs of producing that last unit Example 1 (in your notes):  Demand: P = 100 – 2Q  TC: 640 + 20Q a) Find the monopoly P,Q  Q where MR = MC  MR = 100 – 4Q (twice the slope of the demand curve) dTC  MC = dQ = 20  Set MR = MC o 100 – 4Q = 20 o Q = 20
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