Suppose that you have data on P, Q, Z, and W.

You estimate equations (8B.1) and (8B.3), with the following results.

P = 200 - 10Q + 5Z + 2.5ZQ (8B.1)

P = 40 - 27Q - 1.5ZQ + 2.3W (8B.3)

Given this information, calculate the implied Lerner Index

ECO328_2021_FALL_HW6 (1).pdf x + X -> @ File | C:/Users/Andrews/Downloads/ECO328_2021_FALL_HW6%20(1).pdf F. M Update Apps M Gmail YouTube . M Inbox (359) - mauri... Dashboard ab QuickBooks @ Calendly - College... INDUSTRIAL ORGA... Other bookmarks Reading list E ECO328_2021_FALL_HW6 (1).pdf 2 / 5 80% + ... APPENDIX 8B Identifying Market Power Under what conditions can the price-cost margin be determined if we cannot observe marginal cost directly? One approach to answering this question in- volves estimating a complete model of the market where the shapes of the de- mand and marginal cost curves are specified and profit-maximizing behavior is assumed. To illustrate this approach, suppose that an industry consists of a number of identical firms that produce a homogeneous product. The demand curve is p(; Z), Identifying Market Power where p is the single price in the market, O is output, and Z is another variable that affects demand, such as income or the price of a substitute. Because industry revenues are R = p(Q; Z)Q, we define the effective (or per- ceived) marginal revenue as MR(X) = P + XPQ2, where > is a parameter to be estimated and po = ap/aQ. If the industry is monopo- lized, > = 1 and effective MR(1) is the usual MR measure: p + poO. If the firms in 2 the industry are price takers, A = 0 and effective MR(0) equals price. Various other oligopolistic and monopolistically competitive market structures produce a A that lies strictly between 0 and 1. The profit-maximization or optimality condition is that effective marginal rev- enue equals marginal cost: MR(X) = MC. As a result, ) is a measure of the gap be- tween price and marginal cost. That is, the Lerner's Index is: LP - MC _APQ2_ P where e is the market elasticity of demand. This expression is very similar to those derived in Appendix 8A that depend on the number of firms, the market share, or 3 the Herfindahl-Hirschman Index. The following discussion of the role of market demand shocks in identifying market power is based on Just and Chern (1980), Bresnahan (1982), and Lau (1982). 269 Type here to search W 6:27 PM ? 21.C Sunny ~ ( 80 ( 41) ) D ENG 10/29/2021ECO328_2021_FALL_HW6 (1).pdf x + X -> @ File | C:/Users/Andrews/Downloads/ECO328_2021_FALL_HW6%20(1).pdf F. M Update Apps M Gmail YouTube . M Inbox (359) - mauri... Dashboard ab QuickBooks @Calendly - College... INDUSTRIAL ORGA... Other bookmarks Reading list E ECO328_2021_FALL_HW6 (1).pdf 3 / 5 80% + ... As an example, suppose that the demand curve has the particular linear form p=a, ta,0+ azz + aZO + 1, ( 8B.1) so that the effective marginal revenue is MR(X) = p + Xpo0 = p + Na, + a;Z)Q. (8B.2) A profit-maximizing firm sets its effective marginal revenue equal to its marginal cost. If its marginal cost curve is linear in O and factor price W, MC = Bo + BIO + B2W + Ez, its optimality equation, MR(A) = MC, can be written as P = Bot (B, - Aaj)Q - da;ZQ + B2W+ Ez. (8B.3) Using the appropriate statistical techniques, one can regress p on a constant, Q, ZQ, and W to obtain estimates of the coefficients in Equation 8B.3. By dividing the estimate of the coefficient on the 20 term, -At3, from Equation 8B.3 by the esti- mate of a3 from the demand Equation 8B.1, one obtains an estimate of the market structure parameter A. The reason that one can identify A is that the demand and MR curves rotate with Z due to the ZO interaction term, which affects where the MR curve intersects the MC curve. Alternatively, if we know MC, we can use the information about price from the demand curve to determine A. Rotating the de- 2 mand curve leaves the level of demand unchanged at the rotation point, but changes the elasticity of demand. As the elasticity of demand changes, the price changes, which allows us to estimate A. If there is no ZO term (that is, if C @ File | C:/Users/Andrews/Downloads/ECO328_2021_FALL_HW6%20(1).pdf F. M Update Apps M Gmail YouTube . M Inbox (359) - mauri... Dashboard ab QuickBooks @ Calendly - College... INDUSTRIAL ORGA... Other bookmarks Reading list ... E ECO328_2021_FALL_HW6 (1).pdf 4/5 - 80% + FIGURE 8B.1 Not Identified: Parallel Shift MC of the Demand a,AZ Curve E2 MCm MR z D2 MR, DI Quantity, Q 2 If a3 = 0, and Z increases by AZ, the intercept of the demand curve shifts up by a2AZ, as shown for the new demand curve, D2. The new equilibrium, E2, is still consistent with either of the two marginal cost curves. Thus, the researcher cannot determine from this shift in Z if the industry is competitive or cartelized. In contrast, if a3 # 0, a shift in Z reveals A. In Figure 8B.2, when Z increases, the new demand curve, D3, rotates (for graphical simplicity, D3 is rotated around the original equilibrium point). If the industry is competitive and the marginal cost curve is MC., the new equilibrium on D3 remains E1; whereas, if the industry is cartelized and the marginal cost curve is MC,. the new equilibrium on D, is E3. 3 Thus, whether or not the equilibrium shifts reveals whether the market is competi- tive. Anything (not just variables in the market demand curve) that causes the reside ual demand curve facing a firm to rotate can identify A. For example, a dominant firm's residual demand curve is the market demand curve minus the supply of a competitive fringe. If the fringe supply curve rotates, the residual demand curve ro- tates even if the market demand curve does not. Similarly, a shift in an ad valorem tax rate, t, can identify the market structure. As the chapter shows, information about the shape of the marginal cost curve also can help identify A. It is possible to identify > even if the demand curve does 6:27 PM Type here to search M W ? 21.C Sunny ~ ( 8 ( 41 ) P ENG 10/29/2021