Vertical integration and vertical restraints• Up to now, consider only firm who produces as well as sells final product• Most industries characterized by upstream vs. downstream firms.• Question: focus on problems in vertical setup, and upstream firm’s incentivesto either vertically integrate or approach the integrated outcome usingvertical restraints.• Upstream: produce product. Downstream: retailer/distributor who sells theproduct1. Double marginalization2. Free-riding• Upstream: produce inputs. Downstream: produce and sell final product1. Input substitution2. Price discrimination• Don’t focus on cost aspects (Stigler)Double marginalization 1• Monopolist upstream manufacturer; marginal cost c, chooses wholesale pricepw• Monopolist downstream retailer; marginal cost is pw, chooses retail price pr• Graph• Integrated firm: choose prso that MR(q) = c −→ qi• Nonintegrated outcome: solve backwards1. Retailer: sets prso that MR(q) = pw. M R(q) is the demand curve facedby manufacturer: Monopoly retailer restricts output.2. Manufacturer maximizes using retailer’s demand curve: lower quantity,higher price relative to integrated firm.• Total profits lower in non-integrated scenario.DMRQPcPwQiQwPw’Qw’MR2Pw*Qw*PiPrPr’Pr*• Integrated monopolist: (Qi, Pi)• Nonintegrated: monopolist retailer sets retail price where Pw= MR. Thereby,wholesaler faces demand curve of MR.• Wholesaler optimally sets P∗wso that c = MR2(so “double marginalization”):outcome is (P∗w, P∗r, Q∗w)• Total profits lower in non-integrated scenario.Double marginalization 2Example: Q = 10 − p; c=2Integrated firm: qi=4, pi=6, πi=16Non-integrated scenario (solve backwards):• Retailer:1. Given pw, maxpr(pr− pw)(10 − pr)2. FOC: 10 − pr− (pr− pw) = 0 −→ pr=10+pw2.3. Demand, as a function of pw: Q(pw) = 10 −10+pw2= 5 −pw2. This isdemand curve faced by manufacturer (and coincides with MR curve ofretailer)• Manufacturer1. maxpw(pw− 2)(5 −pw2)2. FOC: 5 −pw+pw−22= 0 −→ pw= 6• pw= 6 −→ pr=8, qn= 2. Lower output, higher price.• πw= 4, πr= 8. Lower total profits.• Lower total profits is incentive to integrate. What else can mftr. do?Double marginalization 3• Main problem is that monopoly retailer sets pr> pw. How can this beovercome?– Resale price maintenance (RPM)Price ceiling: pr= pw. Illegal?– Quantity forcing: force retailer to buy q = qiunits (sales quotas)– General: increase competition at retail level. With PC retail market,pr= pwand problem disappears.• Alternatively, set pw= c and let retailer set prso that MR(q) = c = pw.Then recoup integrated profits πiby franchise fee. Only works if franchisemarket is competitive.Free-riding in retail sector 1: “downstream moral hazard”DM arises since retail sector is not competitive. Now consider problems whicharise if retail sector is competitive.Assume monopolist mftr. and retail sector with two firms competing in Bertrandfashion.Demand function Q(p, s), depending on price p and retail services (advertising) s.Problem: Assume demand goes up if either firm advertises. One firm has noincentive to advertise if other firm does: free-riding.Examples: in-store appearances, online perfume discountersSolve the game backwards:• Bertrand competition: zero profits no matter what. Neither firm advertises−→ low demand.• Mftr. faces lower demand and lower profits.Free-riding in retail sector 2Main problem: under Bertrand competition, retail profits don’t depend onwhether or not there is advertising. Correct problem by tying retailer profits totheir advertising activities: general principle of the residual claimant.1. Exclusive territories: grant retailers monopoly in selling manufacturer’sproduct. Now retailer’s profits increase if it advertises, but run into DMproblem. Explain make-specific new car dealerships?2. Limit number of distributors (same idea)3. Resale price maintenance: set price floor p> pw. Again, this ties retailers’profits to whether or not they advertise.Free-riding at manufacturer level: If there is upstream competition, one mftr’sefforts to (say) improve product image can benefit all manufacturers −→exclusive dealing: forbid retailer from selling a competing manufacturer’sproduct.Input substitution 1Now consider the case where upstream firm produces an input that is used bydownstream firms in producing final good. Focus on case when upstream firmprefers to integrate.Main ideas: Monopoly pricing for one of the inputs shifts downstream demandfor input away from it.Can lead to socially inefficient use of an input.By integrating with DS industry, monopolist increases demand for its input (andperhaps profits).Occurs no matter if downstream industry is competitive or not.Input substitution 2Example (diagram):• Market demand for final good: p = 10 − q• Two inputs:1. Competitive labor market, wage w = 12. Energy E produced by an upstream monopolist. Monopolist produceswith marginal cost m = 1 and sells it at price e.• Final good produced from a production function q = E1/2L1/2.• Competitive downstream industry: final good is sold at p = M C(q).• Analyze 3 things (C/P pp. 551-552; see handout):1. Calculate MC(q) function for DS industry2. Integrated outcome3. Non-integrated outcomeInput substitution 3Calculating DS marginal costsFirst solve for DS firm cost function C(w, e, Q): given input prices w and e, whatis minimal cost required to produce output Q?• DS firms combine E and L to produce a given level of output Q at thelowest possible cost:C(e, w, Q) = minE,LeE + wL s.t. Q = E1/2L1/2given input prices e, w, and output level Q.• Substituting in the constraint:C(e, w, Q) = minEeE + wwQ2E• FOC: E = Qwe1/2, and L = Qew1/2. Substitute back into cost function.• C(e, w, Q) = 2Q(we)1/2. Marginal cost =∂C∂Q=MC(e, w, Q) = 2(we)1/2.Input Substitution 4Integrated firm: Monopoly also controls DS industry• In integrated firm, set e = m = 1, so that MC = 2.• maxp(p − 2)q = (p − 2)(10 − p).• pi= 6, qi= 4. Ei= Li= 4.• πi= (6 − 2) ∗ 4 = 16.Non-integrated scenario• DS: Chooses quantity q so that p = M C ⇔ p = 10 − q = 2(we)1/2=⇒q = 10 − 2(we)1/2• Given this q, demand for E is:E =awe1/2− 2wb.At a = 10, b = 1: E = 101e1/2− 2• US: maxe(e − 1) ∗ E = (e − 1) ∗h101e1/2− 2i• FOC (complicated!): 5e − 2e3/2+ 5 = 0• eu= 7.9265. M C = 5.6308 = pu. qu= 4.3692.•