Wage Bargaining and Startup Valuation in Economics Explained
School
University of California, Los Angeles**We aren't endorsed by this school
Course
ECON 106I
Subject
Economics
Date
Dec 10, 2024
Pages
3
Uploaded by MajorClover10285
Econ 106IWeek 3Jiayin Zhai1Wage BargainingReconsider the wage bargaining game from class, where pilots’ outside options0is privateinformation, and United believes that it is uniformly distributed on [0; 10].As in class,assume that United makes a take-it-or-leave-it wage o↵ersto the pilots. If the pilots rejectthe o↵er, United goes bankrupt.1. Calculate the optimal o↵ersfor profits (before salaries)⇡= 16.Is the outcomeefficient?2. Calculate the optimal o↵ersfor profits (before salaries)⇡= 20.Is the outcomeefficient?Solution:1. We first write down the United’s expected profit:E[⇧] =Pr(s0s)(⇡-s) +Pr(s0> s)·0 =⇡-s10To maximize the expected profit by choosing the optimal o↵er, we take f.o.c. wrts:⇡10-2s10= 0)2s=⇡)s⇤=⇡2When⇡= 16,s⇤=⇡2= 8.Whens02[0,8], the o↵ers⇤will be accepted; whens02(8,10],s⇤will be rejected. Since⇡= 16> s0, it is efficient for United to operate:whens02(8,10],s⇤will be rejected and it is inefficient. The two parties could negotiatea deal to divide⇡= 16.2. When⇡= 20,s⇤=⇡2= 10, sos⇤will always be accepted. Since⇡= 20> s0, it isefficient for United to operate: the outcome is always efficient.1
Econ 106IWeek 3Jiayin Zhai2Buying a Start-upThe founder of a start-up wants to sell the start-up to a competitive market of investors.The start-up will succeed with probabilityq, which is independent of the sale. If the start-up succeeds it is worth$160m in case of a sale (because of the additional funds and theexpertise), and$128m in case of no sale.If the start-up does not succeed it is worth 0.Everybody is risk-neutral.Questions:1. Assume first that both the founder and the investors know thatq= 50%. In equilibrium,does the start-up sell, and if so at which price?2. Assume next that both the founder and the investors know thatq= 25%. In equilib-rium, does the start-up sell, and if so at which price?3. Assume next that neither the founder nor the investors knowqbut both thinkqisequally likely to be 50% or 25%. What is the equilibrium price?4. Now assume thatqcan be either 50% or 25%, but that only the founder knows theactual value ofq, while investors thinkqis equally likely to be 50% or 25%. What isthe equilibrium price? What type of founder (q= 50% or 25%) sells at this price?Solution:1. Investor’s value is 50%·$160m= $80mand the founder’s value is 50%·$128m= $64m,so the founder will sell, and the price will be$80m since the investors’ side is competitive(no bargaining power).2. Investor’s value is 25%·$160m= $40mand the founder’s value is 25%·$128m= $32m,so the founder will sell, and the price will be$40m since the investors’ side is competitive(no bargaining power).3. Now the investor thinksqis equally likely to be 50% or 25%: so the investor’s expectedvalue is 50%·$80m+ 50%·$40m= $60m.The founder also thinksqis equally likely to be 50% or 25%: so the founder’s expectedvalue is 50%·$64m+ 50%·$32m= $48m, so the founder will sell, and the price willbe$60m since the investors’ side is competitive.This is the case of incomplete but symmetric information.4. Now since the investor thinksqis equally likely to be 50% or 25%: so the investor’sexpected value is$60m.But for the founder withq= %50, they will only sell ifp≥$64m. Therefore, atp= $60m, onlyq= %25 will sell, then the investor will notbe willing to payp= $60msince they can only getq= %25. They will setp= $40m(their value forq= %25), and onlyq= %25 founder will sell.2
Econ 106IWeek 3Jiayin Zhai3A Model of Uncertain DemandConsider the problem of supplying an input to a division of a firm or to a firm in a plannedeconomy. Suppose the executive or planner knows the marginal cost function for the input,represented by the MC line. However, the planner is uncertain about the marginal benefit.Her best estimate is the MB line. On that basis, the price should bepand the quantityq.Consider an error scenario in which the actual marginal benefit is lower, as represented bythe MB’ line. For example, the estimated demand curve isD(p) = 15-p, while the realdemand curve isD(p) = 12-p.Questions:1. What is the price and quantity the planner thinks will happen?2. What is the price and quantity that is efficient?3. Under price control, what will be the actual quantity in this economy? Is there under-production or overproduction? What is the efficiency loss?4. Under quantity control, is there underproduction or overproduction?What is theefficiency loss?Solution:1. The price and quantity the planner thinks will happen is pinned down by the intersec-tion of MC and MB (estimated demand curve).2. The efficient price and quantity is pinned down by the intersection of MC and MB’(actual demand curve).3. Under price control, the quantity is given by the intersection of the price level frompart 1 and MB’ curve: there is underproduction since the quantity is lower than theefficient level. The efficiency loss can be seen in the figure.4. Under quantity control, the quantity is given by the quantity level from part 1: there isoverproduction since the quantity is higher than the efficient level. The efficiency losscan be seen in the figure.Also, notice that when MC is steep (supply is inelastic), the efficiency loss is smaller underquantity control, since the variability in quantity is smaller.3