Econ 308 1st Edition Exam #3 Study GuideTest is 7 questions and 1 short answerPROBLEM SET 7 1. Goodyear and Bridgestone face the following profit and price relationships. Bridgestone$100 $60$100 F = 20: G = 36 F = 33: G = 10$60 F = 12: G = 35 F = 11: G = 30Is there a dominant strategy, and is there a Nash equilibrium?Neither player has a dominant strategy nor a nash equilibriumGoodyear: If B plays $100 better to play 100 and if B plays $60, better to play $602. True or False If neither one of two interdependent firms in the same industry has a dominant strategy,then a Nash equilibrium can not exist. Explain.TRUE3. The demand curve for education in a community with only two colleges is P = 100 - Q. The cost of educating an additional student is 8. Complete the table below for the four scenarios described in a-d. There are no fixed costs. a. Both colleges get together and collude to price fix at a profit maximizing level. Shared monopoly p=100-q market demandMr=100-2q MR=MC MC=8 100-2q=8 q=46 p=100-46=54Qa=Qb=q/2=23(46-8)* 23=1058 and same for Bb. Both colleges assume that the other will hold the present tuition constant despite what the competition does. Bertrand modelPa=pb=mc mc=8 p=100-q q=92 profit=0Goodyearc. Both colleges assume that the other will hold the present enrollment constant despite what the competition does. Cournot Model MR=100-qb-2qa MC=8 100-qb-2qa=8 d. College 1 believes college 2 will adjust to its new profit maximizing solution each time college 1 adjusts its enrollment strategy. (Show calculations below.)Assumption Quantity of A Quantity of B Price Profit of A Profit of Ba 23 23 54 1058 1058b 46 46 8 0 0c 30.67 30.67 38.67 940.44 940.44d 46 23 31 1058 529Stockelburg model p=100-qP=100-qa-qb = (46-1/2qa)P=54-1/2qaPROBLEM SET 81. A perfectly competitive firm has MPL = 22- L. Find and graph its value of the marginal product of labor at a product price of P =5. Find its optimal quantity demanded of labor at a wage of w = $10/hr.10=100-5L L=20 5(22-L)=110-5:2. In his current job, Smith can work as many hours per day as he chooses, and he will be paid $1/hrfor the first 8 hours he works, $2.50/hr for each hour over 8. Faced with this payment schedule, Smith chooses to work 12 hr/day. If Smith is offered a new job that pays $1.50/hr for as many hours as he chooses to work, will he take it? Explain.24-h 16<h<24 8+4*2.5=1848-2.50 0<h<16 m2=36-1.5htake new job going to work less hours3. A monopsonist’s demand curve for labor is given by w = 12-2L, where w is the hourly wage rate and L is the number of person-hours hired. If the monopsonist’s supply (AFC) curve is given by w = 2 L, which gives rise to marginal factor cost curve of MFC = 4L, how many unites of labor will he employ and what wage will he pay?MRPL=12-2L w=2l MFC=4L12-2L=4L L=2 w=44. The demand curve for labor facing a monopsonist is given as w = 35- 6L; The supply curve (AFC) for this monopsonist is W = 3 + L, with corresponding MFC = 3+2L, where W represents the hourly wage rate and L is the number of person-hours hired. Find the optimal quantity of labor and wage rate for this profit-maximizing monopsonist.w=35-6L MRPL=35-6LMFC=3+2L 35-6L=3+2L L=4 W=7PROBLEM SET 91. Suppose the price of a new car is $15,000. If the interest rate is .05, maintenance costs are.06, and depreciation is .20, what will the annual rental rate be for the new car?0.05+.06+.2=0.310.31*15000=4650 renewal rate2. Suppose a new robot is expected to generate $5250 additional revenue at the end of each year for 3 years. If annual maintenance costs are $500, the annual interest rate is 8%, and the robot can be salvaged in 3 years for $1000, what is the present value of this robot?52500-500/1+I + 52500-500/(1+I)^2 + 52500-500/(1+I)^3 +1000/(1+I)^3 I=8% PV=13,035.042. If the annual payment on a console bond is $750, what is the price of this bond if the interest rate is (a) 8% (b) 6%?3. ******Explain why a bond you hold will fall in value when interest rates rise.Interest rate on the denominator of each component increases in interest rate every term value goes down bond price and interest rate inversely related4. A machine that costs $100 will yield returns of $30 at the end of each of the next 3 years, at which time it will be sold as scrap for $30. If the interest rate facing this firm is 10 percent, should it purchase this machine?30/(1+i) +30/(1+i)^2+30+30/(1+i)^3PV>100 buy PV< 100 no buy5. Suppose a perpetual bond pays $3000/year to its owner. What is the price of the bond at 5percent interest? At 6