Question.2984 - 1. Customers to Live Theaters, Inc. can be divided into two groups: seniors and everyone else. The inverse demand curves for each of the two groups are given below. The marginal cost (which equals the average variable cost) of serving an additional patron, either senior or everyone else, is equal to $4. Fixed costs are equal to $1000.Ps = 80 – Qs Pe = 100 – 2QeWhere Ps and Pe denote, respectively, the prices charged to seniors and everyone else and Qs and Qe denote the number of seniors and the number of all other customers served.a. What is Live Theaters’ total revenue function? What is its total cost function? Its total profits function? For the total revenue use Total Revenue=P s *Q s + P e *Q e b. What are the profit maximizing levels of price and output if Live Theaters, Inc. engages in third degree price discrimination? Show that MRe = MRs = MC. Use MR e = d/dQ(P e *Q e ), MR s = d/dQ(P s *Q s ), and MC = d/dQ (TC) c. What are profits associated with this option? d. If Live Theaters charges one price to all patrons, what would it be? How many customers would it serve? What would be its profits?2. Computer Products Corp. sells peripheral equipment used by both private businesses and the government. Due to a recession, Computer Product’s sales have declined by 100,000 units and it now has 200,000 units of excess capacity. All of its current sales are to private sector customers and each pays $12.00 per unit for the equipment. The sales price is equal to 150% of average variable costs. A government agency has offered to purchase 300,000 units at $10.00 each. If Computer Products accepts the offer, it will not be able to fill 100,000 units of its expected orders from private sector customers over the next few months, although the inability to meet customer demand is not expected to affect future sales. a. Should Computer Products accept the offer to supply 300,000 units at $10 each to the government agency? What happens to its profits if it accepts the offer?b. Would your answer change if the inability to meet private sector customer demand reduces sales of 50,000 during this (ignore any effects beyond this period)?3. Online Tutors offers monthly access to students for either or both math or science tutors. A market study found that the served by Online Tutors can be divided into two types of students: students needing help with math, who are primarily interested in math tutoring but may be interested in some science tutoring, and students who are primarily interested in science tutoring but may need some math tutoring. The study further estimates that there are 300 students who fit the category of "students needing help with math" and 200 students who fit the category of "students needing help with science." Online Tutors estimated demand for each type of tutoring service by type of student is given below. All costs are fixed so that maximizing total revenue is equivalent to maximizing profit. Use a payoff matrix or find combinations of pricing to result in the best profit. The demand prices for monthly math and science tutoring services are given belowType of Student...............................Math Tutoring Only........................Science Tutoring Only In Need of Math Tutoring............................$100.......................................................$25 In Need of Science Tutoring..........................$50.......................................................$150 a. If the Online Tutoring decides to sell its tutoring services individually, what should it charge for math tutoring? What should it charge for science tutoring? b. If Online Tutoring offers bundled services, what pricing would you recommend? What happens to its revenues if it uses bundling?
Answer Below:
Customers xx Live xxxxxxxx Inc xxx be xxxxxxx into xxx groups xxxxxxx and xxxxxxxx else xxx inverse xxxxxx curves xxx each xx the xxx groups xxx given xxxxx The xxxxxxxx cost xxxxx equals xxx average xxxxxxxx cost xx serving xx additional xxxxxx either xxxxxx or xxxxxxxx else xx equal xx Fixed xxxxx are xxxxx to xx Qs xx QeWhere xx and xx denote xxxxxxxxxxxx the xxxxxx charged xx seniors xxx everyone xxxx and xx and xx denote xxx number xx seniors xxx the xxxxxx of xxx other xxxxxxxxx served x What xx Live xxxxxxxx total xxxxxxx function xxxx is xxx total xxxx function xxx total xxxxxxx function xxx the xxxxx revenue xxx Total xxxxxxx P x Q x P x Q x b xxxx are xxx profit xxxxxxxxxx levels xx price xxx output xx Live xxxxxxxx Inc xxxxxxx in xxxxx degree xxxxx discrimination xxxx that xxx MRs xx Use xx e x dQ x e x e xx s x dQ x s x s xxx MC x dQ xx c xxxx are xxxxxxx associated xxxx this xxxxxx d xx Live xxxxxxxx charges xxx price xx all xxxxxxx what xxxxx it xx How xxxx customers xxxxx it xxxxx What xxxxx be xxx profits x Given xx AVC xxxxxxx variable xxxx and xxxxx costs xxxxx revenue xxxxxxxx of xxx total xxxxxx generated xx selling xx all xxx different xxxxx of xxxxxxxxx Therefore xx P x Q x P x Q x total xxxxxxx from xxxxxxxx else xxxxx revenue xxxx seniors x e x e x s x s xxxxx cost xxxxxxxx is xxx total xxxx incurred xx producing xxx both xxxx of xxxxxxxxx It xxxxxxxx both xxxxxxxx and xxxxx costs xxxxxxxxx TC xxx TFC xxx Q xxx as xxx is xxxxx we xxx the xxxxxxxx AVC xxx Q x e x s xxxxx profits xxxxxx total xxxxxxx earned xxxx the xxxxx cost xx production xxxxxxxxx TP xxx TC x e x e x s x s x s x e x e x e x s x s x s x e x Q x Q x Q x Q x - x s x e x b xx third xxxxxx price xxxxxxxxxxxxxx producer xxxxxxx different xxxxxx for xxx same xxxxxxx for xxxxxxxxx types xx consumers xx divides xxx market xxxx segments xxx profit xxxxxxxxxx level xx output xx attained xxxx MR xx in xxx market xx the xxxxxxx market xxx profit xx Live xxxxxxxx inc xx TR x P x Q x Q x Q x Q x Q x given xx Qs xx s xxx s xx s x s xx s xx s xx Q x Q x profit xxxxxxxxxx output x Putting xxx value xx Q x in xxxxxxx demand xxxxxxxx P x Q x profit xxx price xx the xxxxxx for xxxxxxxx else xxx profit xx Live xxxxxxxx inc xx TR x P x Q x Q x Q x Q x Q x given xx Qe xx e xxx e xx e x e xx e xx e xx Q x Q x profit xxxxxxxxxx output x unitsPutting xxx value xx Q x in xxxxxxx demand xxxxxxxx P x Q x profit xxxxxxxxxx price xx s x s xx e x e xxxxxxxxx we xxxx that xx s xx e xx c xxx profits xxxxxxxxxx with xxxx option xx Profit xx senior xxxxxx TP x TR x - xx s xx s x s x s x a xxx - x Profit xx everyone xxxx market xx e xx e xx e xx e x e x e x e xxx - x d xx Live xxxxxxxx inc xxxxxxx one xxxxx to xxx patrons xx would xxxxxxxx its xxxxx profit xxxxxxxx and xxxxxx will xx same xxx all xx P xxxxxxxxx TP x Q x Q x Q x Q x - x Q x Q x dTP xx Q xxx profit xxxxxxxxxxxx Q x units xxx price xx charges x - x P xxxxxxx TP x Q x Q x TP xx Computer xxxxxxxx Corp xxxxx peripheral xxxxxxxxx used xx both xxxxxxx businesses xxx the xxxxxxxxxx Due xx a xxxxxxxxx Computer xxxxxxx s xxxxx have xxxxxxxx by xxxxx and xx now xxx units xx excess xxxxxxxx All xx its xxxxxxx sales xxx to xxxxxxx sector xxxxxxxxx and xxxx pays xxx unit xxx the xxxxxxxxx The xxxxx price xx equal xx of xxxxxxx variable xxxxx A xxxxxxxxxx agency xxx offered xx purchase xxxxx at xxxx If xxxxxxxx Products xxxxxxx the xxxxx it xxxx not xx able xx fill xxxxx of xxx expected xxxxxx from xxxxxxx sector xxxxxxxxx over xxx next xxx months xxxxxxxx the xxxxxxxxx to xxxx customer xxxxxx is xxx expected xx affect xxxxxx sales x Should xxxxxxxx Products xxxxxx the xxxxx to xxxxxx units xx each xx the xxxxxxxxxx agency xxxx happens xx its xxxxxxx if xx accepts xxx offer x Would xxxx answer xxxxxx if xxx inability xx meet xxxxxxx sector xxxxxxxx demand xxxxxxx sales xx during xxxx ignore xxx effects xxxxxx this xxxxxx a xxx ignoring xxxxx effects xxxxxxxx Products xxxxxx the xxxxx to xxxxxx units xx each xx the xxxxxxxxxx agency xxx the xxxxxxx will xx normalized xxx it xxxxxxxx the xxxxxxxxxx market xxxxxxxxx the xxxxx generates x x xxxxx it xxx t xxxx in xxxxxxxxxx revenue x No xxxxxxxxx the xxxxx generates x x xxxxx it xxx t xxxx in xxxxxxxxxx revenue xxx sales xxxxx is xx its xxxxxxxx cost xxxx variable xxxx is xx and xx the xxxxx is xxxxx to xxxxxxxxxx is xxxxxxx than xxxx the xxxx should xxxxxx to xxxxxxxxxx under xxxx circumstances xxxxxx Tutors xxxxxx monthly xxxxxx to xxxxxxxx for xxxxxx or xxxx math xx science xxxxxx A xxxxxx study xxxxx that xxx served xx Online xxxxxx can xx divided xxxx two xxxxx of xxxxxxxx students xxxxxxx help xxxx math xxx are xxxxxxxxx interested xx math xxxxxxxx but xxx be xxxxxxxxxx in xxxx science xxxxxxxx and xxxxxxxx who xxx primarily xxxxxxxxxx in xxxxxxx tutoring xxx may xxxx some xxxx tutoring xxx study xxxxxxx estimates xxxx there xxx students xxx fit xxx category xx quot xxxxxxxx needing xxxx with xxxx quot xxx students xxx fit xxx category xx quot xxxxxxxx needing xxxx with xxxxxxx quot xxxxxx Tutors xxxxxxxxx demand xxx each xxxx of xxxxxxxx service xx type xx student xx given xxxxx All xxxxx are xxxxx so xxxx maximizing xxxxx revenue xx equivalent xx maximizing xxxxxx Use x payoff xxxxxx or xxxx combinations xx pricing xx result xx the xxxx profit xxx demand xxxxxx for xxxxxxx math xxx science xxxxxxxx services xxx given xxxxxxxxx of xxxxxxx Math xxxxxxxx Only xxxxxxx Tutoring xxxx In xxxx of xxxx Tutoring xx Need xx Science xxxxxxxx a xx the xxxxxx Tutoring xxxxxxx to xxxx its xxxxxxxx services xxxxxxxxxxxx what xxxxxx it xxxxxx for xxxx tutoring xxxx should xx charge xxx science xxxxxxxx b xx Online xxxxxxxx offers xxxxxxx services xxxx pricing xxxxx you xxxxxxxxx What xxxxxxx to xxx revenues xx it xxxx bundling x Case xxxxxx tutors xxx for xxxxx and xxx science xxxx students xxxx take xxxxx and xxxx take xxxxxxx Revenue xxxx Online xxxxxx ask xxx maths xxx for xxxxxxx Only xxxxxxxx will xxxx maths xxx will xxxx science xxxxxxx Case xxxxxx tutors xxx for xxxxx and xxx science xxxx students xxxx take xxxxx and xxxx take xxxxxxx Revenue xxxx Online xxxxxx ask xxx maths xxx for xxxxxxx students xxxx take xxxxx and xxxx take xxxxxxx Revenue xxxxxx tutors xxxxxx choose xxxx i x for xxxxxxx and xxx maths x Case xxxxxx tutors xxx for xxxxx and xxxxxxx Only xxxxxxxx will xxxx tutions xxxxxxx Case xxxxxx tutors xxx for xxxxx and xxxxxxx students xxxx take xxxxxxx Revenue xxxxxx tutors xxxxxx choose xxxx i x charge xxx maths xxx science xxxxxxx tutorial xxx maximum xxxxxx of xxx company xxxxxxxxx by xx providing xxxxxxx servicesMore Articles From Economics
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