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 ndash xx Pe xxxxx 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 rsquo xxxxx revenue xxxxxxxx What xx its xxxxx cost xxxxxxxx Its xxxxx profits xxxxxxxx For xxx total xxxxxxx use xxxxx Revenue x s x s x e x e x What xxx the xxxxxx maximizing xxxxxx of xxxxx and xxxxxx if xxxx Theaters xxx engages xx third xxxxxx price xxxxxxxxxxxxxx Show xxxx MRe xxx MC xxx MR x d xx P x Q x MR x d xx P x Q x and xx d xx TC x What xxx profits xxxxxxxxxx with xxxx option x If xxxx Theaters xxxxxxx one xxxxx to xxx patrons xxxx would xx be xxx many xxxxxxxxx would xx serve xxxx would xx its xxxxxxx a xxxxx MC xxx average xxxxxxxx cost xxx Fixed xxxxx Total xxxxxxx consists xx the xxxxx income xxxxxxxxx by xxxxxxx to xxx the xxxxxxxxx types xx consumers xxxxxxxxx TR x e x e x s x s xxxxx revenue xxxx everyone xxxx total xxxxxxx from xxxxxxx ndash x e x e xxxxx Q x Q x Total xxxx function xx the xxxxx cost xxxxxxxx in xxxxxxxxx for xxxx type xx consumers xx includes xxxx variable xxx fixed xxxxx Therefore xx TVC xxx AVC x TFC xx AVC xx given xx use xxx relation xxx TVC x Q x Q x Total xxxxxxx equals xxxxx revenue xxxxxx less xxx total xxxx of xxxxxxxxxx Therefore xx TR- xx P x Q x P x Q x ndash x s x e x e x e x s x s xxxxx Q x Q x - xxxxx Q x Q x ndash x s x s x Q x Q x - x In xxxxx degree xxxxx discrimination xxxxxxxx charges xxxxxxxxx prices xxx the xxxx product xxx different xxxxx of xxxxxxxxx He xxxxxxx the xxxxxx into xxxxxxxx The xxxxxx maximizing xxxxx of xxxxxx is xxxxxxxx when xx MC xx the xxxxxx In xxx seniors xxxxxx the xxxxxx of xxxx Theatres xxx is xx s x s x s xxxxx Q x Q x Q x ndash x s xxxxx Ps xxxxx Qs xxxxxx hellip xx s xxx s xx s xxxxx Q x MR x MC x amp xx ndash x s x s xxxxxx maximizing xxxxxx - xxxxxxx the xxxxx of x s xx inverse xxxxxx function x s xxxxx Q x ndash xxxxxx max xxxxx In xxx market xxx everyone xxxx the xxxxxx of xxxx Theatres xxx is xx e x e x e xxxxx Q x Q x Q x ndash x e xxxxx Pe xxxxx Qe xxxxxx hellip xx e xxx e xx e xxxxx Q x MR x MC x amp xx ndash x e x e xxxxxx maximizing xxxxxx - xxxxxxxxxxxx the xxxxx of x e xx inverse xxxxxx function x e xxxxx Q x ndash xxxxxx maximizing xxxxx MR x ndash x s xxxxx MR x ndash x e xxxxx Therefore xx show xxxx MR x MR x MC x The xxxxxxx associated xxxx this xxxxxx is xxxxxx in xxxxx senior xxxxxx rdquo xx s xx s x TC x TP x P x Q x ndash x a xxx - xxxxx - xxxxxx in xxxxx everyone xxxx rdquo xxxxxx TP x TR x ndash xx e xx e x e x e xxxxx Q x AVC x ndash 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 ndash x ndash x Q xxxxx Q x Q xxxxx Q x Q x dTP xx ndash x ndash xxx profit xxxxxxxxxxxx Q x units xxx price xx charges x - x P xxxxx Profits xx Q xxxxx Q x Q x TP xxxxx ndash xxxxx TP xxxxxxxx Products xxxx sells xxxxxxxxxx equipment xxxx by xxxx private xxxxxxxxxx and xxx government xxx to x recession xxxxxxxx Product xxxxx 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 ndash x units xx can xxxxx t xxxx in xxxxxxxxxx revenue x No xxxxxxxxx the xxxxx generates x ndash x units xx can xxxxx 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 amp xxxx students xxxxxxx help xxxx math xxx quot xxx students xxx fit xxx category xx amp xxxx students xxxxxxx help xxxx science xxx quot xxxx Online xxxxxx estimated xxxxxx for xxxx type xx tutoring xxxxxxx by xxxx of xxxxxxx is xxxxx below xxx costs xxx fixed xx that xxxxxxxxxx total xxxxxxx is xxxxxxxxxx to xxxxxxxxxx profit xxx a xxxxxx matrix xx find xxxxxxxxxxxx of xxxxxxx to xxxxxx in xxx best xxxxxx The xxxxxx prices xxx monthly xxxx and xxxxxxx tutoring xxxxxxxx are xxxxx belowType xx Student xxxx Tutoring xxxx Science xxxxxxxx Only xx Need xx Math xxxxxxxx In xxxx of xxxxxxx Tutoring x If xxx Online xxxxxxxx decides xx sell xxx tutoring xxxxxxxx individually xxxx should xx charge xxx math xxxxxxxx What xxxxxx it xxxxxx for xxxxxxx tutoring x If xxxxxx Tutoring xxxxxx bundled xxxxxxxx what xxxxxxx would xxx recommend xxxx happens xx its xxxxxxxx if xx uses xxxxxxxx a 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 Only xxxxxxxx will xxxx maths xxx will xxxx science xxxxxxx Case xxxxxx tutors xxx for xxxxx and xxx science xxxxxxxx will xxxx maths xxx will xxxx science xxxxxxx Online xxxxxx should xxxxxx case x e xxx science xxx for xxxxx b xxxx Online xxxxxx ask xxx maths xxx science xxxx students xxxx take xxxxxxx Revenue xxxx Online xxxxxx ask xxx maths xxx science xxxxxxxx will xxxx tutions xxxxxxx Online xxxxxx should xxxxxx case x e xxxxxx for xxxxx and xxxxxxx bundled xxxxxxxx The xxxxxxx profit xx the xxxxxxx increases xx by xxxxxxxxx bundled xxxxxxxxMore Articles From Economics
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