The Shakespeare Theatre has a monopoly on productions of Othello in Washington,

Question

The Shakespeare Theatre has a monopoly on productions of Othello in Washington, DC. They hire you to analyze whether oering a “young adult” discount could help increase prots. After some economic analysis, you discover that the demand curve for Othello tickets is dierent for those under 35 years old than for those over 35 years old. In particular, the demand for the younger crowd is Q D <35 = 620 20P, while the demand for the older crowd is QD>35 = 1400 40P. Nice job! Shakespeare Theater tells you that their costs are a xed $12,350 to put on the show, plus $5 in marginal cost for each individual who attends (same cost regardless of age). (a) If Shakespeare Theatre can separate the two groups (they will just look at IDs to determine age), what price should they charge to each group? How many people from each group will buy tickets? What is the theatre’s total prot? (b) If DC passes a law banning age discrimination in pricing, and Shakespeare Theatre can no longer price discriminate (but is still a monopoly) - what price will they charge? What quantity will be sold? What is the total prot? (c) Compare the deadweight loss in the two above scenarios. Why is it dierent?

Explanation / Answer

a.  If Shakespeare Theatre can separate the two groups

Then In each group he will charge the price where, MR = MC

So for Adults

   Q D <35 = 620 20P

P = 620/20 - Q/20

TR = P*Q = (620/20 - Q/20)*Q

MR = dTR/dQ = 31 - Q/10

MC = 5

So, Putting MR = MC

  31 - Q/10 = 5

Q for Adults= 260

P for Adults = 620/20 - Q/20 = 620/20 - 260/20 = $18

Now for Older People

   Q D >35 =1400 40P

P = 1400/40 - Q/40

TR = P*Q = (1400/40 - Q/40)*Q

MR = dTR/dQ = 35 - Q/20

So, Putting MR = MC

  35 - Q/20 = 5

   Q for older= 600

P for Older = 1400/40 - Q/40 = 1400/40 - 600/40 = $20

Total Profit = TR - TC

   = PA*QA + PO*QO - TC

   = 260*18 + 600*20 - 12350 - 5*860

   = $42,150

b. Shakespeare Theatre can no longer price discriminate

Then Total Demand Q= Q<35 + Q>35 = 2020 - 60P

P = 2020/60 - Q/60

TR = P*Q = (2020/60 - Q/60)*Q

MR = dTR/dQ = 202/6 - Q/30

So, Putting MR = MC

202/6 - Q/30 = 5

Q = 8601720-

P = 202/6 - 860/60 = $19.33

Total Profit = 19.33*860 - 12,350 - 5*860

= 16,626.66 - 16,650

= $23.34

Dead weight loss of monopoly = 1/2(Moonpoly price - perfect compititive price)*(Qpc -Qm) + 1/2( perfect compititive price - mc)(Qpc - Qm)

= (18 - 5)(520 - 260) + (20 - 5)*(1200 - 60)

So DEad weight loss in pprice discrimination case = 13*260 + 15*600

   = 3380 + 9000 = 12380

And Dead weight loss in pprice discrimination case

= (20-19.33)(1720-860)

= 567.6

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