Question

On Sundays people in Los Angeles consider taking a boat to Catalina Island to spend the day on the beach there. The utility that a person gets from visiting Catalina is 1 − [n/120] − p, where n is the number of visitors on the island and p is the price of round-trip transportation (by boat). (Note that a visitor obtains more satisfaction if there are fewer other visitors on the island.) The utility of staying home is zero.

Part A: In equilibrium, how many people visit the island on a given Sunday? (Your answer should depend on p.)

Part B: Suppose that the boat companies can transport people to and from the island at zero cost. If the boat transportation market is perfectly competitive, what is the equilibrium price p∗ and what is the number of visitors n∗?

Part C: Compute the total surplus in this market in the equilibrium of part (b).

Part D: How does an externality arise in this problem and is it positive or negative?

Part E: Now suppose that the demand for boat transportation is served by a monopoly firm. That is, a single firm sets the price p. What price will the monopolist set and how many people will visit the island?

Part F: Compute the total surplus for the outcome of part (e). Is the monopoly good or bad for the economy? Explain.

Answer 1

Solution: Gtvan uty=-a-P nonoof visituvs Pprice ofundtrie v lity of stay ing hame PortA n eailib rim no of peaple vistt island on iven Sunday is U1-(nlia)P Apar Son visi island og long al U>o, uhare is his utility fm Staying home col have -6l12o) -Po (* = \३০ (1-p) PaY+B: I boat Companies trans potpeople tolond fom tHe island at reo cortpecHy Competitive

then eawilbrim price p and no of. visitors n asre: e are given that trantpartatian 0 fence ina perfectly Compettve market,ptmzo Compete, aganist each oter by (ic) boat compani Casthing prices tll pice eawals t marginal Coft cohich i equal to o 시ray we have n2s (i-p) Hene, there ill be 8o visiters Parte:Total %plus in market in te eauilbin is Utly to each person net Consmer Surpus ofprica paid times of rumber at višitors 120 CI-2/i6) -0) 120 C-0)

Profit for boat ompanie Cocanse purfectly Compertitive) Total Srplus Porto: externalty anse ndthe Sign externalrty in tems of additima Enthis Cole there is an fndidual hal if an negatie ulility an person visits he, is land exerting Hene each individual Csho visits the island i m other visitor negative externality leng a thy Here each person deci des tovisit a have pasrtve otility u ene allo will Aitat Prica po Poxte: demand fr both Ceved ky munopoly

frm ingle fim sete pme p, price that n Polist aill Set and peaple ill vitt island are; Demand eure for e monopolist we have. n lao (-p) Hence profit functnr manopolrst Pn-c 2 oc-) The monopolits maxinisej profiti and Foc tor it is dTdn nM60 Hen ce P ((6 (20)) 2 Hn ee monopolrst coil Set P12 and tere wt be (60 visitrs V

PortFotal Surplus for outome parte) and monopoly good Bad for the elsnomy Gonfumer Surplus utiltyto each person net of PYice paid times tte no of visitors - Go C-12-1 Profit for manspoly = PEn C) 30 Total Suplus 30 Ot 30 Here monopoly is better in deng of Social celfare he monopoly leads to le nmbey tSitors and hence duces te extant of negatve exeynality tHaving monepoly i better.