Question

Tasmanian abalone fishing boats, each costing $500,000, trawl the waters of Tasmania for abalone. The total dollar value of abalone caught by the boats collectively varies with number of boats (N) and is

Total $ Value (1000’s of $’s) = 1000N − N 2

This gives a marginal collective total value of the catch of

Marginal $ Value (1000’s of $’s) = 1000 − 2N

All boats are identical, so each boat has the same size and value of catch. The revenue for each boat is

Average $ Value (1000’s of $’s)/Boat = 1000 − N

a) What is the socially optimal number of boats?

b) Given that each boat is individually owned, how many boats will actually operate?

c) Explain why the inefficiency in number of boats arises. Using an appropriate diagram, show the associated deadweight loss. Calculate the numerical size of this deadweight loss

Answer 1

MARGINAL COST FISMING BOAT ED BY BOATS COLLECTIVELYCTR) AL COST OF RUNNING A FISHING MC = $ 500 C6005) CiN THOUSANDS) TOTAL VALUE GENERATED BY BOH! 1000's of $15) = 1000N -N? 12 COLLECTIVE VALUE GENERATED BY BOATS CMR) (1000)s of $75)-1000 - 2N REVENUE AVERAGE REVENUE O " NP MARGINAL COLLEC TOTAL REVEWUE AR= 1000 -N cin 1000's of $'$) TOTAL REVENUE, TR=1000N-N2 MARGINAL REVENUE, MR=1000 - 2N (a) SOCIALLY OEP OPTIMAL NUMBER OF BOATS IS AT POINT WHERE MARGINAL cosT op OF RUNNING A BOAT EQUALS MARGHA MARGINAL REVENUE GENERATED BY BOAT mc = MR 500 - 1000 - 2N N=2sd OTIMA NUMBER OF BOATS SOCIALLY OPTIMAL NUMBER - IS 250 (b, EACH BOAT is tester INDIVIDUALLY OWNED, PEOPLE comiNaTO IN THIS BUSINESS. TILL THE WILL KEEP COMING TO IN THIS TIME PROFIT GENERATED BY BOAT IS POSITIVE VE ALL BOATS ARE IDENTICALAVERAGE REVENUE GENERATED BY EACH BOAT is AVERAGE VALUE (1000-N). MARKET INAGOVE Scanned with CamScanner

IN ABOVE CASE, MAR BE AT E, MARKET EQUILIBRIUM HO WOULD POINT WHER AR=MC 1000-N = 500 = Ne Soo TF EACH BOAT IS INDIVIDUALLY OWNED E 500 BOATS WOULD BE THERE (C) DEAD WEIGAT LOSS is THERE BECAUSE 500 BOATS ARE PRESENT IN TASMANIAN WATERS INSTEAD OF SOCIALLY OPTIMAL NUMBER OF 250. THE FORE, THERE is INEFFICIENT OUTCOME WITH RESPECT TO NUMBER OF BOATS WHEN A NEW BOAT IS APPED TO FLEET IT GENERATES SOME REVENUE INDIVIDUALLY BUT ALSO CUTS IN THE REVENUE GENERATED BY ALL OTHER BOATS, TH HENCE, A NEGATIVE EXTERNALITY is GENERATED BÝ OTHER BOATS loool REVENUE d- T OL : WL soo WX - - - JB Foo NUMBER NUMBER E BOATs 250 REGION (ESAB) is THE DEAD WEIGHT Scannedosis Camlanner

AREA(REGION ESAB) = DEAD WEIGHT LOSS SINCE REGIO Is A TRIANGE AREA= 4x BASE X MEIGHT = 4x(500-250)*(500) = 500X250 66 2500 (1000s) 2 DEADWEIGHT LOSS=$ 625,000 (3000s) Scanned with CamScanner