Question

4) In a certain state, it is found that the distribution of income for lawyers is given by the Lorenz curve L (r) = while that of surgeons is given by L2(r) = {x4 + }r Compute the Gini index for each Lorenz curve. Which profession has the more equitable income distribution? 5) An investment will generate income continuously at the constant rate of $1000 per year for 6 years. If the prevailing annual interest rate remains fixed at 7% compounded continuously, what is the present value of the investment? 6) Money is transferred contimuously into an account at the constant rate of $800 per year. The account earns interest at the annual rate of 20% compounded continuously How much will be in the account at the end of 5 years? 7) The demand and supply functions, D(g) and S(q), for a particular commodity are given. Specifically, q units of the commodity will be demanded (sold) at a price of p D(g) dollars per unit, while q units will be supplied by producers when the price is p=S(q) dollars per unit. Find the consumers' surplus and the producers' surplus at equilibrium 14 D(g) = q+ S4)=2 2

Answer 1

등지 S 2 + L,(X) to We need benecth Calculot this area curve Area benecth Li(X) LiCx) d 3 2 11 + 3 6 13 36 Gini index for LicK) 13 36 13-13 3 6 30 a14 13 83 1 4 L2(x)= Area beneath Lx)= +,) 4x

6-840. 1.3 7 1.3 Gini indey for Lica) 7 2 2 0.314 N 31.4. Gini Index for LICK 1388 1. SMaller index fer L,Cn) 31.4 Gini then equitabu hes Pro Fesion 210w Lawyen distribution. in come C Because, loner thu Gini Index higher ould h the equality U

f discounted fu tur cah toms Sum PV = Pu of 10000 P/A, 7., 6) 1-1 inveyfment 1000 x 4.767 = #4767 Arswer 4767 Fv= Sum of Fv of cash om ih nea Fufur al 3 g0011.2) 800( と) + 80u(12)+ 800 (ト 2)と FV + 800 C.2 ) 9532.32 1 Anuwer is 9532.7 2 At equili bviun (3)d (a 14 2 9 42 14 9+2 244)-9(9+2) = S 2 207 2) 2 (28-9(9+2 )) = 1009 +2) 56 228-2a (9+2) = 1094 00

Producer surplus (て) (50 -51) 1 At equilibriuns surplus 3.S Consumev Producer surplus 1