Question

A winery produced x thousand bottles of premium wine when the price for each bottle is S(x)= 1.4x^2-50x+1480. The monthly demand for the bottles of wine is related to the price by D(x)= -x^2+34.8x+1928. 1.) Find the consumers surplus and the producer's surplus when the market is at equilibrium. Show work. 2.) Find the change in the consumers and producer surplus when the price increases by $20? Explain why? Show work.

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Answer 1

supply (sen) 500 P- a PA G dary Given Demand (m) and equilibrium condition : Deusz slon) to you? -501 +1480 = -n't 34 8 nt 1928 2047?_04082-448 =0 0.3n² - 10.64-56=0 [Dividing by 8] on both sides 30²-1064 - 560=0 [Mulluplying by 10] Vause of m= -b I Jb²4au , b = -106, a=3 20 CS Scanted leht 11062-14X3X (-560), P2 or Q e-560 CamScanner 2x3

= 106 + 111236 +6720 6 X = 106 = 17956 6 106 2 134 -46.7 40 6 The value of n cannot be -ve, Value of > Hence = 40 P* = 1720 [ using either lg. for Dlm) or slm) =) Value area à Consumer Surplus is triangle Finding som eg for Den) In=0 تع 2 Pi= 1980 => Area of Aa= x40x ( 1928 – 1720] 4160 - 2 20x208 Producer Surpuis å area 'b Frangle Finding a from eq. for long] neo P2 = 1480 Area of Ab= 1x40x [1720-1480] = 4900 -@ CS Scanned with CamScanner

27 A G PE $1920 B ng? lo Pr X-4002 125 Pn= 8 + $20= $1740 As pruve sure, chuantity Demanded falle (de) cuantity supplied duses eda) - the (when frie is 1740) Vung Demond ofn = (-) +3498m 44988-= 1740 -M? +34.8% +' 188 - 0 21² - 340% u - 188 20 By using na bh 6²400 n= 39.55 { Rejecting the we value] - diz 39.55 10 or ره za Also da ( When price is 1740) Very supply fu 14u²-50n +1480 = 1740 foln ²-501 260 50 7n?- Qin - 130=0 or Fu²-250n-1300=0 a= 250+ |(250)? 4x7X (-1300 2x7 n=250 +314.48 14 564.48 de 14 40.32 CS Scanned with40.32 CamScanner

> hoce in Consumer Surplus is area B +6 New consumer Surplus = I x 39.55 X(1923 - 1940 A trangle 40) 371707. = 4160 371707 Hence fall in consumer surplus L new es = 442.3 = [Area (3+c)] L old is → Rise in producer surplus = Area Bt CAD New produs surplus = B+e+D+E+F = 1x 40-32 x 61480+ 1740) = 5249.6 Honce Rise in producer Surplus = 524106_4800 450.0 = 450 App. Arch Bre+D CS Scanned with CamScanner