Question

The demand for A product is Q_D = 150-4P, while the supply is Q_S = 100 + P. What are the equilibrium price and quantity? If a subsidy of $5 per unit is imposed calculate the new equilibrium and the changes is consumer, producer and total surplus.

Answer 1

Qs = lootp Qd = Iso- up In Equilibrium Iso-up =loot P Iso-100 = Ptup so =sp pinto Qd equation P = $10 Substituting @=150-4 (10) = 150-40 Q4 = 110 units. If subsidy of $5 per unit has been imposed on sello Buyers, New Demand curve, equation will be. Qd = 150 - U(P-5) ad = 15o-up+20 New Qd = 170 -up New Equilibrium New ad - og

OX 170-up = lootP 170-100 = ptup SP = 70 P = 70 Now P = $14 substituting pinto wood equatio New Qd = 17o-up! = 170 ~4(14) = 170 s6 New at = 114 units Inititial c.s = Area of A (CAD) = + XBXH =0.5x llox (37.5 -10) o =sSX 27.5 P.S = $ \ 512.5 = Area of rectangle (B) + Area of D (E) = LX Bt I XBXH

Price o 20 no to 80 100 110/120 140 160 180 Quantity P.S = 100 x (10-0) to.sx (11o-loo) (10-0) = 10olo to.sxlox 10 tso =1000 =loso P.S Total surplus =(.5+P.S = 1512.s tloso

T.S= $2,562.5 Aftea subsidy of $5. New C.S= Area of A (DIF) = 1 X BXH =0.5X114 x (42.5 -14) = 57*28.5 = $1,624.s is = Area of rectangle (B+C) + - of a (Eth) Area - LÁ B to S X 8x - = 100x14 +0.5* (114 – 100) (14-0) - 1400 to.sxlu x14 = 14oot 98 = 1498 TS = c.stp.s = 1624's +1498 =$ 3122.5 change in value CS, P. TE Afor subside

in c.s = New c.S – old cos = 1624.5- 1512.5 = $112 (Increase ) A in p.S - New P.S- Old P.S. - loso = 1498 =uus (Increase , A in TS = New TS- Old TS = 3122.5-25635 = $560