The demand and supply functions for basic cable TV in the local market are given as: Calculate the consumer and producer surplus in this market. If the government implements a price ceiling of $15 on the price of basic cable service, calculate the new levels of consumer and producer surplus. Are all consumers better off

Hello your question is poorly written attached below is the complete question

a) Cs = 800,000 ,  Ps = 1,500,000

b) Cs = 1437500,  Ps = 525,000

Explanation:

Demand function ( Qd ) = 200,000 - 4000 P

supply function ( Qs ) = 20,000 + 2000 P

at equilibrium :  200,000 - 4000P = 20,000 + 2000P

therefore ; P = 180,000 / 6000 = 30

Q = 20,000 + 2000 ( 30 ) = 80,000

a) Determine consumer and producer surplus in the market

consumer surplus ( Cs ) This is the area above the price and below the demand curve  = 1/2 * ( 50 - 30 ) 80,000 = 800,000

producer surplus ( Ps ) This is the area above supply and below price

= 30 * ( 80,000 ) -  1/2 (80,000 - 20,000 ) (30)

= 1,500,000

b) Determine the new levels of consumer and producer surplus with a price ceiling of $15

Pc (ceiling price ) = $15

Qd = 200,000 - 4000 ( 15 )  = 140,000

Qs = 20,000 + 2000 ( 15 ) = 50,000

∴ New consumer surplus = area ( a , Pc, b, d )

= ( 30 - 15 ) (50,000) + 1/2(50-30) (80,000) - 1/2 (80,000 - 50,000 ) (37.5 - 30)

   = 1437500

New producer surplus = area ( Pc , b, e 0 )

= ( 15 ) ( 50000) - 1/2 ( 50,000 - 20,000 ) (15)

= 525,000

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