Question

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

Answer 1

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

answer:

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