A market has supply and demand curves that follow the following set of equations

Question

A market has supply and demand curves that follow the following set of equations: Supply rightarrow P = 4Qs + 10 Demand rightarro P = -5Qd + 280. For both of these problems pictures are not required but the problems may be much easier if you draw some. Find the equilibrium price and quantity in this market and the consumer and producer surplus from the equilibrium price and quantity. If there is a ceiling price in this market of 90, find the new consumer and producer surplus. Use these numbers to find the size of the deadweight loss and explain from these numbers whether or not consumers, as a whole, would be in favor of this ceiling.

Explanation / Answer

1. a

P = 4Qs + 10        ----------- (1)      

P = -5Qd+ 280    ----------- (2)

At equilibrium

Eq. 1 = eq. 2

4Q +10 = -5Q +280

9Q = 270

Q = 30

P = 130

Calculation of consumer surplus

P = -5Qd+ 280

To get y intercept, put Qd = 0

P = -5*0 + 280 = 280

At equilibrium , Qd = 30

consumer surplus = (1/2)*(280 – 130)*30 =3750

Thus, Consumer surplus / unit = 3750/30 = 125

Calculation of Producer surplus

P = 4Qs + 10

To get y intercept again, put Qs = 0

P = 10

Now , total producer surplus = (1/2)*(130-10)*30 = 1800

Thus,

Producer surplus per unit = 1800/30 = $60

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