Suppose market demand and market supply are given by the equations:
QD = 40 − P
QS = P − 4
a. How much is total consumer surplus at the equilibrium price in this market?
b. How much is total producer surplus at the equilibrium price in this market?

Please explain what producer surplus is. I have never done a problem with the y-intercept like this and I am confused. For CS, I got 162. No fake answers please (I will report). Thanks much & have a wonderful day!

Respuesta :

Consumer surplus is a measure of benefit to consumers resulting from paying less than the maximum price they are willing to pay.

Producer surplus is a measure of benefit to producers resulting from selling at a price higher than the minimum price at which they are willing to sell.

Referring to the supply-demand curve, these economic surpluses are represented by the area between either curve and the horizontal line fixed at the equilibrium price.

In this case, demand is zero when P = 40; this means there is a consumer surplus whenever P < 40. Similarly, supply is zero when P = 4; then there is a producer surplus whenever P > 4. In particular, any price below this point corresponds to a supply shortage. Realistically, producers would provide the good only if P > 4.

Set supply equal to demand and solve for P to find the equilibrium price:

40 - P = P - 4   ⇒   P = 22

At the minimum price P = 4, consumers demand 40 - 4 = 36 units and producers supply 4 - 4 = 0 units. At equilibrium price, consumers demand 40 - 22 = 18 units and producers supply 22 - 4 = 18 units. Then

CS = 1/2 (36 units - 18 units) ($22/unit - $4/unit) = $162

and

PS = 1/2 (18 units - 0 units) ($22/unit - $4/unit) = $162

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