Question

If the demand function for math anxiety pills is p = D(x) = −4x + 57 and the corresponding supply function is p = S(x) = 5x + 3, determine the producer surplus at the market equilibrium point.

Answer 1

Answer :

Demand function : D(x) = - 4x + 57

Supply function : S(x) = 5x + 3

At equilibrium : D(x) = S(x)

-4x + 57 = 5x + 3

57 - 3 = 5x + 4x

54 = 9x

x = 54/9 = 6 = Q (equilibrium quantity)

At this quantity level the equilibrium price =

5*6 + 3 = 33 = p

Now for the supply function when : x = 0

p = 5*0 + 3 = 3 = p0

Therefore producer surplus = (1/2) * (p - p0) * Q

= (1/2) * (33 - 3) * 6 = (1/2) * 30 * 6 = 90

Answer : The producer surplus is 90 at the market equilibrium point