To calculate the change in producer surplus, we need to find the area between the original supply curve and the new supply curve, bounded by the old and new prices. Given that the inverse supply curve is Q = 9p^2, we can determine the quantities supplied at the original and new prices:
Original price (p1) = 5
Original quantity supplied (Q1) = 9(5)^2 = 225
New price (p2) = 2
New quantity supplied (Q2) = 9(2)^2 = 36
To find the change in producer surplus, we calculate the areas under the two supply curves:
Original producer surplus = (1/2) * (p1) * (Q1)
= (1/2) * 5 * 225
= 562.5
New producer surplus = (1/2) * (p2) * (Q2)
= (1/2) * 2 * 36
= 36
Change in producer surplus = New producer surplus - Original producer surplus
= 36 - 562.5
= -526.5
Therefore, the change in producer surplus is -526.5. It seems there may have been an error in the answer saved, as it should be -526.5 instead of -130.5.