Final answer:
The resulting consumer surplus (CS) is 196 and the producer surplus (PS) is 784 when a subsidy of 54 is applied, given the demand and supply curves.
Step-by-step explanation:
The demand curve is given by P = 64 - 0.5Q and the supply curve is given by P = 1 + 1.75Q. With a subsidy of 54, we need to find the resulting consumer surplus (CS) and producer surplus (PS). To solve for CS and PS, we need to find the equilibrium quantity and price.
To find the equilibrium, we set the quantity demanded equal to the quantity supplied:
64 - 0.5Q = 1 + 1.75Q
2.25Q = 63
Q = 28
Substituting the value of Q back into the demand curve, we can find the equilibrium price:
P = 64 - 0.5(28)
P = 50
Now that we have the equilibrium quantity and price, we can find CS and PS. CS can be found by taking the area between the demand curve and the equilibrium price, up to the equilibrium quantity. PS can be found by taking the area between the supply curve and the equilibrium price, from zero to the equilibrium quantity.
CS = 0.5 * (64 - 50) * 28 = 196
PS = 0.5 * (50 - 1) * 28 = 784