Final answer:
The equilibrium point is (1.9, -9.5). The consumer surplus at the equilibrium point is -9.975, and the producer surplus is 4.75.
Step-by-step explanation:
The equilibrium point occurs when the demand and supply curves intersect. To find the equilibrium point, we need to set the quantity demanded equal to the quantity supplied and solve for x:
d(x)= s(x)
-4+15x-18 = 1+5x-4
Simplifying the equation, we get:
10x = 19
x = 1.9
The equilibrium point is (x, d(x)) = (1.9, -4+15(1.9)-18) = (1.9, -9.5).
(b) To calculate the consumer surplus at the equilibrium point, we need to find the area between the demand curve and the equilibrium price. We can use the formula for the area of a triangle: (base * height) / 2. The base is the quantity bought at the equilibrium price (1.9 units) and the height is the difference between the maximum price the consumer is willing to pay and the equilibrium price (-9.5 - 1 = -10.5).
Consumer Surplus = (1.9 * -10.5) / 2 = -9.975
(c) To calculate the producer surplus at the equilibrium point, we need to find the area between the supply curve and the equilibrium price. Again, we can use the formula for the area of a triangle. The base is the quantity sold at the equilibrium price (1.9 units) and the height is the difference between the equilibrium price and the minimum price the producer is willing to accept for the item (1 - -4 = 5).
Producer Surplus = (1.9 * 5) / 2 = 4.75