Final answer:
In a perfectly competitive market described by the given demand and supply functions, the equilibrium quantity is 100 and the equilibrium price is 50. The consumer surplus is 1500 and the producer surplus is 2000, making the total economic surplus 3500 for each period.
Step-by-step explanation:
To calculate the total economic surplus in a perfectly competitive market, we need to identify the equilibrium price and quantity where the demand and supply functions intersect. We set the per-period demand function P = 80 - 0.3Q equal to the per-period supply function P = 10 + 0.4Q and solve for Q:
80 - 0.3Q = 10 + 0.4Q
70 = 0.7Q
Q = 100
Substituting Q back into either of the functions gives us the equilibrium price (P):
P = 80 - 0.3(100) = 50
The consumer surplus is the area between the demand curve and the market price, while the producer surplus is the area between the market price and the supply curve. The consumer surplus can be found by calculating the area of a triangle with a base of 100 (the equilibrium quantity) and a height of 30 (the difference between the highest price consumers are willing to pay and the equilibrium price, which is 80 - 50). Thus, consumer surplus equals (1/2)*100*30 = 1500.Similarly, the producer surplus is found by calculating the area of a triangle with a base of 100 and a height of 40 (the difference between the equilibrium price and the price at which producers would have been willing to supply the good, which is 50 - 10). Thus, producer surplus equals (1/2)*100*40 = 2000.
The total economic surplus (consumer surplus + producer surplus) each period is therefore 1500 + 2000 = 3500.