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Response Details:
To find equilibrium price and quantity, we first equate the supply and demand equations given. The equilibrium occurs when supply=demand, so we have:
5P = 100 - 5P (supply = demand)
Adding 5P to both side, we have 10P = 100, or P = 10. So, the equilibrium price is 10.
To find quantity, we substitute this equilibrium price into either the quantity or price equation, we get 100 - 5(10) = 50 (or if we substituted into supply, we also get 5(10)=50)
Thus, equilibrium quantity is 50.
Now, consumer surplus is the triangle region above the equilibrium price and under the demand curve. We can plot this graph:
We can get the endpoints because we see that at a price of 20, quantity is 0 and at a quantity of 100, price is 0.
So, to find consumer surplus (CS), we need to find the area of that triangle. We see the height of the triangle is 10 and the base is 50. The area of a triangle is (1/2)(base)(height) or in this case, (1/2)(50)(10)=250. Thus, the consumer surplus is 250.
Producer surplus can be found the same way, we find the area of that triangle. In this case, the triangle has the same base and height and so we also have (1/2)(50)(10) = 250. Thus, producer surplus = 250.
Total surplus is then just CS+PS which is 250+250=500
So in summary, P = 10, Q = 50, CS = 250, PS = 250, TS=500.
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