Consider a market determined by the following supply and demand curves: 1. P=2Q 2. P=100-2Q Determine the agents' surpluses and calculate the social surplus.

To determine the agents' surpluses, we need to find the equilibrium price and quantity, and then calculate the individual surpluses for both the buyers and the sellers.

To find the equilibrium price and quantity, we set the supply and demand equations equal to each other:

$$2Q = 100 - 2Q$$

Simplifying the equation:

$$4Q = 100$$

$$Q = \frac{100}{4} = 25$$

Plugging the value of Q back into one of the equations to solve for the equilibrium price:

$$P = 2Q = 2(25) = 50$$

So, the equilibrium price is 50 and the equilibrium quantity is 25.

To calculate the individual surpluses, we need to find the area of the triangle above and below the equilibrium price.

For the buyers' surplus, we can find the area below the demand curve and above the equilibrium price.

Buyers' surplus = $$0.5\times(100-50)\times25=625$$

For the sellers' surplus, we can find the area above the supply curve and below the equilibrium price.

Sellers' surplus = $$0.5\times(50-0)\times25=625$$

Finally, to calculate the social surplus, we add the buyers' and sellers' surpluses together:

Social surplus = Buyers' surplus + Sellers' surplus

Social surplus = $$625+625=1250$$