Demand for a commodity is given by P=10-2Qd, supply for the commodity is given by P=.4 +Qs. Assuming no externalities, find the market clearing price, quantity, consumer and producer surplus.
First, please note that we request that students only ask one question at a time on eNotes. I consider finding the price and quantity to be one question as they are done in very similar ways. I will give answers for that question but not for the surpluses, which are an entirely different operation.
We can find the equilibrium price and quantity by using the equations given for the supply and demand curves. The equation for the demand curve was P = 10 – 2Q and the equation for the supply curve was P = .4 + Q. Since both equations are given in terms of P, the two equations are equal to one another. We can find the equilibrium quantity by setting them equal to one another and solving:
.4 + Q = 10 - 2Q
3Q = 9.6
Q = 3.2
This means that the equilibrium quantity is 3.2 (units are not given in your question). To find the equilibrium price, we must plug the quantity in to either of the demand or supply curve equations.
P = 10 – 2(3.2) or P = .4 + 3.2
Whichever equation we use, the equilibrium price is 3.6 (again, no units are given).
So, by doing these calculations, we can find that the market clearing price is 3.6 and the market clearing quantity is 3.2.