Question

The demand equation is given by QD=50-10P and the supply equation is given by QS=2P, what is consumer surplus at the equilibrium?

Answer 1

At the equilibrium price of $4.17, the equilibrium quantity is 8.3. The consumer surplus at the equilibrium is $17.34.

Step-by-step explanation:

At the equilibrium, the quantity demanded (QD) is equal to the quantity supplied (QS), so we can set the demand equation equal to the supply equation:

QD = QS

50 - 10P = 2P

Now, we can solve for the equilibrium price (P) by rearranging the equation:

50 = 12P

P = 50/12

P = 4.17

Substituting the equilibrium price back into the demand equation, we can find the equilibrium quantity (Q):

QD = 50 - 10(4.17)

QD = 8.3

Consumer surplus at the equilibrium can be calculated as the area between the demand curve and the equilibrium price line:

Consumer Surplus = 0.5 * (QD * P)

Consumer Surplus = 0.5 * (8.3 * 4.17)

Consumer Surplus = 17.34