Assume in a market individual supply function of a commodity A is given by SA=4PA-6 and individual demand function is DA=8-2P. Ttere are 2000 suppliers of commodity A with identical supply function and there are 4000 buyers of the commodity A with identical demand function , where SA is quantity supplied , DA is quantity demanded and PA is price of commodity A. Find
A) Market Equilibrium price (PA)
B) Equilibrium quantity (Qd)
A) Market Equilibrium Price (PA):
PA = 4
B) Equilibrium Quantity (Qd):
Qd = 2000
To find the market equilibrium price (PA) and equilibrium quantity (Qd), we need to find the price at which the quantity demanded (Qd) equals the quantity supplied (Qs).
A) Market Equilibrium Price (PA):
1. Set the quantity demanded (DA) equal to the quantity supplied (SA):
DA = SA
2. Substitute the given functions into the equation:
8 - 2P = 4P - 6
3. Simplify the equation:
8 + 6 = 4P + 2P
14 = 6P
4. Divide both sides of the equation by 6 to isolate P:
P = 14/6
P = 7/3
Therefore, the market equilibrium price (PA) is 7/3.
B) Equilibrium Quantity (Qd):
To find the equilibrium quantity, substitute the equilibrium price (PA) into either the demand or supply function and solve for Qd.
Using the demand function, DA = 8 - 2P:
1. Substitute the equilibrium price (PA = 7/3) into the demand function:
DA = 8 - 2(7/3)
2. Simplify the equation:
DA = 8 - 14/3
DA = 24/3 - 14/3
DA = 10/3
Therefore, the equilibrium quantity (Qd) is 10/3.