In: Economics
I. Given: Qd = 1100 - (2)P Qs = 3P - 100 1. Equilibrium Price of good x 2. Equilibrium Quantity of good x 3. Price Elasticity of demand at Pe 4. Arc Elasticity where P = 250 and P = 200
1. Equilibrium is attained where demand becomes equal to its supply.
Or, 1100 - 2P = 3P - 100
Or, 5P = 1200
Or, P = $240
This is the equilibrium price.
2. Equilibrium quantity can be found out by putting the value of equilibrium price in the demand or supply equation.
Q = 1100 - 2.240 = 1100 - 480 = 620 units.
3. Price elasticity can be found out by by using the formula:
Percentage change in Price÷Percentage change in Quantity
Let us write the demand function as the following:
P = 550 - Qd/2
This equaltion shows that when price changes by $1, equilibrium quantity will decline by 1/2 units.
Thus, at equilibrium price and quantity,
Ed = (240/620 ) × (-1/2 ÷ 1) = 0.387 × -1/2 = -0.1935
( The formula used is : (P/Q) × (Change in Q/Change in P)
4. At P = 250,
Qd = 600
At P = 200,
Qd = 700
Here, change in P = 200 - 250 = -50
Change in Q = 700 - 600 = 100
Thus, Ed = (250/600) × (100/-50) = -0.833.