Question

In: Economics

I. Given: Qd = 1100 - (2)P Qs = 3P - 100 1. Equilibrium Price of...

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

Solutions

Expert Solution

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.


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