Question

The quantity two bedrooms apartments supplied in Townville is currently 100 units, and the rent for these apartments is $1000 per month.

You are in charge of increasing this quantity supplied to 150 units by regulating prices (i.e., rent).

Your economic advisor tells you that, at a price of $1000, the supply in Townville has an elasticity of 10 (suppose that the elasticity of supply is constant along the supply curve).

What price do you need to set for 150 units to be supplied in Townville?

Answer 1

To supply 150 units of apartments in Townville, the price needs to be set at $1500 per month.

Step-by-step explanation:

To find the price needed to supply 150 units, we can use the concept of price elasticity of supply. The price elasticity of supply formula is:

Price Elasticity of Supply = (Percentage Change in Quantity Supplied) / (Percentage Change in Price)

In this case, we know the current quantity supplied is 100 units and the price is $1000. The elasticity of supply is given as 10. Now we can find the percentage change in quantity supplied:

Percentage Change in Quantity Supplied = ((new quantity - old quantity) / old quantity) * 100

Plugging in the values, we get:

Percentage Change in Quantity Supplied = ((150 - 100) / 100) * 100 = 50%

Now, let's solve for the percentage change in price:

Percentage Change in Price = ((new price - old price) / old price) * 100 = ((new price - $1000) / $1000) * 100

Given that the elasticity of supply is 10, we can solve for the new price:

Elasticity of Supply = (Percentage Change in Quantity Supplied) / (Percentage Change in Price)

10 = 50% / (new price - $1000) / $1000) * 100

Simplifying the equation, we get:

1 = 50% / (new price - $1000) / $1000)

Now we can solve for the new price:

(new price - $1000) / $1000) = 50%

(new price - $1000) = $1000 * 50%

new price = $1000 + ($1000 * 50%)

new price = $1000 + ($500)

new price = $1500

So, to supply 150 units, the price needs to be set at $1500 per month.