Consider a market with a demand curve of P = 164–q and a supply curve of P = 3q. What is the price elasticity of supply at the market equilibrium?

To find the price elasticity of supply at the market equilibrium, we first need to find the equilibrium price and quantity.

Step 1: Set the demand and supply equations equal to each other to find the equilibrium quantity (q).

164 - q = 3q

This simplifies to:

4q = 164

So, q = 41.

Step 2: Substitute q = 41 into either the demand or supply equation to find the equilibrium price (P).

Using the supply equation:

P = 3q = 3*41 = 123

Step 3: The price elasticity of supply is calculated as the percentage change in quantity supplied divided by the percentage change in price.

The supply curve is P = 3q. We can rewrite this as q = P/3.

The derivative of q with respect to P is 1/3.

So, the price elasticity of supply (Es) at the equilibrium is:

Es = (1/3) * (P/q) = (1/3) * (123/41) = 1

Therefore, the price elasticity of supply at the market equilibrium is 1. This means that a 1% increase in price will result in a 1% increase in quantity supplied, indicating unit elastic supply.