Consider a market with a demand curve of P 198-q and a supply curve of P=4q.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).

198 - q = 4q

This simplifies to:

198 = 5q

So, q = 198/5 = 39.6

Step 2: Substitute q = 39.6 into either the demand or supply equation to find the equilibrium price (P).

P = 198 - 39.6 = 158.4

Step 3: The price elasticity of supply (Es) is calculated as the percentage change in quantity supplied divided by the percentage change in price. The formula for Es when dealing with linear supply curve is Es = (P/Q) * (dQ/dP).

However, in this case, the supply curve is P = 4q, which is a straight line passing through the origin, indicating that supply is perfectly elastic. This means that suppliers are willing to supply any amount at the current price level.

Therefore, the price elasticity of supply at the market equilibrium is infinite or undefined.

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

Set the demand equation equal to the supply equation:

198 - q = 4q

Solving for q gives q = 198 / 5 = 39.6.

Substitute q = 39.6 into either the demand or supply equation to find the equilibrium price P. Using the demand equation:

P = 198 - 39.6 = 158.4

The price elasticity of supply (Es) is given by the formula:

Es = (dQ/dP) * (P/Q)

The derivative of the supply curve with respect to price (dQ/dP) is 1/4.

So, the price elasticity of supply at the market equilibrium is:

Es = (1/4) * (158.4 / 39.6) = 1

Therefore, the price elasticity of supply at the market equilibrium is 1.