Understanding Price Elasticity: A Key Concept in Economics
What is price elasticity and how is it calculated for a good with demand given by P=583−3Q at P=112?
Price elasticity measures the responsiveness of quantity demanded of a good to changes in its price. In this case, for a good with demand described by the equation P=583−3Q, we are asked to calculate the point price elasticity at a price level of P=112. How can we determine this value?
Calculating Price Elasticity for a Good with Demand Given by P=583−3Q at P=112
Price elasticity of demand can be determined by evaluating the derivative of quantity with respect to price and multiplying it by the price divided by the quantity. Let's break down the steps for calculating the point price elasticity at P=112 for the given demand equation P=583−3Q:
The demand equation for the good is given as P=583−3Q, where P represents the price and Q represents the quantity demanded.
1. Find the derivative of quantity with respect to price:
dQ/dP = -3
2. Substitute the given price P=112 into the demand equation to find the corresponding quantity demanded Q:
112 = 583 - 3Q
Rearranging the equation, we find:
3Q = 471
Q = 157
3. Calculate the point price elasticity:
Point Price Elasticity = (dQ/dP) × (P/Q) = (-3) × (112/157) ≈ -2.14 (rounded to two decimal places)
The negative value of -2.14 indicates that the good is elastic, meaning a percentage change in price will result in a larger percentage change in quantity demanded in the opposite direction.
Understanding price elasticity is crucial for businesses and policymakers to make informed decisions about pricing strategies and market dynamics.