Question

The equation for a supply curve is 4P = Q. What is the elasticity of supply as price rises from 3 to 4? What is the elasticity of supply as the price rises from 7 to 8? Would you expect these answers to be the same?

Short answer

The elasticity of supply for both price changes (from 3 to 4 and from 7 to 8) is 1, which indicates a unitary elastic supply. The percentage change in quantity supplied exactly matches the percentage change in price, resulting in an elasticity of supply value of 1 for both price changes. Therefore, we would expect the answers to be the same.

Step-by-step solution

We have the supply curve equation given as \(4P = Q\). This equation shows the relationship between the price of a good (P) and the quantity of that good (Q) that is supplied by the market. #Step 2: Find the percentage change in price and quantity for each price change#

Given the supply curve equation \(4P = Q\), we can find the percentage change in price and quantity for each price change. For price change from 3 to 4: Percentage Price Change = \(\frac{4 - 3}{3} = \frac{1}{3}\) Quantity change: \(Q_1 = 4(3) = 12\) and \(Q_2 = 4(4) = 16\) Percentage Quantity Change = \(\frac{16 - 12}{12} = \frac{1}{3}\) For price change from 7 to 8: Percentage Price Change = \(\frac{8 - 7}{7} = \frac{1}{7}\) Quantity change: \(Q_1 = 4(7) = 28\) and \(Q_2 = 4(8) = 32\) Percentage Quantity Change = \(\frac{32 - 28}{28} = \frac{1}{7}\) #Step 3: Calculate the elasticity of supply for each price change#

Using the percentage changes in price and quantity, we can now calculate the elasticity of supply. Elasticity of Supply = \(\frac{\text{Percentage Quantity Change}}{\text{Percentage Price Change}}\) For the price change from 3 to 4: Elasticity of Supply = \(\frac{\frac{1}{3}}{\frac{1}{3}} = 1\) For the price change from 7 to 8: Elasticity of Supply = \(\frac{\frac{1}{7}}{\frac{1}{7}} = 1\) #Step 4: Compare the elasticity of supply and discuss the results#

Elasticity of Supply for both price changes is 1. Thus, we can conclude that the supply for this particular good is unitary elastic. In this case, the percentage change in quantity supplied exactly matches the percentage change in price, resulting in an elasticity of supply value of 1 for all price changes. Therefore, yes, we would expect the answers to be the same.

Key concepts

Supply Curve

In microeconomics, the supply curve plays a pivotal role in describing the relationship between the price of a good and the quantity of that good that producers are willing to supply. It’s typically represented graphically, with price on the vertical axis and quantity on the horizontal axis. For a linear supply curve, like the one given in the problem with the equation \(4P = Q\), the curve shows a direct positive relationship between price (\(P\)) and quantity (\(Q\)).
This means that as prices rise, producers are generally willing to supply more of the good. The positive relationship reflected in the supply curve assumes that all other factors remain constant. It's a simplified model that helps us understand how market supply adjusts in response to price changes. Understanding supply curves is fundamental for analyzing market supply and demand dynamics.

Price Elasticity

Price elasticity of supply (PES) is a measure used in economics to show the responsiveness, or elasticity, of the quantity supplied of a good or service to a change in its price. The elasticity of supply is calculated by dividing the percentage change in the quantity supplied by the percentage change in price.
The elasticity can be expressed as \(\frac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}}\). If the elasticity is greater than one, the supply is considered elastic; if it is less than one, it is inelastic; and if it equals one, the supply is unitary elastic. In the example from the exercise, the elasticity of supply was found to be 1 for both price changes, indicating a unitary elasticity where the percentage change in quantity supplied exactly matches the percentage change in price.

Quantity Supplied

Quantity supplied is the amount of a particular good or service that producers are willing to supply at a given price. According to the law of supply, there is a direct relationship between price and quantity supplied, meaning that suppliers will want to offer more of a good at higher prices.
In the step-by-step solution, the problem illustrated how to calculate the quantity supplied at different price points using a linear supply equation. For example, when the price rises from 3 to 4, the quantity supplied goes from 12 to 16 units, showing how supply responds to changes in price.
The calculation based on the formula \(Q = 4P\) reveals that understanding quantity supplied in tandem with price changes helps in determining how responsive supply is to price changes, which is reflected in the elasticity calculation.

Microeconomics

Microeconomics is a branch of economics that focuses on the actions of individuals and industries, like the dynamics between buyers and sellers, borrowers and lenders. It studies the interactions within markets from the perspective of decision-making units. Supply, demand, and the elasticity of these curves are core concepts in microeconomics.
For students of microeconomics, grasping the concept of supply elasticity helps in understanding how different factors can influence market outcomes. The analysis conducted in the supply elasticity problem encapsulates how microeconomic principles are utilized to predict responses to market changes, ensuring balanced decisions and strategies for both producers and consumers. Through a deep dive into microeconomics, learners can understand the complexities of markets and how various elements are interrelated to determine supply and demand equilibria.