Chapter 5: Problem 35

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

Expert verified

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.

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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

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#

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