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Chapter 5: Problem 33

The equation for a demand curve is \(\mathrm{P}=48-3 \mathrm{Q}\) What is the elasticity in moving from a quantity of 5 to a quantity of \(6 ?\)

Short Answer

Expert verified
The price elasticity of demand in moving from a quantity of 5 to a quantity of 6 is -2.2. This indicates that the good is elastic and demand is sensitive to price changes.

Step by step solution

01

Calculate Prices at Quantities 5 and 6

Using the demand curve equation \(P=48-3Q\), we'll find the prices at quantities 5 and 6. - At Q=5: \(P = 48 - 3(5) = 33\) - At Q=6: \(P = 48 - 3(6) = 30\)
02

Determine the Percentage Change in Quantity and Price

Now we'll calculate the percentage change in quantity and price. - Percentage change in quantity: \(\frac{New \ Quantity - Old\ Quantity}{Old\ Quantity} = \frac{6-5}{5} = 0.2\) - Percentage change in price: \(\frac{New\ Price - Old\ Price}{Old\ Price} = \frac{30-33}{33} = -0.0909\)
03

Calculate the Elasticity of Demand

We'll use the percentage change in quantity and percentage change in price to find the elasticity of demand: \[E = \frac{\% \Delta Q}{\% \Delta P} = \frac{0.2}{-0.0909} = -2.2\] The price elasticity of demand in moving from a quantity of 5 to a quantity of 6 is -2.2. Since the elasticity is negative, this is a normal good, and since the absolute value is greater than 1, it is elastic, meaning the demand is sensitive to price changes.

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Most popular questions from this chapter

The federal government decides to require that automobile manufacturers install new anti-pollution equipment that costs \(\$ 2,000\) per car. Under what conditions can carmakers pass almost all of this cost along to car buyers? Under what conditions can carmakers pass very little of this cost along to car buyers?

If demand is inelastic, will shifts in supply have a larger effect on equilibrium price or on quantity?

The average annual income rises from \(\$ 25,000\) to \(\$ 38,000,\) and the quantity of bread consumed in a year by the average person falls from 30 loaves to 22 loaves. What is the income elasticity of bread consumption? Is bread a normal or an inferior good?

Under which circumstances does the tax burden fall entirely on consumers?

The equation for a supply curve is \(4 \mathrm{P}=\mathrm{Q}\). 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?
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