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Chapter 5: Problem 5

Suppose the quantity of steak purchased by the Jones family is 110 pounds per year when the price is \(\$ 2.10\) per pound and 90 pounds per year when the price is \(\$ 3.90\) per pound. The price elasticity of demand coefficient for this family is a. 0.33 b. 0.50 c. 1.00 d. 2.00

Short Answer

Expert verified
The price elasticity of demand coefficient for the Jones family's steak purchases is approximately 0.33 (answer choice 'a').

Step by step solution

01

Calculate the percentage change in the quantity of steak purchased

To calculate the percentage change in the quantity of steak purchased, we need to find the difference between the two quantities given and divide it by the average quantity of steak purchased. Percentage Change in Quantity = \(\frac{Q2-Q1}{(Q1+Q2)/2} × 100\) where Q1 is the initial quantity of steak purchased and Q2 is the final quantity of steak purchased. Q1 = 110 pounds per year Q2 = 90 pounds per year Percentage Change in Quantity = \(\frac{90-110}{(90+110)/2} × 100 = -20.0\%\) (Since the quantity demanded decreases, it's negative)
02

Calculate the percentage change in the price of steak

To calculate the percentage change in the price of steak, we need to find the difference between the two prices given and divide it by the average price of steak. Percentage Change in Price = \(\frac{P2-P1}{(P1+P2)/2} × 100\) where P1 is the initial price and P2 is the final price. P1 = $2.10 per pound P2 = $3.90 per pound Percentage Change in Price = \(\frac{3.90 - 2.10}{(2.10 + 3.90)/2} × 100 = 72.73\% \) (Since the price increased, it's positive)
03

Calculate the Price Elasticity of Demand (PED)

Now, we need to divide the percentage change in quantity by the percentage change in price to find the PED. PED = \(\frac{Percentage Change in Quantity}{Percentage Change in Price} = \frac{-20.0\%}{72.73\%} = -0.275\) Since the PED is negative, we can take the absolute value of it to compare our results to the given answer choices: Absolute Value of PED = \(| -0.275 | = 0.275\)
04

Find the correct answer choice

Now let's compare our calculated PED value to the given answer choices: a. 0.33 b. 0.50 c. 1.00 d. 2.00 Our calculated PED value (0.275) is closest to the answer choice (a) 0.33. So, The price elasticity of demand coefficient for this family is approximately **0.33** (answer choice 'a').

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Most popular questions from this chapter

If the government wanted to raise tax revenue and shift most of the tax burden to the sellers, it would impose a tax on a good with a a. steep (inelastic) demand curve and a steep (inelastic) supply curve. b. steep (inelastic) demand curve and a flat (elastic) supply curve. c. flat (perfectly elastic) demand curve and a steep (inelastic) supply curve. d. flat (perfectly elastic) demand curve and a flat (elastic) supply curve.

If a 5 percent reduction in the price of a good produces a 3 percent increase in the quantity demanded, the price elasticity of demand over this range of the demand curve is a. elastic. b. perfectly elastic. c. unitary elastic. d. inelastic. e. perfectly inelastic.

To determine whether two goods are substitutes or complements, an economist would estimate the a. price elasticity of demand. b. income elasticity of demand. c. cross-elasticity of demand. d. price elasticity of supply.

The price elasticity of demand coefficient for a good will be lower a. if there are few or no substitutes available. b. if a small portion of the budget will be spent on the good. c. in the short run than in the long run. d. if all of the above are true.

If an increase in bus fares in Charlotte, North Carolina, reduces the total revenue of the public transit system, this is evidence that demand is a. price elastic. b. price inelastic. c. unitary elastic. d. perfectly elastic.
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