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What are the various kinds of demand elasticity?

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  • Hello, I'm struggling with this. Please help! Keesha's monthly demand for hot dogs depends on the price of hot dogs (Ph) and her income (I), both measured in dollars, as follows: Qh= (I)/(10*Ph) Keesha's income is $2,000 a month and the price of hot dogs is $5. I need to find the (Price) elasticity of demand and tell whether her demand is elastic, inelastic, or unit elastic. I also need to find her (Price) elasticity of demand using the arc elasticity when Price changes from $5 to $6. Then finally, I need to solve her income elasticity of demand for hot dogs and decide if the hot dogs are a normal or inferior goods. I know this is a lot! I'd appreciate any help at all! Thanks!

  • Answer:

    Price elasticity of demand when price of hot dogs goes up from $5 to $6. First find out how the quantity of hot dogs demanded is at both $5 and $6. At $5: Qh = 2,000/(10*5) = 2,000/50 = 40 At $6: Qh = 2,000/(10*6) = 2,000/60 = 33 (approx.) Then use the formula: Price Elasticity = % change in Qh demanded/ % change in Ph Find % change by taking (new quantity/price - old) / (total {new + old} / 2) % change in Qh = (33 - 40) / [(33 + 40) / 2] = -.192 (approx.) % change in Ph = (6 - 5) / [(6 + 5) / 2] = .182 (approx.) Price Elasticity = -.192 / .182 = 1.05 (approx.) For the second question on arc elasticity, I'm sorry, I don't know how to find that. Formula to find Income Elasticity is the same as the one above except that instead of price, replace with income. Formula: % change in Qh demanded / % change in I % change in I = (new income - old) / (total {new + old} / 2) note: In this I am quite sure that you can actually pick a new income for Keesha since you were not provided with one. I'm going to choose her new income as $3,000. % change in I = (3,000 - 2,000) / {(3,000 + 2,000) / 2} = .40 Since the income changed we also need a new Qh at I = $3,000 and to use this to find the % change in Qh demanded Qh = 3,000/(10*5) = 3,00 /50 = 60 % change in Qh demanded = (60 - 40) / {(60 + 40) / 2} = .40 Elasticity of Income = .40 / .40 = +1 The positive sign indicates that hot dogs is a normal good. As income increases so does the demand for more hot dogs.

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Price elasticity of demand when price of hot dogs goes up from $5 to $6. First find out how the quantity of hot dogs demanded is at both $5 and $6. At $5: Qh = 2,000/(10*5) = 2,000/50 = 40 At $6: Qh = 2,000/(10*6) = 2,000/60 = 33 (approx.) Then use the formula: Price Elasticity = % change in Qh demanded/ % change in Ph Find % change by taking (new quantity/price - old) / (total {new + old} / 2) % change in Qh = (33 - 40) / [(33 + 40) / 2] = -.192 (approx.) % change in Ph = (6 - 5) / [(6 + 5) / 2] = .182 (approx.) Price Elasticity = -.192 / .182 = 1.05 (approx.) For the second question on arc elasticity, I'm sorry, I don't know how to find that. Formula to find Income Elasticity is the same as the one above except that instead of price, replace with income. Formula: % change in Qh demanded / % change in I % change in I = (new income - old) / (total {new + old} / 2) note: In this I am quite sure that you can actually pick a new income for Keesha since you were not provided with one. I'm going to choose her new income as $3,000. % change in I = (3,000 - 2,000) / {(3,000 + 2,000) / 2} = .40 Since the income changed we also need a new Qh at I = $3,000 and to use this to find the % change in Qh demanded Qh = 3,000/(10*5) = 3,00 /50 = 60 % change in Qh demanded = (60 - 40) / {(60 + 40) / 2} = .40 Elasticity of Income = .40 / .40 = +1 The positive sign indicates that hot dogs is a normal good. As income increases so does the demand for more hot dogs.

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