Question

For each demand function, find an expression for the price elasticity of demand. 1. D(p)=60−p 2. D(p)=40p −2

3. D(p)=(p+2) −1

Answer 1

Price elasticity of demand is a measure of how responsive demand is to changes in price. To find the expressions for the price elasticity of demand for each function, you can use the formula and differentiate the demand function with respect to price.

Step-by-step explanation:

Price elasticity of demand is a measure of the responsiveness of demand to changes in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

For the demand functions given:

1. D(p) = 60 - p
2. Price elasticity of demand can be calculated by differentiating the demand function with respect to price, and multiplying by the ratio of price to quantity demanded:
3. 
   
4. 
   
5. E(p) = (p / D(p)) * (dD(p) / dp)
6. D(p) = 40p - 2
7. Price elasticity of demand can be calculated similarly:
8. 
   
9. 
   
10. E(p) = (p / D(p)) * (dD(p) / dp)
11. D(p) = (p + 2)^(-1)
12. Again, the price elasticity of demand can be calculated using the same formula:
13. 
    
14. 
    
15. E(p) = (p / D(p)) * (dD(p) / dp)