Question

Given the demand equation
Q = 12,000 - 10P^2.
a). For this equation, write the expression for the point price elasticity of demand as a function of P.
b). Over what range of prices is the demand inelastic ?

Answer 1

1

Answer on Question #74220 - Economics / Microeconomics

Question: Given the demand equation

$$Q = 12,000 - 10P^2$$

a). For this equation, write the expression for the point price elasticity of demand as a function of P.s

Answer:

$$Q = 12000 - 10P^2$$

First order of this equation is:

$$\frac{dQ}{dP} = -20P$$

The point price elasticity of demand can be expressed as:

$$E_P = \frac{\left(\frac{dQ}{dP}\right)}{\left(\frac{Q}{P}\right)}$$ $$E_P = \frac{(-20P)}{\left(\frac{Q}{P}\right)}$$ $$E_P = \frac{-20P^2}{Q}$$

b). Over what range of prices is the demand inelastic?

Answer:

If the price is 5 than quantity demanded will be:

$$Q = 12000 - 10(5)^2$$ $$Q = 11750 \dots \dots \dots \dots \dots \dots \dots \tag{1}$$

When, the price is 10 than quantity demanded will be:

$$Q = 12000 - 10(10)^2$$ $$Q = 11000 \dots \dots \dots \dots \dots \dots \dots \tag{1}$$

The price elasticity of demand is:

$$E_P = -10 \times \frac{5 + 10}{11750 + 11000}$$ $$E_P = -0.004 \text{ or } -0.44\% \text{ss}$$

The price elasticity is negative that means the demand inelastic in the price range of (5; 10).

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