Question

Suppose demand for good A is given by DA = 500 - 10 Pa + 2 Pb + 0.70I where Pa is the
price of good A, Pb is the price of some other good B, and I is income. Assume that Pa is
currently $10, Pb is currently $5, and I is currently $100.
a. What is the elasticity of demand for good A with respect to the price of good A at the
current situation? Interpret the nature of elasticity of demand.

Answer 1

1

ANSWER ON QUESTION #74466, ECONOMICS / MICROECONOMICS

Q. Suppose demand for good A is given by $\mathrm{D_A} = 500 - 10\mathrm{P_a} + 2\mathrm{P_b} + 0.70\mathrm{I}$ where $\mathrm{P_a}$ is the price of good A, $\mathrm{P_b}$ is the price of some other good B, and I is income. Assume that $\mathrm{P_a}$ is currently $10, \mathrm{P_b}$ is currently $5, and I is currently $100.

a. What is the elasticity of demand for good A with respect to the price of good A at the current situation? Interpret the nature of elasticity of demand.

Answer:

$$\mathrm {D} _ {\mathrm {A}} = 5 0 0 - 1 0 \mathrm {P} _ {\mathrm {a}} + 2 \mathrm {P} _ {\mathrm {b}} + 0. 7 0 \mathrm {I}$$ $$\mathrm {P} _ {\mathrm {a}} = \$ 1 0$$ $$\mathrm {P} _ {\mathrm {b}} = \$ 5$$ $$\mathrm {I} = \$ 1 0 0$$

Put these values in above demand function:

$$\mathrm {D} _ {\mathrm {A}} = 5 0 0 - (1 0 * 1 0) + (2 * 5) + (0. 7 0 * 1 0 0)$$ $$\mathrm {D} _ {\mathrm {A}} = 4 8 0 \Rightarrow \mathrm {Q} _ {0}$$

If the price of good A is increased to $15 then its quantity demanded will be:

$$\mathrm {D} _ {\mathrm {A} 1} = 5 0 0 - (1 0 * 1 5) + (2 * 5) + (0. 7 0 * 1 0 0)$$ $$\mathrm {D} _ {\mathrm {A} 1} = 4 3 0 \Rightarrow \mathrm {Q} _ {1}$$

Then, the elasticity of demand for good A with respect to the price of good A is:

$$E _ {d} = \frac {\left[ \frac {Q _ {1} - Q _ {0}}{\left(\frac {Q _ {1} + Q _ {0}}{2}\right)} \right]}{\left[ \frac {P _ {1} - P _ {0}}{\left(\frac {P _ {1} + P _ {0}}{2}\right)} \right]}$$

2

$$E _ {d} = \frac {\left[ \frac {430 - 480}{\left(\frac {430 + 480}{2}\right)} \right]}{\left[ \frac {15 - 10}{\left(\frac {15 + 10}{2}\right)} \right]}$$ $$E _ {d} = -0.27$$

The price elasticity of demand is negative. It means the elasticity of demand for good A with respect its price is inelastic.

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