Answer to Question #158490 in Microeconomics for nfraser

Question

1.      Study the following table carefully

income Price of X Quantity of X Price of Z Quantity of Z

40000 300 200 200 250

70000 500 90 600 100

         

Calculate the following:

(a)   Income elasticity of demand for good X

(b)  Cross elasticity of demand of good Z when the price of good X changes

(c)c Price elasticity of demand for good Z

Answer 1

a) Let's calculate income elasticity of demand for good X:

$$E_y=\dfrac{\%\ change\ in\ quantity\ demanded}{\%\ change\ in\ income},$$ $$E_y=\dfrac{\dfrac{Q_2-Q_1}{Q_1}}{\dfrac{Y_2-Y_1}{Y_1}}=\dfrac{\dfrac{90-200}{200}}{\dfrac{70000-40000}{40000}}=-0.73$$

b) Let's calculate cross elasticity of demand of good Z when the price of good X changes:

$$E_{zx}=\dfrac{\dfrac{\Delta Q_z}{Q_z}}{\dfrac{\Delta P_x}{P_x}}=\dfrac{\dfrac{100-250}{250}}{\dfrac{500-300}{300}}=-0.9$$

c) Let's calculate price elasticity of demand for good Z:

$$E_p=\dfrac{\dfrac{\Delta Q}{Q_1}}{\dfrac{\Delta P}{P_1}}=\dfrac{\dfrac{100-250}{250}}{\dfrac{600-200}{200}}=-0.3$$