Question

In: Economics

The demand for a good (X) is estimated to be Q x = 2,200 - 2...

The demand for a good (X) is estimated to be Q x = 2,200 - 2 Px + 4Py - .1M + .5A x , where A x represents the amount of advertising spent on X and the other variables have their usual interpretations. Suppose the price of good X is $550, good Y sells for $40, the company utilizes 3,000 units of advertising, and consumer income is $20,000.

a. Calculate the own price elasticity of demand at these values of prices, income, and advertising. Is demand elastic, inelastic, or unitary elastic?

b. Calculate the cross price elasticity of demand at these values of prices, income, and advertising. Is demand elastic, inelastic, or unitary elastic?

c. Calculate the income elasticity of demand at these values of prices, income, and advertising. Is demand elastic, inelastic, or unitary elastic?

Please show work.

Expert Solution

Q_x = 2,200 - 2 Px + 4Py - 0.1M + .5A x

Q_x = 2,200 - 2(550) + 4(40) - 0.1(20,000) + 0.5(3,000)

Q_x = 2,200 - 1,100 + 160 - 2000 + 1,500

Q_x = 760

a) Own price elasticity of demand = (∆Q_X /∆P_X) * (P_X / Q_X) [Where, (∆Q_X /∆P_X) is the price coefficient of good X in the demand function]

= -2 * (550 / 760)

= -1.45

The absolute value of Own price elasticity of demand is 1.45. Since Own price elasticity of demand is greater than 1, the demand for good X is elastic.

b) Cross price elasticity of demand = (∆Q_X /∆P_Y) * (P_Y / Q_X) [Where, (∆Q_X /∆P_Y) is the price coefficient of good Y in the demand function]

= 4 * (40 / 760)

= 0.21

Since Cross price elasticity of demand is positive, the two goods X and Y are substitutes.

c) Income elasticity of demand = (∆Q_X /∆M) * (M / Q_X) [Where, (∆Q_X /∆M) is the income coefficient in the demand function]

= -0.1 * (20,000 / 760)

= -2.63

Since Income elasticity of demand is negative, the goods X is an inferior good.

Rahul Sunny answered 2 months ago

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