The demand for good X is estimated to be Qxd = 10,000 − 4PX + 5PY + 2M + AX where PX is the price of X, PY is the price of good Y, M is income, and AX is the amount of advertising on X. Suppose the present price of good X is $50, PY = $100, M = $25,000, and AX = 1,000 units.

a) Calculate the quantity demanded of good X.
b) Calculate the own price elasticity of demand for good X. Is demand for good X elastic or inelastic?
c) If the firm selling good X wants to increase total revenue, would you recommend lowering or increasing price? Explain your answer.
d) Calculate the cross-price elasticity between goods X and Y. Are the goods X and Y substitutes or complements?
e) Calculate the income elasticity of good X. Is good X normal or an inferior good?

Explanation:

a) Calculate the quantity demanded of good X ; Plugging all the values into the equation ;

= 10,000 − 4(50) + 5(100) + 2(25,000) + 1000

Qxd = 61,300units

b) Calculate the own price elasticity of demand for good ;

= d(Qxd)/dpx X px/Qxd = -4 x 50/61,300

= 0.0033. hence he demand for goods is inelastic

c) l will surely recommend lowering the price as this is evident from the value of the price elasticity of demand which is negative as such an increase in the price of their goods will give rise to total loss

d ) cross-price elasticity between goods X and Y = %change in quantity/ %change in price

e) Calculate the income elasticity of good X. Is good X normal or an inferior good? = dQ/dM X M/Q = 2(25000) /61300

= 0.82.

Yes! Good X is a normal goods since the value of the income elasticity is positive.

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