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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?

Respuesta :

Answer:

Explanation:

  • Given the equation ; Qxd = 10,000 − 4PX + 5PY + 2M + AX
  • where PX is the price of X = $50
  • PY is the price of good Y = $100
  • M is income = $25,000
  • and AX is the amount of advertising on X = 1,000 units

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.

The answer to the given questions would be as follows:

a). Quantity Demanded [tex]= 61300 ;[/tex]

b). Price Elasticity of Demand [tex]= - 0.0033[/tex] &

c). Demand Inelastic ; Increase Price to increase TR ;

d). Cross Price Elasticity [tex]= 0.0082,[/tex]

e). Goods are Substitutes Income Elasticity [tex]= 0.816,[/tex]

f). Good is Normal

Price Elasticity

a). Quantity Demanded

[tex]'Qxd' = 10,000 − 4PX + 5PY + 2M + AX[/tex]

Putting Values of [tex]PX = 50, PY = 100, M = $25,000,[/tex]

[tex]AX = 1,000 :[/tex]

[tex]Qxd = 10000 - 4 (50) + 5 (100) + 2 (25000) + 1000[/tex]

[tex]= 10000 - 200 + 500 + 50000 + 1000[/tex]

[tex]Qxd = 61300[/tex]

b). Price Elasticity of Demand is the responsive change in demand, due to change in price, the

formula : [tex][tex]( d QX / d PX ) ( PX / QX )[/tex]d QX / d PX = - 4[/tex]

Price Elasticity of Demand [tex]= - 4 PX / QX[/tex]

Putting the value of QX &

[tex]PX , - 4 (50) / 61300 = - 0.0033[/tex]

Price Elasticity of Demand [tex]< 1[/tex] , the Demand is Inelastic

c). In case of Inelastic Demand : Price &amp;

Total Revenue are directly related, total revenue can be increased with an increase in price and vice versa.

So, the firm should increase price to increase total revenue.

d). Cross Price Elasticity of Demand shows a responsive change in demand, due to change in related goods' price,

formula :

[tex][tex]( d QX / d PY ) ( PY / QX ) \\[/tex]d QX / d PY[/tex]

[tex]= 5Cross Price Elasticity[/tex]

[tex]= 5 (100) / 61300[/tex]

[tex]= 0.0082[/tex] Cross Price Elasticity is positive.

So, good Y price and good X demand are directly related, hence they are Substitutes.

e). Income Elasticity of Demand shows responsive change in demand, due to change in Income,

formula :

[tex][tex]( d QX / d M ) ( M / QX )[/tex]d QX / d M = 2[/tex]

Income Elasticity of Demand [tex]= 2 (25000) / 61300[/tex]

[tex]= 50000 / 61300[/tex]

[tex]= 0.816[/tex]

Thus, Income Elasticity of Demand is is positive.

So, income and good demand are directly related, hence good is Normal.

To learn more, refer "Demand" here:

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