The demand for good X is given by the following equation: Q X = 10 P X -2.4 P Y

Question

The demand for good X is given by the following equation:

                                                QX = 10 PX-2.4 PY I1.2 AX0.001 AY-0.003

where PX and PY, and PZ are the prices of X and Y, I is per capita income, AX is advertising on good X, and AY is advertising on good Y.

(a) Should the price of X be increased or decreased if the firm is interested in maximizing revenue?

(b) Are goods X and Y gross substitutes or complements?

(c) By how much must the price of X change if per capita income decreases by 4% and the goal is to keep QX constant?

(d) Calculate the elasticity of demand for good X with respect to advertising on good X. Interpret your answer. Can you tell whether the firm is spending too much or too little on advertising?

(e) If the manufacturer of good Y stops advertising completely, what would be the impact on demand for good X according to this demand equation?

Explanation / Answer

QX = 10 PX-2.4 PY I1.2 AX0.001 AY-0.003

ans a) price elasticity of X, Ex = - (dQx/dPx)*(Px/Qx)

                                              = 24 Px-3.4 PY I1.2 AX0.001 AY-0.003 *(Px/10 PX-2.4 PY I1.2 AX0.001 AY-0.003 )

                                              =24/10 = 2.4      ( absolute terms) or - 2.4 ( negatrive relation)

so elasticity is greater than 1 , so demand is highly elastic, so price needs to be decreased in order to increase revenue and maximize revenue

b) as given consumption function is cobb douglas consumption function. therefore , powers are aech independent variable is nothing but elascticity

elaticity of X w.r.t Y is 1

so elasticity is positive . this means X and Y are substitute goods

c) when income decrease by 4% , than quantity demanded will decrease by

Ei = % change in demand/% change in income =

1.2      = % change in demand/- 4%

% change in demand =- 4.8% ( decrease)

so in order to keep demand constant , we need to decrease -price, by how much , we'll find out using price elasticity

Ex=   - % decrease in demand/ % increase in price

2.4 = 4.8/ % increase in price

% increase in price required =11.52%

d) the elasticity of demand for good X with respect to advertising on good X= 0.001

this 1% change in adevertising expenditure on X will increase demand by 0.001. so effect is very low . this may be due to as firm is spending very less on advertising,

e) ealsticity of demand of X w.r.t advertising on Y is low and negative, but If the manufacturer of good Y stops advertising completely,than demand for X will increase

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.