Suppose we have the following hypothetical demand function: Qx = 600 - 3px + 0.04I - 2pz Where Px = $ 70, Pz = 68, I = $ 24,000 (disposable income per capita). A. How can we Classify product X and...

Suppose we have the following hypothetical demand function:

Qx = 600 - 3px + 0.04I - 2pz

Where Px = $ 70, Pz = 68, I = $ 24,000 (disposable income per capita).

A. How can we Classify product X and Z relationship? Substitute goods, Complementary goods o Independent? Show calculations.

B. What is the reduced demand function?

C. If we increase the price 3%, what impact would have in increase in total revenues of product X?

D. Interpret in words the meaning of the coefficient of the variable I. 

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gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

Given hypothetical demand function:

Qx = 600- 3px + 0.04I -2pz

Here the cross elasticity of demand can be calculated as:

dQx/dPz = -2

since the cross elasticity of demand is negative, the demand for X increases as the price of Z decreases, which means X and Z are complementary goods.

The demand function is linear in nature and can be reduced to a form:

Px = ax+ b

Price elasticity of demand can be calculated as 

dQ/dPx = -3 

which means the quantity goes down by 3 when the price of X goes up by 1.

So, if the price of X goes up by 3% or by a factor of 0.03, the quantity (and hence the revenue of X) will come down by 9% or by a factor of 0.09.

I denote the disposable income and its coefficient is the Marginal propensity to consume, i.e. the how much demand will increase per unit increase in disposable income. 

hope this helps.

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