A South American country exports coffee and estimates the demand function to be D (p) = 75 - 3p2. If the country wants to raise revenues to improve its balance of payments, should it raise or lower the price from the present level of $3 per pound?

Question

Bryan

Business

4 July, 08:39

A South American country exports coffee and estimates the demand function to be D (p) = 75 - 3p2. If the country wants to raise revenues to improve its balance of payments, should it raise or lower the price from the present level of $3 per pound?

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Answers (2)

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Marisa Shannon · Answer 1

The price per pound $3

The equation is D (p) = 75-3p^2 ...

D (p) = 75 - (3*3^2).

=75 - (27)

=48 ...

In law of demand, the higher the price the lower the quantity demanded and vice versa ...

So, if the price is raised, the patronage will reduce and as such might not be able to improve it's balance of payment ...

Candidly, it's adviceable to continue with the same price ...

Carley Stokes · Answer 2

South American country should lower price

Explanation:

The elasticity of demand can be computed by finding the derivative of the demand function as D (p) = 75-3*p^2

the elasticity of demand=-p*D' (p) / D (p)

D' (p) is the derivative of D (p)

elasticity of demand=-p*d/dp (75-3p^2) / (75-3p^2)

d/dp (75-3p^2) = 0 - (2*3p^2-1)

=-6p

elasticity of demand=-p*-6p/75-3p^2)

=6p^2 / (75-3p^2)

since p=$3

elasticity of demand=6 * (3^2) / (75-3 (3^2)

=6*9 / (75-3*9)

=54 / (75-27)

=1.125

Since elastic of demand is greater than 1, a reduction in price would lead more revenues as more small % change reduction in price would bring about more % increase in quantity demanded