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Ramsey Prices Equation - Economic Maths

Hi everyone,

The following equation has tripped me up pretty badly; can't seem to get a handle on it.

I have to show that:

Unparseable latex formula:

CS_i = \frac{1}{2} \times \frac{Q_i^{2}}{s_i} \quad where \\[br][br]i \in \{H, B\} \\[br][br]using the demand functions Q_H = 1 - s_H \times P_H, \quad Q_B = 1 - s_B \times P_B \quad where \\[br][br]s_H = 1 \quad and \quad s_B = \frac{1}{2}

The result is intuitively obvious to me, as in, it's just another way of expressing that consumer surplus is half base times height, with P on the Y axis and Q on the x axis.

That said, I've failed miserably at trying to derive the CS function from the demand functions.

Any suggestions?

Reply 1

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