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Apologies in advance, I haven't been able to find the terminology/vocabulary to describe what may very well be a basic issue.

I am exploring differences between energy purchase tariffs. The first tariff (Z) is a flat rate. On the second tariff, part of the time is at one rate (X) and part of the time is at another rate (Y). I am hoping to understand what percentage of my usage would need to be at rate X and rate Y in order to breakeven, almost like I had been at rate Z.

For example:

X = 12.00
Y = 44.35
Z = 35.06

I am reverse engineering this answer, so, apparently, if I use 29% of my energy (1kWh) at tariff X (3.45p) and 71% of my energy (1kWh) at tariff Y (31.61p) this is the equivalent to using all my energy at 35.06p/kWh. How can we calculate the percentages to facilitate this proportioning?

Thank you!

danwri
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1 Answers1

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Let $p$ denote the fraction of time you pay rate $X$. Then, $(1-p)$ is the fraction of time you pay rate $Y$. Hence, the average cost of using the second tariff is $$ pX + (1-p)Y. $$ Hence, the breakeven point is the solution of $p$ to $$ pX + (1-p)Y = Z, $$ which evaluates to $$ p = \frac{Y-Z}{Y-X}.$$ For your values of $X,Y,Z$, this gives $p \approx 0.287$, which corresponds to $28.7\%$.

Andreas Lenz
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