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Your calculations have included the GST on the Origin fee ($1100) but not the total invoice ($5000) If you paid the Origin invoice, the electrician's bill would have been (5000 - 1000) + GST. Which equals $4400. Plus the Origin fee out of your pocket ($1100) is $5500 all up. You haven't...

No. Assuming there was no markup on the Origin fee, the electrician fee to you would have been $4000 + GST, and the Origin fee is $1000 + GST. Or $5500 all up.