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I am giving my first steps on microeconomics and I can't fully understand why by applying a per unit subsidy, the supply curve is shifted by a fixed amount. In wikipedia's words:

Marginal subsidies on production will shift the supply curve to the right until the vertical distance between the two supply curves is equal to the per unit subsidy

But let's say that my supply curve is given by $$ Q_s = -200 +3 \cdot P $$ If a per unit subsidy is applied, the new supply curve is now given by: $$ Q_s = -200 +3 \cdot (P+50) $$ But if the unit of the subsidy is $[\frac{\$}{units}] $ the units of the equation don't match: $$ Q_s [units] = -200[units] +3[\frac{units}{\$}] \cdot (P[\$]+50[\frac{\$}{units}]) $$ So shouldn't a per unit subsidy change the slope of the supply curve rather than shifting it?

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The confusion stems from the fact that the price is also a $\frac{\$}{units}$

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