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9. (Bonus 10 points) We introduce two equations in the class: (1) Productivity Outputs Inputs Productivity growth current productivity - previous productivity (2) previous productivity Please prove the following formula using the above two equations: If inputs increase by X% and outputs increase by Y%, then 1+ Y% Productivity growth -1 (3) 1+X% Note: you should prove that this formula is correct for any inputs and outputs instead of special inputs and outputs. Hints: You can use "O" to represent previous outputs and "I" to represent previous inputs. Then previous productivity=0/1 Next, you can find out the current outputs and the current inputs, and then derive the equation for current productivity. Last, you can plug in the equations for previous productivity and for current productivity to (2) to derive (3)