Bill Gates Wants to Introduce a Wedge Between the Marginal Product of Labor and the Marginal Product of Capital

Intermediate micro students have fallen in love with the following algebra;  MK_k/r = MP_l/w   .  In English, the cost minimizing firm should purchase robots until the extra output it produces per dollar spent on robots equals the extra output it produces per dollar spent on labor.

Bill Gates wants to introduce a tax on robots.    Suppose this raises the price of a robot to r+tax.   The cost minimizing firm will substitute to labor and the new optimality condition will be:

MK_k/(r+tax)  = MP_l/w

How costly will this wedge be for the macro-economy?   Will a future Hsieh and Klenow dare to battle Bill Gates?  Is there an equity vs. efficiency tradeoff?

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