Matty Kahn teraches college I hear

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?

---------------

OK, start with this:

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.

The instantaneous cost comparison is transaction costs compared per action, yhere is no time in his problem.  So the robot performs an action, some part of the robot wears and costs dough, and the human costs labor per hour.  Professor is stuck, he has to have a time to completion, and that is really uncertain, if not unmeasurable.

Where can he professor get a time standard?

Measure time to completion from the industry statistics, and that is what the professor implies. Those prices all come from somewhere, and something is taking statistics of events and indexing them with a lock.

Change the problem a bit, and skip the fake vatriable.  Look at the past of the industry, take the probability distribution of robot purchases and human hires; match what typical result to your distribution of sales events.  Then work the distribution convolutions directly, skip time.

And, by the way, the answer to the question?

Microsoft, and Bill Gates,  owe the US and state government some 40 billion dollars in lost taxes for secretaries and accountants who lost their jobs, according to Bill's logic