Find the marginal cost of producing the 185th unit of output in the attached table. Show all steps used.

To find the marginal cost of producing the 185th unit of output in this scenario, the first thing we have to do is see how much the output changed when the fourth unit of labor was added.  When there were only three units of labor being used, the workers produced 155 units of output.  When the fourth unit of labor was added, the output rose to 185 units.  When we subtract 155 from 185, the difference is 30.  That means that the fourth unit of labor added 30 units of output.

Next, we need to think about cost.  We know from the question that each unit of labor costs $500.  That means that our costs went up by $500 when we added the fourth unit of labor.  (We have to assume here that there are no costs other than the cost of labor.  We do not have any information about the cost of any materials that are being used, so we must say that labor is the only cost.)  This is the marginal cost for the last 30 units of output because we are looking for how much the cost of production changed when we produced those last 30 units.

Now we have to find the marginal cost of the 185th unit of output.  Each of the units between 155 and 185 has the same marginal cost.  Their marginal cost is the cost of the last unit of labor divided by the number of units of output that that unit of labor produced.  Therefore, all we have to do is to divide $500 (our costs) by 30 units of output.  This gives us our marginal cost per unit.  500/30 = 16.67, making $16.67 the marginal cost of the 185th unit of output.

So, our steps are 1) find the marginal output of the 4th unit of labor; 2) find the cost of the 4th unit of labor; 3) divide the marginal output by the cost of the 4th unit.