Marginal Product Help Please?

Question

Brother Jed takes heathens and reforms them into righteous individuals. There are two inputs needed in this process: heathens (who are widely available) and preaching. The production function has the following form: rp=min{h,p}, where rp is the number of righteous persons produced, h is the number of heathens who attend Jed’s sermons, and p is the number of hours of preaching. For every person

converted, Jed receives a payment of s from the grateful convert. Sad to say, heathens do not flock to Jed’s sermons of their own accord. Jed must offer heathens a payment of w to attract them to his sermons. Suppose the amount of preaching is fixed at p*, and that Jed is a profit-maximizing prophet.

a. if h<p*, what is the marginal product of heathens? What is the value of the marginal product (marginal revenue) of an additional heathen?

b. If h>p*, what is the marginal product of heathens? What is the value of the marginal product of an additional heathen in this case?

Please Help!

Answer 1

a. MP=1, because up until the point where the number of heretics equals the amount of preaching, each heretic will produce another righteous person.  Marginal revenue is s-w.  Each righteous person gives him s, but he must pay w to make the heathens come.

b. Here the MP is zero, because the amount of preaching is lower than the number of heathens.  The MR is -w, because he won&#039;t get any more s, but he will still have to pay w.

Answer 2

a. if h&lt;p*, what is the marginal product of heathens? What is the value of the marginal product (marginal revenue) of an additional heathen?

Well, if h is less than p*, then adding an additional h will increase the number of righteous persons by 1, given rp = min{h,p}.

So the marginal product of an additional heathen is one righteous person.

The value of one righteous person in terms of revenue is s.  So the marginal revenue from an additional heathen is s.

b. If h&gt;p*, what is the marginal product of heathens? What is the value of the marginal product of an additional heathen in this case?

Well, if h is greater than p*, then adding an additional h will have no effect on productivity, given rp = min{h,p}.

So the marginal product of an additional heathen is 0.

Since the marginal product is 0, marginal revenue is also 0.

EDIT:  Hey, Danajaan.

Yeah, in each case we do have to pay w for the extra heathen, but that has to do with marginal cost, not marginal revenue.  You&#039;re confusing revenue with profit, which is revenue minus cost.