Thread: Marginal Revenue Product

A factory owner who employs m workers find that they produce k=1.6m(1.6m+40)^3/2 units of product per day.
The total revenue R in dollars is R=489k/(310848+4k)^1/2

So when there are 20 workers, the price per unit is____ dollars

When there are 20 workers, the marginal revenue is ______ dollars/(one unit of product)

The steps that i have done so far is i took the 20 and plugged it into k=1.6(20)((1.6(20)+40))^3/2 and I got 19550.088
and the second answer i tried to solve it by placing the answer that i got from the previous questions which was 19550.088 and plugged it into R=489(19550.088)/(310848+4(19550.088)^1/2 and I got 15326.951


The answers don't seem to be correct. Could someone tell what i am doing wrong please.

You just calculated the total revenue. However, the revenue per unit which is per unit so: 15326 / 19550 = 0.07875... (this equals the price per unit since the revenue in this model must be the price)

The marginal revenue is the derivative. Derive R/k to k and plug in your value for k, then get the marginal revenue per unit (for fixed workers). I got 0.5417...