The Question

Suppose a firm has a production function given by


where L and K denote inputs used in the production of y units of output.

(a) Determine whether marginal products are diminishing

(b) Show that production technology exhibits decreasing returns to scale

My attempt

(a) So the marginal products, $MP_L$ , $MP_K$ are:



To determine if the marginal products are diminishing one needs to simply derive the equations again. Which would be:




When both Marginal products are derived, their results are both are $<0$ which would imply that they are diminishing.

(b) This is where I get a little confused, is it not because we know that the Marginal products are diminishing, we know that the production technology exhibits decreasing returns to scale?

  • $\begingroup$ Marginal product is about how output changes when only one input changes. Returns to scale is about how output changes when all inputs change in same proportion. $\endgroup$ – Paul Oct 30 '16 at 20:29

They are two different concepts I think.

Diminishing product means that holding other things fixed, one unit of extra input($K$ or $L$ here) yields less and less additional output, which you have known.

Meanwhile DRS is saying that if you multiply both $K$ and $L$ by some scalar $ t > 1$, the corresponding output would be less than $t$ times the original output.

| improve this answer | |
  • $\begingroup$ so then I simply assign any +ive value $\forall{L,K}$ and it would demonstrate such? $\endgroup$ – FreakconFrank Oct 30 '16 at 20:33
  • 1
    $\begingroup$ @PloniAlmoni $\forall t>1$, $F(tK, tL) = (tK)^{1/4}(tL)^{1/4} = t^{1/4+1/4}F(K, L)$. So you can see it does exhibit DRS here. In fact, in this form of production function you can easily see that $L^\alpha K^\beta$ will be DRS whenever $\alpha+\beta<1$. $\endgroup$ – Eric Chen Oct 30 '16 at 20:40

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.