I know that the total cost function of a firm in the short run is:

TC = wL + rK,

where rK is essentially a constant. I understand the variables w, L and K, but I still don't get what r is. I mean, what do I input as "r" when I'm trying to draw up a total cost function?

Thank you.

  • $\begingroup$ If w is the wage that you pay per unit of labour hired, then what would r be for capital? $\endgroup$ – Maarten Punt Feb 12 at 8:07
  • $\begingroup$ I mean to say, is it rent? Or like if I purchase the capital good is it just the price? $\endgroup$ – Saad Feb 12 at 8:21
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    $\begingroup$ Are you purchasing the worker (slavery) or are you renting his labor? The cost function is for a given time period, so you are doing the same with the capital good. $\endgroup$ – Giskard Feb 12 at 8:56
  • $\begingroup$ Thank you, but is it possible for you to give me an example to make it slightly easier for me to understand? $\endgroup$ – Saad Feb 12 at 9:13

The $r$ in the total cost function is the interest rate, which at the same time constitutes the price of capital. You can think of it as an explicit cost, e.g. if you rent the capital or pay interest to the bank, or as an implicit (opportunity) cost, e.g. if you own the capital and by using it yourself you give up the opportunity to rent it out.

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  • $\begingroup$ Thank you, that does make sense. But how do I go about calculating this for one unit of capital that I purchase? Is it just the amount I pay for it? $\endgroup$ – Saad Feb 12 at 15:55
  • $\begingroup$ Also, is this the same value that is calculated by the equation for rental price of capital? $\endgroup$ – Saad Feb 12 at 16:36
  • $\begingroup$ The language is a bit confusing. The $r$ is often just called the "price of capital", as I also did in my answer, whereas what is meant is not a payment for purchasing one unit of the capital, but for renting one unit of capital for one unit of time. So yes, it's the "rental price of capital". $\endgroup$ – VARulle Feb 13 at 8:15

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