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For Keynes the economy's interest rate is defined from the equality between money supply and demand. However, he also defines the rate of return on assets (which in equilibrium would all be equal). What is the difference between these two rates.

More clearly, one rate is derived from the equality of money supply and demand ($r^{*} | M^d=M^s$) and the other is derived from the equilibrium between the rates of return ($r_i = a_i + q_i - c_i +l_i | r_i=r_j$).

r = asset rate of return
q = asset's profit
c = cost of carrying the asset
l = liquidity premium

What is the difference between $r^{*}$ and $r_{i}$?

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Required rate of return on assets $r_i$ is the return an investor into some sort of business activity/capital investment, or various other assets, would demand in order to invest. The $i$ would denote business or activity, that is you can have required rate of return on your investment into Apple, Samsung or whatnot.

$r$ is the rate at which you can borrow and lend at a general money market. Although, note in real life money markets are organized via financial intermediaries, which due to various reasons leads interest rate at which you lend and borrow different. But in a stylized model of money market there would be just single rate $r$ at which people can lend and borrow and that’s what Keynes describes.

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  • $\begingroup$ Thank you very much. And is it possible that there is equality between them ($r^{*}=r_i$)? $\endgroup$
    – Felipe Morelli
    Commented Jan 9, 2023 at 21:16
  • $\begingroup$ @FelipeMorelli in some models that is possible $\endgroup$
    – 1muflon1 ♦
    Commented Jan 9, 2023 at 21:22
  • $\begingroup$ Another explanation I heard was the following: one of the assets in the portfolio would be government bonds ($r_{b} = a_{b} + q_{b} - c_{b} + l_{b} | b \in i $). And in this case $q_{b}$ would be equal to $r^{*} | M^{d} = M^{s}$. $\endgroup$
    – Felipe Morelli
    Commented Jan 11, 2023 at 10:17
  • $\begingroup$ @FelipeMorelli in some models people do just use bonds but I am pretty sure Keyens was not just talking about government bonds $\endgroup$
    – 1muflon1 ♦
    Commented Jan 11, 2023 at 10:28

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