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I do understand that he argues that in order to draw the loanable funds supply curve, you have to already know the volume of income, i.e. production, and therefore the interest rate in advance. But why couldn't you just test for coherence in the following way? Assume a level of income. Draw the corresponding loanable funds supply curve. Calculate the interest rate at the intersection of the supply and the demand curve, i.e. the interest rate for which the capital market clears. Determine if the income level corresponding to this interest rate is indeed the income level we assumed in the first place. If it is, this interest rate is an/the equilibrium rate, if it's not, it's not. Is there anything wrong with this argument?

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You can use some some initial $Y_0$ to find an interest rate, but this is precisely the indeterminacy problem. We would like to be able to derive the equilibrium interest rate without assuming some initial values.

Furthermore, note the indeterminacy problem is actually present even in canonical Keynesian models (See Hansen, 1951) and Neo-Keynesian models (see Beyer & Farmer 2004).

However, the Keynes critique is now a bit outdated. Keynes was writing in a past before macroeconomic was even given proper formal treatment (by modern standards), and at a time when macro had no micro-foundationds. Nowadays you can solve the indeterminancy problem in macroeconomic model of either variety by assuming central bank follows some interest rate setting rule, such as Taylor rule or making some specific assumptions about model's micro-fundamentals (see Romer's Advanced Macroeconomcis for discussion of this). Although as the Beyer & Farmer point out in their paper even central bank interest setting rules won't solve this issue always so the problem is somewhat open.

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  • $\begingroup$ i'm asking myself, however, if one couldn't just assume some Y0, calculate the equilibrium interest rate, and then calculate the Y corresponding to this interest rate. If Y0 doesn't equal Y, we have ruled out this interest rate as a possible equilibrium rate, because it would result in a level of production that wouldn't result in this interest rate. $\endgroup$ Oct 3 '20 at 15:26
  • $\begingroup$ @JuliusHimmel no. Of course, once you have some $Y_0$ and calculate $i$ and then using this $i$ you calculate back Y, $Y=Y_0$. For example, if we have x-y=2 then once you choose x=2 y will be 0 and then if you ‘forget’ x and just plug 0 you found previously of course you find that x=2, but that does not help even a bit because you are still using initial values that have to be assumed to find equilibrium. We want to avoid using $Y_0$ at all. In fact the ‘solved’ $i$ in way you propose would be no different just from assuming some $i_0$ from the outset. $\endgroup$
    – 1muflon1
    Oct 3 '20 at 15:40
  • $\begingroup$ i'm not proposing to find the level of income for which the corresponding loanable funds supply curve intersects the demand curve at the previously chosen interest rate. that would be circular of course. i'm proposing to find the level of production RESULTING from the chosen interest rate. Just as the IS-model, at a given level of government spending and a given propensity to consume, is production as a function of the interest rate. $\endgroup$ Oct 3 '20 at 16:10
  • $\begingroup$ @JuliusHimmel but in these macroeconomic models almost everything is endogenous. Finding a level of production based on some $i_0$ will introduce exactly the same circularity as above. In fact this indeterminacy problem will appear in IS-LM model without Taylor rule or some specific micro assumptions. $\endgroup$
    – 1muflon1
    Oct 3 '20 at 16:14
  • $\begingroup$ your point being that it's impossible to represent production as a function of the interest rate because in order to calculate the level of investment, one needs to know the volume of the loanable funds supply and therefore income in advance? $\endgroup$ Oct 3 '20 at 16:21

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