§4. Individual Adjustment with Loans

Up to this point in the second approximation we have reasoned as though the Individual did not have freedom Edition: current; Page: [270] to borrow or lend in the loan market. We purposely excluded that possibility for the moment and went ahead as if the man were shut off from the loan market completely, so that any investment must be out of his own income and not be made with borrowed money. Were this the case (as in practice it often is) Chart 37 would correctly represent the result of the individual's shift. It would be a one-way shift, entirely along the Opportunity line.

But if now we return to the hypothesis of a perfect loan market, accessible to all concerned and to any extent desired, then Chart 37 does not fully picture our problem because it fails to take account of the fact that the individual not only can shift along the Opportunity line, but can also shift along a Market line by borrowing and lending. That is, he now has two "can" lines, both the Market line of Chapter X and the Opportunity line of this chapter.

Chart 38 pictures the double movement of Individual 1. Starting at O1', he moves along the Opportunity line to P1 where the Opportunity line becomes tangent to the M line, then along the M line to Q1 where the M line becomes tangent to a W1 line. That is, the fixed rate of interest will cause the individual so to shift that the marginal rate of return over cost (investment opportunity rate and the marginal rate of time preference (degree of impatience) will, each of them, be equal to the market rate of interest. Chart 38 depicts Individual 1's adjustment of his rate of investment opportunity and his degree of impatience to the market rate of interest. The rate of interest is, as always, represented in the slope of the M line, and the rate of return over cost is represented in the slope at P1 of the O1 line. Edition: current; Page: [271] These two slopes are the same, since the two lines are there tangent.

The slopes of the M line and the O1 line at P1 are identical since the two lines are tangent at that point. The degree of impatience is represented by the identical slopes of the M line and of the W1 line at their point of tangency Q1. Since the M line is a straight line, the slopes of the O1 line and the M line at P1 and the slopes of the M line and the W1 line at Q1 are all identical and the identity of the opportunity rate, the impatience rate, and the market rate is shown.

Edition: current; Page: [272]