In the simple model of this chapter, aggregate investment was assumed to be autonomous with respect to national income. The simple multiplier was \(1 /(1-z)\), where \(z\) was the marginal propensity to spend. And with autonomous investment, the marginal propensity to spend is simply the marginal propensity to consume.

But now suppose firms' investment is not completely autonomous. That is, suppose that \(I=\bar{I}+\beta Y\), where \(\bar{I}\) is autonomous investment and \(\beta\) is the "marginal propensity to invest" \((\beta>0)\). Explain how this modification to the simple model changes the simple multiplier, and why.