Final answer:
The parameters t, g, m in the Keynesian cross model represent the tax rate, autonomous investment, and marginal propensity to import, respectively. The aggregate expenditure multiplier is dependent on these parameters, and in a closed economy when households increase savings (decrease b), overall saving increases leading to the 'paradox of thrift' where increased saving can result in lower economic output.
Step-by-step explanation:
The introduction of the parameters t, g, and m in the modified Keynesian cross model represent the tax rate, the autonomous portion of investment not affected by the interest rate, and the marginal propensity to import, respectively. The tax rate (t) affects disposable income and therefore consumption. The autonomous investment (g) can stimulate the economy independent of changes in the interest rate. The marginal propensity to import (m) represents the fraction of income spent on imports and is a subtraction from aggregate expenditures.
To derive the aggregate expenditure multiplier, we must first establish the aggregate expenditure function, AE = C+I+G+X-M. The multiplier depends on 1/(1 - b(1-t) + m), where b is the marginal propensity to consume, t is the tax rate, and m is the marginal propensity to import. The multiplier effect indicates how much total output would change in response to an autonomous change in aggregate expenditure.
When the economy is closed, NX = 0, and if households become more thrifty by decreasing their marginal propensity to consume (b), the equilibrium saving, S, would increase. This occurs because less of disposable income is spent on consumption which leads to higher saving. This is called the "paradox of thrift" because while saving is usually considered good for individuals, if everyone saves more, it can lead to reduced consumption and thus lower aggregate demand and output in the economy.