Consider the following behavioural equations that describe the goods market in a closed economy: = 0 + 1 = = where is consumption, disposable income, income and taxes. The remaining exogenously given parameters are: 0 > 0 is the autonomous part of consumption, 0 < 1 < 1 defines the marginal propensity to consume, and 0 < < 1 is the tax rate, assuming that taxes are a constant fraction of income. Also assume that government spending, , and investment, , are both exogenous

1. What can cause a decrease in the autonomous part of investment? Compute the necessary change in government spending in order for output to remain constant.
2. Can governments really achieve the level of output they want? Discuss possible limitations.