Final answer:
In this closed economy, the aggregate expenditure (AE) is $20, with consumption (C) at $10 and investment (I) at $10.
Step-by-step explanation:
In this closed economy of Strangetopia without trade, the government does not spend money or tax households or firms. Households save everything they earn, with autonomous consumption set at $10 and autonomous investment by firms also set at $10. The real interest rate is 100% and consumer responsiveness to the real interest rate is 0.5.
To find the aggregate expenditure (AE) in this economy, we need to sum up consumption (C) and investment (I). The consumption function can be calculated by multiplying the marginal propensity to consume (1 - the marginal propensity to save) by disposable income. Since households save everything, the marginal propensity to save is 1, meaning the marginal propensity to consume is 0. In this case, the consumption function is $10, and autonomous investment is $10. Therefore, AE = C + I = $10 + $10 = $20.