Final answer:
The equilibrium level of real GDP in a Keynesian model is where total spending equals output. The consumption function and savings can be derived using autonomous consumption, the marginal propensity to consume, and tax rates. The equilibrium can be found using the multiplier effect on autonomous spending.
Step-by-step explanation:
Finding the Equilibrium Level of Real GDP
According to the Keynesian model, in an economy without a government or foreign sector, the equilibrium level of real GDP is where the total spending (aggregate expenditure) equals the total output (real GDP). The marginal propensity to consume (MPC) and the marginal propensity to save (MPS) provide insights into how households change their consumption and savings levels in response to a change in income. The consumption function can be expressed as C = a + MPC(Yd), where 'a' is autonomous consumption and Yd is disposable income. The equilibrium occurs where the aggregate expenditure (AE) is equal to the real GDP (Y).
In the question's scenario, we have autonomous consumption, a level of investment (which is autonomous spending), and other details such as taxes, government spending, imports, and exports. To find the consumption function, we take into account the autonomous consumption and multiply the MPC by disposable income, which considers the tax rate. To calculate savings at each level of GDP, we subtract consumption from GDP. Aggregate expenditure combines consumption, investment, government spending, and net exports (exports minus imports).
To find the equilibrium level of real GDP, we use the formula: real GDP = multiplier × autonomous spending, where the multiplier is 1/(1 - MPC). The equilibrium is where AE = Y, which also can be visually represented on a Keynesian Cross Diagram.