Derive the IS curve with the help of the Keynesian cross : Deriving the IS Curve using the Keynesian Cross: The IS curve represents the relationship between aggregate output (real income) and the equilibrium level of the goods market in an economy. The IS curve is derived by equating aggregate demand to aggregate supply.
Here’s how the IS curve is derived using the Keynesian cross:
Aggregate Demand (AD): Aggregate demand is the sum of consumption (C) and investment (I) in the economy. In the Keynesian cross model, aggregate demand is represented as: AD = C + I
Equilibrium Condition: Equilibrium in the goods market occurs when aggregate demand (AD) equals aggregate supply (Y). In other words: AD = Y
Consumption Function: Consumption is typically a function of disposable income (Y – T), where T represents taxes. In the simplest form, the consumption function is represented as: C = a + c(Y – T) where “a” represents autonomous consumption and “c” represents the marginal propensity to consume (MPC).
Equilibrium Condition (Simplified): Substituting the consumption function into the aggregate demand equation: Y = C + I Y = a + c(Y – T) + I Y = a + cY – cT + I
Solving for Equilibrium Output (IS Curve): Rearranging the equation to solve for equilibrium output (Y): Y – cY = a – cT + I Y(1 – c) = a – cT + I Y = (a – cT + I) / (1 – c)
This equation represents the IS curve, which shows the relationship between equilibrium output (Y) and taxes (T) when consumption (C) and investment (I) are considered. The position of the IS curve is affected by changes in autonomous consumption (a), the marginal propensity to consume (c), and investment (I).
Factors Affecting the Position of an IS Curve:
- Autonomous Consumption (a): An increase in autonomous consumption shifts the IS curve upward, indicating higher equilibrium output levels for any given level of taxes.
- Marginal Propensity to Consume (c): A higher marginal propensity to consume leads to a steeper IS curve, indicating that changes in taxes have a larger impact on equilibrium output.
- Investment (I): An increase in investment shifts the IS curve upward, reflecting higher equilibrium output levels at any given level of taxes.
- Fiscal Policy Changes: Changes in government spending or taxes will shift the IS curve. An increase in government spending or a decrease in taxes will shift the IS curve upward.
In precis, the IS curve is derived using the Keynesian cross version, representing the equilibrium courting among combination call for and aggregate deliver in the products marketplace.