Question

1a. Derive government spending and tax multiplier in the Keynesian-cross model using calculus

1b. Consider the model of Keynesian cross with fixed planned investment expenditure, government spending and taxes. Assume that consumption function is given by C=a+mpc*(Y-T), where the parameter a >0 is called autonomous consumption, and the marginal propensity to consume satisfies 0< mpc <1. Compute equilibrium output (income) as a function of parameters (a and mpc) and exogenous variables. How does equilibrium output depend on a? mpc? Government spending? Taxes?

1c. Suppose that the real interest rate is 2% and expected inflation rate is 4%. What does Fisher equation predict nominal interest rate t

Answer 1

Q. 1a

Q1b

In the Keynesian Cross Model, the equilibrium is at E*, where Y*= AD (aggregate demand). The 45degree line is the aggregate supply of the economy.

We know that Y = AD + change in inventory

To the left of Y* at Y1, AD> Y and therefore change in inventory < 0, this excess demand in the market causes un intended inventory de accumulation and the producers increase their outpit level so that Y1 moves towards Y*.

To the right of Y* at Y2, AD< Y and thus change in inventory > 0. This causes unintended inventory accumulation. Hence the producers cut down their output level from Y2 to Y*. Thus we can say the economy converges to Y* from either sides.Hence the equilibrium E* is a stable equilibrium.

Since, the Government expenditure is exogenously determined hence it is denoted by a parallel shift of the (C + I ) curve in the diagram.

'a' denotes the autonomous consumption of an economy which is denoted by the intercept in the above figure. A change in the intercept alters the equilibrium output.

An increase in taxes would lead to a fall in consumption expenditure and thus reduction of equilibrium output and vice versa.

mpc determines the slope of the Consumption curve, a change in slope changes the equilibrium output.

Q1c

given

real interest rate (r) = 2%
expected inflation π = 4%

According to Fisher's equation

nominal interest rate i = r + π = 2 + 4 = 6%