Please solving these problems with process. Consider the following closed econom
ID: 2496404 • Letter: P
Question
Please solving these problems with process.
Consider the following closed economy where prices are fixed: Consumption function: C = 10 + 3/4 (Y - T) Investment function: I = 5 - r Tax and Government spending: T = G = 12 C denotes consumption, Y denotes output, I denotes investment, r denotes the real interest rate in percentage, T denotes the lump-sum tax, and G denotes the government spending. Derive an equation for the IS curve (which shows the combinations of the interest rate and output for the goods market equilibrium) for this economy. Put the output on the horizontal axis and the interest rate on the vertical axis. Suppose that the country's money demand function depends on the real interest rate only. That is, M/p = A - a middot r where A and a are constant numbers. Discuss the p shape of LM curve (which shows the combinations of the interest rate and output for the money market equilibrium) with this money demand function. Continue to assume that the country's money demand function depends on the real interest rate only as in part (b). Further suppose that the government of this economy has raised its expenditure from 12 to 15, which is financed by borrowing. Then, what is the incremental decrease increase in the output from the initial equilibrium? Also, what is the incremental decrease, increase in the real interest rate from the initial equilibrium? Provide a brief but intuitive explanation on your finding. Instead of the assumption in part (b), now suppose that the country's money demand function depends on the real income only. That is, M/p = k middot Y where k is a constant number. Discuss the shape of LM curve (which shows the combinations of the interest rate and output for the money market equilibrium) with this money demand function. Further, suppose that the government of this economy has raised its expenditure from 12 to 15, which is financed by borrowing. Then, what is the incremental decrease increase in the output from the initial equilibrium? Also, what is the incremental decrease increase in the real interest rate from the initial equilibrium? Provide a brief but intuitive explanation on your finding.Explanation / Answer
(a) In equilibrium,
Y = C + I + G
Y = 10 + 0.75(Y - T) + 5 - r + 12
Y = 17 + 0.75(Y - 12) - r
Y = 17 + 0.75Y - 9 - r
0.25Y = 8 - r
Y = 32 - 4r .....[Equation of IS]
(b) Money demand depends only on real interest rate (r). The coefficient of r in the equation is negative. Assuming a is positive, as r increases (decreases), money demand decreases (increases). Therefore the demand for money curve will be downward sloping with a vertical intercept equal to A [when r = 0].
(c) Marginal propensity to consume (MPC) = 3/4 = 0.75
Spending Multiplier = 1 / (1 - MPC) = 1 / (1 - 0.75) = 1 / 0.25 = 4
So, as government spending increases by 1 unit, output increases by 4 units.
As government spending increases by 3 units (= 15 - 12), output increases by 4 x 3 = 12 units.
From IS equation,
r = (32 - Y) / 4 = 8 - 0.25Y
As Y increases by 1, r decreases by 0.25.
As Y increases by 12, r decreases by 12 x 0.25 = 3 units.
(d) In this case, money demand curve is a straight line passing through origin (Since, when Y = 0, (M/P) = 0).
However, when government raises its expenditure, change in the output (Y) is determined by the MPC and not by shape of the money demand curve. Therefore, change in Y and r remains the same as in part (c).