Differential equations problem 8. Solve the following macroeconomic model. Let C(t) be the consumption, I(C) the...
8. Solve the following macroeconomic model. Let C(t) be the consumption, I(t) the investment of capital and Y(t) the national rent. C(t) = aY (t) + b C(t) + I(t)=Y(t), I(t)= kC'(t), Y(0) = Y., 0<a<1,b,k > 0 Solve for Y(t) & I(t). Calculate the long run value of y(t)/I(t)
in the macroeconomics model below matrix In the macroeconomic model below, Y is aggregate output, C is aggregate consump- tion, Io is aggregate investment, Go is government spending, T is the total amount of taxes collected by the government, and t is income tax rate. The variables Y, C, and T are en dogenous, Go, lo, and t are exogenous, and a, b, and k are parameters. Express this system of equations in a matrix form, clearly wrting out and...
7. In the following macroeconomic model, the unknowns are Y (national income) and C (consumption): Y=C+5 C=10+ 0.8Y a. Solve for Y and C.
Differential Equations Only people that are proficient in differential equations should even attempt to solve No sloppy handwriting I must be able to easily and clearly read your answer Circle final answer. Here are some EXAMPLES of what the answer should look similar to. If your answer is mildly different from these examples, then you are more than likely incorrect. Solve the given symbolic initial value problem and sketch a graph of the solution. y" + 4y = 68 -...
. Consider the following macroeconomic model Y C+ C f(Y T) T=qBY where Y is GDP, C is consumption, T' denotes taxes, and a and B are con- stants. Assume that f'€ (0,1) and 8 (0, 1). (a) From above given system of equations derive the equation Y B)Y a)I (b) Differentiate the equation in (a) implicitly w.r.t. I and find an expres- sion for dy/dI (c) Examine the sign of dy/dI and comment on your findings. (d) Give economic...
(2-2) Problem 1, 12 points Let A and consider the system of differential 1 -2 equations y' = Ay. kx a) Find the characteristic polynomial of A b) Use the Laplace transform method to compute eAt. c) Solve the system y - Ay, 0)o
6) In the macroeconomic model below, Y is aggregate output, C is aggregate consump- tion, I. is aggregate investment, Go is government spending, T is the total amount of taxes collected by the government, and t is income tax rate. The variables Y, C, and T are en- dogenous, Go, Io, and t are exogenous, and a, b, and k are parameters. Express this system of equations in a matrix form, clearly writing out and labeling each of the matrices....
A and B only Consider the Solow growth model with the following production function where y is output. K is capital, s is the productivity and is labor. Assume that 0 < α < 1 Further, suppose that labor grows at a constant rate n. That is. 1 + n. Also, assume that capital depreciates at rate d and that gross investment in capital is fraction s of output. a Letting k-N, obtain the law of motion for capital accumulation...
15.2.2 15.2.1 Consider the following macroeconomic model: Y = C+1, C = a +by (a > 0, 0<b< 1). The endogenous variables Y and C are national income and consumption respec- tively, and the exogenous variable I is investment. Find the equilibrium values of Y and C in terms of I and the parameters a, b. Find also an expression for the change in Y when I increases from Io to I1, determine its sign and comment on its magnitude....
Economic model is characterised by the following data: * Private consumption C = 800 + 0.9*DI * Gross investment Ig = 400 * Government spending G = 500 * Sum of Taxes T = 300 * Disposable income DI = Y – T Calculate: * Equilibrium level of income Y (Y= 14300) * Private consumption at macroeconomic equilibrium C = 13400 Develop equation of saving and calculate amount of saving at the point of macroeconomic equilibrium. S=. 600 Task 4....