Economics Dynamics Problems 139

# Economics Dynamics Problems 139 - G for all t E t = C t I t...

This preview shows page 1. Sign up to view the full content.

Discrete dynamic systems 123 is highly probable. Even with ak < 1, two possibilities arise: (i) if a < 0 then ak < 2 (ii) if 0 < a < 1 then 0 < ak < 2 with various paths for y t . This should not be surprising because we have already established that the discrete logistic equation has a variety of paths and possible cycles. 3.10 The multiplier–accelerator model A good example that illustrates the use of recursive equations, and the variety of solution paths for income in an economy, is that of the multiplier–accelerator model first outlined by Samuelson (1939). Consumption is related to lagged income while investment at time t is related to the difference between income at time t 1 and income at time t 2. 11 In our formulation we shall treat government spending as constant, and equal to G in all periods. The model is then C t = a + bY t 1 I t = v ( Y t 1 Y t 2 ) G t
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: G for all t E t = C t + I t + G t Y t = E t which on straight substitution gives rise to the second-order nonhomogeneous recursive equation Y t − ( b + v ) Y t − 1 + vY t − 2 = a + G The particular solution is found by letting Y t = Y ∗ for all t . Hence Y ∗ − ( b + v ) Y ∗ + vY ∗ = a + G i.e. Y ∗ = a + G 1 − b In other words, in equilibrium, income equals the simple multiplier result. The complementary result, Y c , is obtained by solving the homogeneous compo-nent Y t − ( b + v ) Y t − 1 + vY t − 2 = which has the characteristic equation x 2 − ( b + v ) x + v = with solutions r , s = ( b + v ) ± ± ( b + v ) 2 − 4 v 2 11 Samuelson originally related investment to lagged consumption rather than lagged income....
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern