Figure P6.15 shows the model of the dynamics of an economic system (Wingrove, 2012). In this diagram x represents the rate of growth in real Gross National Product (GNP), x0 the long-term trend (dc value) of the GNP, Δx the change over the long-term trend of the GNP, r_x the real and psychological disturbance inputs that affect the economy, r_m the random monetary inputs, and Δu fluctuations in unemployment rate. The diagram has two feedback loops: one through Friedman’s model in which the economy dynamics are approximated by

and a second loop through Okun’s law that relates the GNP to unemployment changes. Assuming the following parameter values: K_x = 2years, ω_n = 1.5rad/year, ζ = 0:8, K_u = 0:4 and G_x = -0.4. Find the range of G_u for closed loop stability.

Transcribed Image Text:

F(s) = 2 + 25 On +1 On