Jianjun Miao - Economic Dynamics in Discrete Time (The MIT Press)

Cobweb diagram for the system xt+1 = 2xt(1 xt)

Impact of dividend taxes on the stock price

Nullclines: The left and right panels plot the isoclines xt = 0 and yt = 0, respectively

Phase diagram

Phase diagram for example 1.5.1

Cobweb diagrams for the three dynamical systems f(x) = x + x3, g(x) = xx3, and h(x) = x + x2

Saddle-node bifurcation for the map f(x; a) = x2 + a

Transcritical bifurcation for the map f(x; a) = ax(1 x)

Pitchfork bifurcation for the map f(x; a) = axx3

Period-doubling bifurcation for the map f(x; a) = x2 + a

Bifurcation diagram for the logistic system f(x) = ax(1 x)

Cobweb diagram and the orbit starting at x0 = 0.3 for the logistic system f(x) = 4x(1 x)

The tent map f(x) and its iterates f2(x) and f3(x) on [0, 1]

Logistic function f(x) = 4x(1 x) and its third iterate f3(x)

Transitional dynamics in response to a temporary technology shock

Graphic representation of a Markov chain

Graphic representation of the birthdeath Markov chain

Graphic representation of the unrestricted one-dimensional random walk

Option value. Plotted is the value function V(z) for the irreversible project investment problem.

Value function. Plotted is the value function V(s) for the discrete choice problem.

The determination of the saving function and its properties

Policy functions. Plotted are consumption and assets as functions of cash on hand.

Evolution of cash on hand. Plotted is xt+1 as a function of xt for the largest and the lowest income levels.

Optimality of the (s, S) policy. Illustrated is the solution for the one-period problem.

Minimization of Gn(x)

Reward to investing. Plotted is the function (Q, K) for a fixed value of K in the case without fixed costs.

Three regions of states for (K, z). Plotted are the two boundaries that partition the state space into the buy region, sell region, and inaction region in the case without fixed costs.

Reward to investing. Plotted is the function (Q, K) for a fixed value of K in the presence of fixed costs.

Chebychev polynomial basis functions up to nine degrees on the unit interval

Linear B-splines with nine equally spaced breakpoints {0, 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, 1}

Cubic B-splines with seven equally spaced breakpoints {0, 1/6, 1/3, 1/2, 2/3, 5/6, 1}

Phase diagram for the log-linearized basic RBC model

Labor market equilibrium for the log-linearized basic RBC model

Phase diagram after a permanent TFP shock for the log-linearized basic RBC model

Labor market responses following a permanent TFP shock for the log-linearized basic RBC model

Comparison of impulse responses to a TFP shock with different levels of persistence

Comparison of impulse responses to a TFP shock with different levels of persistence

Comparison of impulse responses to a TFP shock for different values of the risk aversion parameter

Comparison of impulse responses to a TFP shock for different values of the Frisch elasticity of labor supply

Comparison of impulse responses to a TFP shock for different values of the habit formation parameter

Impulse responses to a permanent TFP shock

Impulse responses to a TFP shock and an investment-specific technology (IST) shock

Impulse responses to a government-spending shock at different levels of persistence

Impulse responses to a preference shock at different levels of persistence

Priors and posteriors

Offer curve

One stable nonmonetary steady state and one unstable monetary steady state

Locally stable monetary steady state

Two-period cycle equilibrium

Feasibility and budget lines

Three positive steady states and G(0) > 1

Two positive steady states and G(0) < 1

Zero positive steady state and G(0) < 1

Indeterminancy

Unique positive and stable steady state

Locus kt = kt+1kt = 0 and vector fields

Locus bt = bt+1bt = 0 and vector fields

Phase diagram. The bubbly steady state is (kg, b*). It is a saddle point. The Diamond bubbleless steady state is (kD, 0). There are infinitely many equilibria converging to the Diamond steady state.

Determination of equilibrium in Aiyagaris (1994) model. The intersection of the Ea(r) curve and the FK curve gives the equilibrium interest rate and the capital stock.

Determination of equilibrium in Aiyagaris model in example 18.1.1

Determination of equilibrium in Huggetts (1993) model

Two stationary equilibrium rates of return on currency that finance the constant government deficit G

Steady-state equilibrium market tightness and wage

Steady-state equilibrium vacancies and unemployment

Phase diagram

Adjustments of vacancies and unemployment

Equilibrium reservation productivity and market tightness

Effect of higher productivity on equilibrium vacancies and unemployment

Impulse responses to a positive 1 percent shock to monetary policy

Impulse responses to a positive 1 percent shock to the natural rate

Impulse responses under optimal commitment and discretionary policies

L as a function of L

Derivatives of YL with respect to the values of rL and GL, for alternate degrees of persistence of the financial disturbance

Fiscal multiplier as a function of