Consider a continuous-time version of the dynamic Arrow-Hurwicz model for the same data given as in Exercise 7.

1. Determine trajectories of a price vector satisfying a system of equations of the dynamic continuous-time Arrow-Hurwicz model taking a proportionality coef- ficient o equal to 0.25, 0.35, 1.25 and determine whether these trajectories are feasible. 2. Determine if and when (at what moment) a structure of prices stabilizes around the equilibrium price structure. 3. Present graphs of price trajectories as functions of time.

Exercise 7

 

Two traders come to a market with bundles of goods: a¹ = (10, 20). Their utility functions are following: a² = (20),

Exercise 2

There is given a market of two traders and two goods described by the static Arrow-Hurwicz model, in which:

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(a) u(x11, X12) = ln x1+ Inx12, u(x21, x22) = ln x21 + In x22, (b) u(x11, 12) = x +x1/4, u(x21, x22) = x1 + x2*,. 1/4 1/4 1/4 Consider a discrete-time version of dynamic discrete-time Arrow-Hurwicz model. A broker announces initial prices: p(0) = (2,4). Using a form of the excess demand function and a structure of the Walrasian equilibrium price vector found in Exercise 2 for the static Arrow-Hurwicz model: 1. Determine trajectories of a price vector satisfying a system of equations of the dynamic discrete-time Arrow-Hurwicz model, taking a proportionality coefficient o equal to 0.25, 0.35 and 1.25. Calculate price ratios 20and compare them with the equilibrium price ratio 2. State which trajectories determined in point 1 are feasible. 3. State if and when (in which period) a structure of prices stabilizes around the equilibrium price structure and whether it reaches this structure in time horizon T = 15. 4. Present graphs of the price trajectories in the state space. 5. Present graphs of the price trajectories as functions of time.