Consider a continuous-time version of the dynamic Arrow-Debreu-McKenzie model for the same data given as in Exercise E5.

Exercise E5

An owner of a strawberry plantation hires one worker who has 24 units of time. The employee can allocate part of the time to work and part to rest. He/she owns 20% of shares in profits of the plantation. The only production factor in producing strawberries is the labour of the worker. The process of production of strawberries is described by a power production function of a form:

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1. Determine trajectories of a price vector satisfying a system of equations of the dynamic continuous-time Arrow-Debreu-McKenzie model taking a proportional- ity coefficient o equal to 0.01, 0.05, 0.1 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.