Consider the supply and demand equations Q St 2P t aP t 1 20 Q Dt 100 8P t for some parameter, a Assuming that the market is in equilibrium, show that P t 12 0 1aP t 1 If P 0 10, find an expression for P t in terms of t and a If the solution displays oscillatory convergence, state the range of valu...

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Consider the supply and demand equations: Q St = 2P t + aP t-1 20 Q Dt

Question:

Consider the supply and demand equations:
Q_St = 2P_t + aP_t-1 −20
Q_Dt = 100 − 8P_t
for some parameter, a.
Assuming that the market is in equilibrium, show that P_t = 12 − 0.1aP_t-1.
If P₀ = 10, find an expression for P_t in terms of t and a.
If the solution displays oscillatory convergence, state the range of values of a and find the particular value of a if P₁ = 9.5.