Demand and Supply model In the notes and lessons, we saw that quantity demanded and quantity supplied may be related by the recurrence relations Pn+1-Pn =α (Dn - Pn), Dn+1-Dn =β (Pn - Dn), where Pn is the level production after n time intervals, Dn is the quantity demanded by the consumer and α and β are proportionality constants. Suppose α=β=k. Which of the following gives the best description of the behaviour of the quantity demanded and level of production when k=2? A. The level of production oscillates with a decreasing amplitude. The quantity demanded also oscillates with a decreasing amplitude. The level of production and quantity demanded diverge from each other as the number time steps n goes to infinity. B. The level of production oscillates with a decreasing amplitude. The quantity demanded also oscillates with a decreasing amplitude. The level of production and quantity demanded reach equilibrium as the number time steps n goes to infinity. C. The level of production and quantity demanded are constant. D. The level of production oscillates with an increasing amplitude. The quantity demanded also oscillates with an increasing amplitude. The level of production and quantity demanded diverge from each other as the number time steps n goes to infinity.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Demand and Supply model

In the notes and lessons, we saw that quantity demanded and quantity supplied may be related by the recurrence relations

P_n+1-P_n=α (D_n- P_n),

D_n+1-D_n=β (P_n- D_n),

where P_n is the level production after n time intervals, D_n is the quantity demanded by the consumer and α and β are proportionality constants.

Suppose α=β=k. Which of the following gives the best description of the behaviour of the quantity demanded and level of production when k=2?

A. The level of production oscillates with a decreasing amplitude. The quantity demanded also oscillates with a decreasing amplitude. The level of production and quantity demanded diverge from each other as the number time steps n goes to infinity.
B. The level of production oscillates with a decreasing amplitude. The quantity demanded also oscillates with a decreasing amplitude. The level of production and quantity demanded reach equilibrium as the number time steps n goes to infinity.
C. The level of production and quantity demanded are constant.
D. The level of production oscillates with an increasing amplitude. The quantity demanded also oscillates with an increasing amplitude. The level of production and quantity demanded diverge from each other as the number time steps n goes to infinity.

Expert Solution

Step 1

The two relations are given below :

P_n+1-P_n=α (D_n- P_n),

D_n+1-D_n=β (P_n- D_n)

When $P_{n}$ is the level production after n time intervals, D_n is the quantity demanded by the consumer and α and β are proportionality constants.

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