Economics Dynamics Problems 47

# Economics Dynamics Problems 47 - now assume that demand...

This preview shows page 1. Sign up to view the full content.

Continuous dynamic systems 31 Figure 2.2. where quantities, q d and q s and price, p , are assumed to be continuous functions of time. Substituting the demand and supply equations into the price adjustment equation we derive the following dp dt α ( b d ) = α ( a c ) which is a Frst-order linear nonhomogeneous differential equation. Using a typical software programme for solving differential equations, the so- lution path is readily found to be p ( t ) = c a b d + ± p 0 ² c a b d ³´ e α ( d b ) t which satisFes the initial condition. ±or d–b > 0 the solution path for different initial prices is illustrated in Fgure 2.2 Example 2.5 Suppose we have the same basic demand and supply model as in example 2.4 but
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: now assume that demand responds not only to the price of the good but also to the change in the price of the good. In other words, we assume that if the price of the good is changing, then this shifts the demand curve. We shall leave open the question at this stage of whether the demand curve shifts to the right or the left as a result of the price change. The model now takes the form q d = a + bp + f dp dt b < , f ±= q s = c + dp d > dp dt = α ( q d − q s ) α > (2.7)...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online