- #1
Burjam
- 52
- 1
Homework Statement
Consider an item that is initially sold at a market price of $10 per unit. Over time, market forces push the price toward the equilibrium price, $20, at which supply balances demand. After 6 months, the price has increased to $15. the Evans Price Adjustment model says that the rate at which the market price changes is proportional to the difference between the market price and the equilibrium price.
Homework Equations
N/A
The Attempt at a Solution
dp/dt = 20-p, where p=market price in dollars and t=time in months
∫dp/20-p = ∫1dt
ln (20-p) = t+c
20-p = e^(t+c)
20-p = e^t*e^c
20-p = Ae^t, where A=e^c
p = 20-Ae^t
10 = 20-Ae^0
10 = 20-A
A=10
Now that I've solved for A with the initial condition, I have hit a roadblock. I'm pretty sure my initial setup of this problem is off. When I substitute 15 in for p, I get a negative t, which is impossible. Please help.