## Related questions with answers

An item is initially sold at a price of $\$ p$ per unit. Over time, market forces push the price toward the equilibrium price, $\$ p^*$, at which supply balances demand. The Evans Price Adjustment model says that the rate of change in the market price, $\$ p$, is proportional to the difference between the market price and the equilibrium price.

**(a)** Write a differential equation for $p$ as a function of $t$.

Solutions

VerifiedThe market price of an item is expressed as $\$p$ and the equilibrium price of an item is expressed as $\$p^*$. We will use Evans Price Adjustment model to write a differential equation.

Here we model the ODE describing the Evans Price Adjustment model. It is given that $p$ is an initial market price per unit, $p^*$ is an equilibrium price, and we know that the rate of change of price $p$ (i.e. $dp/dt$) is proportional to the distance between the market price and the equilibrium price (i.e. $p(t)-p^*$).

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