The demand for q units of a product depends on the price p (in dollars) accordin

Question

The demand for q units of a product depends on the price p (in dollars) according to Find and explain the meaning of the instantaneous rate of change of demand with respect to price when the price is as follows. If price decreases by $1, the demand will drop approximately 4 units. If price decreases by $4, the demand will drop approximately 1 unit. If price increases by $1, the demand will increase approximately 4 units. If price increases by $1, the demand will drop approximately 4 units. If price increases by S4, the demand will drop approximately 1 unit. If price decreases by $0. 50, the demand will drop approximately 1 units. If price increases by $1, the demand will increase approximately 1/2 unit. If price decreases by $1, the demand will drop approximately 1/2 unit. If price increases by $1, the demand will drop approximately 1/2 unit. If price increases by $0. 50, the demand will drop approximately 1 units.

Explanation / Answer

Since,

Q = 1000/p - 1

Rate of change of demand ( with respect to time )

dQ/dt = 1000 d (1/p) / dt

dQ/dt = 1000 * ( -1/2) * (p)^-3/2 * dp/dt

When P = 25$,

dQ/dt = -4 * dp/dt

That means when rate of change in Price ( dp/dt) is 1$, rate of change in demand would drop by 4$. hence option 4.

In the second case,

when p = 100$

dQ/dt = -0.5 * dp/dt

Option 4.

Let me know if you have trouble understanfing this

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