QuestionFor the demand equation $p=1400-4 q$, verify that demand is elastic and total revenue is increasing for $0<q<175$. Verify that demand is inelastic and total revenue is decreasing for $175<q<350$.
Begin by finding $\eta$ in terms of $q$. The formula for $\eta$ is $\eta=\frac{p}{q} \cdot \frac{d q}{d p}$. Since $p=1400-4 q, \frac{d q}{d p}=$ $\square$ (Simplify your answer.)

Studdy Solution
Verify elasticity and total revenue for $175 < q < 350$:
For demand to be inelastic, $|\eta| < 1$.
$$\left| -\frac{350}{q} + 1 \right| < 1$$
Solve the inequality:
$$\frac{350}{q} < 2$$
Solve for $q$:
$$350 < 2q$$ $$q > 175$$
This confirms that demand is inelastic for $175 < q < 350$.
For $175 < q < 350$, $1400 - 8q < 0$, so total revenue is decreasing.
The demand is elastic and total revenue is increasing for $0 < q < 175$. The demand is inelastic and total revenue is decreasing for $175 < q < 350$.