The demand function for specialty steel products is given, where p is in dollars

Question

The demand function for specialty steel products is given, where p is in dollars and q is the number of units. p = 150 3 squareroot 110 - q Find the elasticity of demand as a function of the quantity demanded, q. eta = Find the point at which the demand is of unitary elasticity. q = Find intervals in which the demand is inelastic and in which it is elastic. (Enter your answers using interval notation.) Inelastic elastic Use information about elasticity in part (b) to decide where the revenue is increasing, and where it is decreasing. (Enter your answers using interval notation.) Increasing decreasing Use information about elasticity in part (b) to decide where the revenue is maximized. q =

Explanation / Answer

elasticity of demand = dQ/Q / dP/P ;

= (dQ/dP)*(P/Q);

we have p^3 = 150^3 (100-q)

3 p^2 dp= -150^3 dq;

dq/dp = -3p^2 / (150^3);

(dq/dp)*(p/q) = -3p^3 / q(150^3)=-3(150^3 (100-q)) / q(150^3)= 3 - 300/q;

elasticity = 3-300/q;

b)at q=150 demand is unitary elasticity;

c)when q < 150 ; inelastic;

q > 150 elastic;

d) for q>150; revenue will increase;

for q< 150 revenue will decrease;

maximum when q=150;

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