Could someone please explain how to do this question?
3. The demand function for a company's product is p=60 000(x + 3000)-1, with demand 3000 units weekly.
a) Compute the elasticity of demand at the current demand.
Should the company raise or lower the price if it wants to increase revenue?
c) What price will maximize revenues? What will be the demand at this price?
i don't know a lot about economics but i think i can take a shot at this.
elasticity is defined as Ed
= (p/x)*(dx/dp), where p is price and x is demand. so solve the equation you have above for x in terms of p and take the derivative:
= (p/x)*(dx/dp) = (p/x) * d/dp[ 60000/p -3000 ] = (p/x) * (-60000/p2
) = -60000/(px) = -(x + 3000)/x
now, evaluate for x = 3000 and you have Ed
as expected it's negative since demand goes down as price goes up, and it's magnitude is larger than 1 which means that fractional change in demand is larger than the fractional change in price when a change in price is made. hence an increase in price leads to a decrease in revenue, so the company should decrease the price to increase revenue.
now, revenue r = x*p. so that gives
r = 60 000x*(x + 3000)-1
now, this doesn't have a maximum for any value of x. it starts approaches 60000 asymptotically ( x/(x+3000) is always less than 1). so i suppose for part © the answer would be that no such price exists? or is there something i'm missing?
Edited by no vacancy, 21 November 2010 - 12:03 PM.