Answer:
Price is 25
Quantity is 1,250
Total revenue= 31,250
Elasticity at that point = -0.1
Explanation:
Total revenue (TR) is given by TR=Price x Quantity . We can get the price from the demand equation. Then
[tex]TR=P \times Q= (50-0.2Q)\timesQ=50Q \times 0.2Q^2[/tex]
where Q is the quantity and P is the price. To find the maximum revenue we take derivatives with respect to the quantity and equalize it to zero
[tex]\frac{d}{dQ}TR=50-0.04Q=0[/tex]
solving for Q we have that Q=1,250 replacing in the demand curve we can get the price [tex]P=50-0.02Q=50-0.02\times 1250=25[/tex]
Total revenue is [tex]1250\times25=31,250[/tex]
Elasticity at this point is [tex]\eta_{x,p_x}=\frac{dQ}{dP}\frac{P}{Q}=-5\frac{25}{1250}=-0.1[/tex]
