A fast-food outlet finds that the demand equation for its new side dish, “Sweetdough Tidbit,” is given by p = 54(q + 1)2, where p is the price (in cents)

A fast-food outlet finds that the demand equation for its new side dish, “Sweetdough Tidbit,” is given by

p = 54(q + 1)2,

where p is the price (in cents) per serving and q is the number of servings that can be sold per hour at this price. At the same time, the franchise is prepared to sell q = 0.5p − 1servings per hour at a price of p cents. Find the equilibrium price p, the consumers’ surplus CS and the producers’ surplus PS at this price level. What is the total social gain at the equilibrium price?

equilibrium pricep= ¢consumers’ surplusCS= ¢producers’ surplusPS= ¢total social gain