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* = 0.5*p* − 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 price*p*= ¢consumers’ surplus*CS*= ¢producers’ surplus*PS*= ¢total social gain