Always Round Tire finds that their demand curve is P = 50 − .02 Q.What price and quantity combination will maximize the firm's revenue? What are the total revenue and price elasticity at this point?

Question

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The Answer is Marginal revenue has twice the slope of the demand curve: MR = 50 − 0.04Q.The quantity that maximizes revenue is where marginal revenue equals zero: 50 − 0.04Q = 0
Solving,Q = 50/0.04 = 1,250.P = 50 − 0.02 * (1,250)= $25.Hence,revenue will be maximized when they produce 1,250 units and charge a price of $25.At this revenue maximizing quantity and price,the total revenue is: TR = P * Q = 25 * 1,250 = $31,250.The price elasticity of demand is equal to (% change in Q)/ (% change in P).If the price increases from $25 to $26,the quantity demanded is 26 = 50 - 0.02Q = 24/0.02 = Q = 1,200.Therefore,the price elasticity of demand = (1,200 - 1,250/1,250)/ (26 - 25 / 25)= 0.04 / 0.04 = 1.

Always Round Tire Finds That Their Demand Curve Is P