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?
What will be an ideal response?
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.
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