Suppose the revenue function for a company can be defined as; TR = Price (P) x Quantity (Q) If Q = 100 –P is the demand curve: a. What is the total revenue function for this firm in terms of P? TR = P x (100 – P) = 100P – P2 b. What is the total revenue function for this firm in terms of Q? TR = (100 – Q) x Q = 100Q – Q2 c. What level of production (Q) would maximize sales revenue? MR = 100 – 2Q = 0 100 = 2Q Q = 50 d. What is the extra or marginal revenue associated with an additional unit sold? MR = (1 x 100 x Q1-1) – (2 x 1 x Q 2-1) = 100 – 2Q Why is it not equal to the price? Marginal revenue is the change in revenue as the firm sells another unit of output. Because the firm has to cut its price to sell another unit, it makes that price on the additional unit, but earns less on all the units it could have sold at the higher price. Because of this effect on the amount earned on other units, the marginal revenue will always be less than the price. e. What is the price level that maximizes sales? P = 100 – Q = 100 – 50 = 50 f. Can the firm independently choose price and quantity to maximize total revenue?
