AB has used market research to determine that if a price of $250 is charged for product G, demand will be 12,000 units. It has also been established that demand will rise or fall by 5 units for every $1 fall/rise in the selling price. The marginal cost of product
G、is $80. Required If marginal revenue = a – 2bQ when the selling price (P) = a – bQ, calculate the profit-maximising selling price for product G.
G、is $80. Required If marginal revenue = a – 2bQ when the selling price (P) = a – bQ, calculate the profit-maximising selling price for product G.
【参考答案及解析】
a = $250 + ((12,000/5) × $1) = $2,650 MR = 2,650 – (2 × 0.2)Q = 2,650 – 0.4Q Profits are maximised when MC = MR, ie when 80 = 2,650 – 0.4Q 2,650 – 80 = 2,570 × 10/4 = 6,425 Profit-maximising demand = 6,425 Now, substitute the values into the demand curve equation to find the profit-maximising selling price P = a – bQ P = 2,650 – (0.2 × 6,425) ∴Profit-maximising price = $(2,650 – 1,285) = $1,365
a = $250 + ((12,000/5) × $1) = $2,650 MR = 2,650 – (2 × 0.2)Q = 2,650 – 0.4Q Profits are maximised when MC = MR, ie when 80 = 2,650 – 0.4Q 2,650 – 80 = 2,570 × 10/4 = 6,425 Profit-maximising demand = 6,425 Now, substitute the values into the demand curve equation to find the profit-maximising selling price P = a – bQ P = 2,650 – (0.2 × 6,425) ∴Profit-maximising price = $(2,650 – 1,285) = $1,365