16.07.2022 - 07:38

# Noah and Naomi can produce garden benches, garden chairs, or both; they are price takers in both markets. Their cost function for garden benches is: CB(QBQC)= 80QB + (QB)2+QBQC and Marginal Cost = MCB=80+2QB+QC, Cost Function for Garden Chairs: CC(QBQC)=2

Question:

Noah and Naomi can produce garden benches, garden chairs, or both; they are price takers in both markets. Their cost function for garden benches is: CB(QBQC)= 80QB + (QB)2+QBQC and Marginal Cost = MCB=80+2QB+QC, Cost Function for Garden Chairs: CC(QBQC)=25QC+(Qc)2+QCQB Marginal Cost: MCC=25+2QC+QB The price of a garden bench PB=$120, the price of a garden chair PC=$60

a. What are Noah and Naomi’s profit-maximizing sales quantities of benches and chairs? Round to one decimal place and show work for Benches and Chairs.

b. What is the profit-maximizing quantities if the price of benches increases to $135? Round your answers to 1 decimal place and show work. Answers (1) • April 5, 2023 в 02:45 a. To determine the profit-maximizing sales quantity, we need to find the quantity at which marginal cost equals price for each product. For garden benches: PB = MCB$120 = 80 + 2QB + QC 2QB + QC = $40 For garden chairs: PC = MCC$60 = 25 + 2QC + QB 2QC + QB = $35 We can solve these two equations simultaneously to find the profit-maximizing sales quantities: 2QB + QC =$40 2QC + QB = $35 Multiplying the first equation by 2 and subtracting the second equation gives: 3QB =$5 Therefore, QB = 1.7 (rounding to one decimal place), and QC = 16.6. So, the profit-maximizing sales quantities are 1.7 garden benches and 16.6 garden chairs. b. If the price of garden benches increases to $135, we need to recalculate the profit-maximizing sales quantities. For garden benches: PB = MCB$135 = 80 + 2QB + QC 2QB + QC = $55 For garden chairs: PC = MCC$60 = 25 + 2QC + QB 2QC + QB = $35 Solving these two equations simultaneously gives: 3QB =$20 Therefore, QB = 6.7 (rounding to one decimal place), and QC = 11.7. So, the profit-maximizing sales quantities are 6.7 garden benches and 11.7 garden chairs. Explanation: Profit maximization occurs when marginal revenue (in this case, the price) equals marginal cost. To find the profit-maximizing sales quantities, we set the price equal to the marginal cost and solve for the respective quantities. When the price of garden benches increases, the profit-maximizing sales quantities change because the marginal revenue has also changed. We need to solve for the new profit-maximizing quantities using the updated prices and marginal costs.