Find expert answers and community insights on IDNLearn.com. Get the information you need from our community of experts who provide accurate and comprehensive answers to all your questions.

You are the manager of a monopoly, and your analysts have estimated your demand and cost functions as P = 200 − 3Q and C(Q) = 1,500 + 2Q2, respectively.a. What price–quantity combination maximizes your firm’s profits?

Sagot :

The price-quantity combination that maximizes the firm’s total profit will be $210 and 30 units respectively.

What is Bulk Pricing?

The price of goods and services in the market determines the quantity that consumers want. Assuming that non-price factors are removed from the equation, higher prices lead to lower quantities demanded, and lower prices lead to higher quantities demanded. A price is what a producer receives for the sale of one unit of goods or services. An increase in price will almost always increase the supply of that good or service, while a decrease in price will decrease the supply.

Calculating the maximum profit :

The inverse market demand function = 300 - 3Q

The total revenue will be:

                               = (300 - 3Q) × Q

                             = 300Q - 3Q²

The marginal revenue will be:

                             = 300 - 6Q

The total cost is given as:

                             = 1500 + 2Q².

The marginal cost will be:

                         = 4Q

The equilibrium level of output will then be: MR = MC

                              300 - 6Q = 4Q

                               6Q + 4Q = 300

                                  10Q = 300

                                     Q = 300/10

                                      Q = 30.

The quantity is 30 units.

The equilibrium price will then be:

                          P = 300 - 3Q

                        P = 300 - 3(30)

                               P = 300 - 90

                                    P = 210

Therefore, the price is $210.

The maximum profit that the firm will earn will be:

                         Profit = Revenue - Cost

                          = (210 × 30) - [(1500 × (2 × 30²)]

                                = 6300 - (1500 + 1800)

                                       = 6300 - 3300

                                              = $3000

Therefore, the profit will be $3000.

Learn more about price - quantity :

brainly.com/question/26075805

#SPJ4

Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.