Textbook problems worked out
- 1. Examples of Problems from Text • Below are three problems worked out from the textbook with all of the steps included. Since the textbook leaves out many of the key steps in these examples I have worked them out for you.
- 2. Problems 8-5 • P = 100 – 2Q • C(Q) = 10 + 2Q • Total Revenue = Price * Quantity • P * Q = Q (100 -2Q) • TR = 100Q – 2Q2 • MR = 100 – (2) 2Q2-1 • MR = 100 – 4Q • C(Q) = 10 + 2Q • Marginal Cost = MC • MC = 2 • MR = MC to maximize profits • 2 = 100 – 4Q • 4Q = 98 • Q = 24.5 • P = 100 – 2Q • P = 100 – 2 (24.5) • P = 51 • Profit = TR – TC • Profit = (24.5*51) – (10 + 2*24.5) • Profit = 1190.50
- 3. Problem 8-6 • P(Q) = 70-.5Q • MC1 = 3Q1 • MC2 = Q2 • Total Revenue = Price * Quantity • P* Q = Q (70-.5Q) • TR = 70Q-.5Q2 • MR = 70 – (2).5Q2-1 • MR = 70 – Q • Q = Q 1 + Q2 • Substitute so: • MR = MC • 70 – (Q1 +Q2) = 3Q1 • 70 – (Q1 +Q2) = Q2 • So • 70 – 3Q1 - Q1 -Q2 = 0 • 70 – 4Q1 = Q2 • Substitute into other Equation • 70 – (Q1 + 70 – 4Q1) = 70 – 4Q1 • 70 – Q1 - 70 + 4Q1 = 70 – 4Q1 • 3Q1 = 70 – 4Q1 • 7Q1 = 70 • Q1 = 10 • Solve for Q2 in other equation • 70 – (Q1 +Q2) = 3Q1 • 70 – (10 +Q2) = 3(10) • 70 – 10 – Q2 = 30 • 60 – Q2 = 30 • 30 – Q2 = 0 • 30 = Q2 • Q = Q1 + Q2 • Q = 10 + 30 • Q = 40 • Price • P(Q) = 70-.5Q • P(Q) = 70-.5 (40) • P(Q) = 70-20 • P(Q) = 50
- 4. Problem 8-7 • P = 100 – 2Q • C(Q) = 5 + 2Q • Total Revenue = Price * Quantity • P * Q = Q (100 -2Q) • TR = 100Q – 2Q2 • MR = 100 – (2) 2Q2-1 • MR = 100 – 4Q • C(Q) = 5 + 2Q • Marginal Cost = MC • MC =2 • MR = MC to maximize profits • 2 = 100 – 4Q • 4Q = 98 • Q = 24.5 • P = 100 – 2Q • P = 100 – 2 (24.5) • P = 51 • Profit = TR – TC • Profit = (24.5*51) – (5 + 2*24.5) • Profit = 1195.50