Question

1. The demand for the book is P = 96 – 3Q. A bookstore can order copies that will cost $7. If the bookstore orders 11 books, what is the total profit?

2. A firm faces the demand curve: P = 2611 - 10Q. What is the firm’s revenue maximizing price?(round to two decimal places if necessary).

3. If TC = 42 + 20Q + 4Q² , what is the marginal cost at when Q=10?

4. Assume P = 84 - 1Q and TC = 42 + 2Q². What level of production maximizes profit? (round to two decimal places if necessary).

Answer 1

1) P = 96 - 3Q

TC = 7

Q = 11

P = 96 - 3*11 = 63

Profit per book = 63 - 7 = 56. For 7 units, total profit would be = 56 * 7 = 392

2) P = 2611 - 10Q

Total revenue = P * Q

Total revenue = (2611 - 10Q) * Q = 2611Q - 10Q²

Maximum revenue occurs at output level when marginal revenue is zero which can be calculated as the derivative of total revenue with respect to Q and put it equal to zero (as marginal revenue calculates slope, we put it equal to zero as the slope would be zero at some stagnant point of profit level, staze when profit starts falling after reaching its maximum level)

[d(Total Revenue) / dQ] = 2611 - 20Q = 0

Q = 130.55

At output level of 130, the revenue would be maximum.

3) TC = 42 + 20Q + 4Q²

MC = d(Total cost) / dQ (derivative of total cost with respect to Q)

MC = 20 + 8Q

At Q = 10, Marginal cost = 20 + 8 * 10 = 100

4) P = 84 - Q

TC = 42 + 2Q²

MC = d(Total cost) / dQ (derivative of total cost with respect to Q) = 4Q

Total revenue = Price * Quantity = (84 - Q) * Q = 84Q - Q²

MR = d(Total Revenue) / dQ (derivative of total revenue with respect to Q) = 84 - 2Q

At profit maximizing output, Marginal revenue equals marginal cost

4Q = 84 - 2Q

6Q = 84

Q = 14

At Q = 14, profit would be maximum.