Question

# State whether the following question is true or false. Support your answer with brief explanation....

State whether the following question is true or false. Support your answer with brief explanation.
If a firm with marginal cost equal to \$2 faces a demand curve defined as Q_d = 100 - 5P, then profit is at a maximum when price is \$10.   [3 marks]

If a firm with marginal cost equal to \$2 faces a demand curve defined as Q_d = 100 - 5P, then revenue is at a maximum when price is \$10.   [3 marks]

A firm should increase expenditures on marketing and product variation up to the point where an additional dollar spent generates a marginal revenue of no less than one dollar.                                   [3 marks]

If a firm is experiencing decreasing returns to scale, then a doubling of output will require more than a doubling of all inputs.               [3 marks]

The more price elastic is the demand for a good or service, the higher will be the price mark-up over the marginal cost of production.           [3 marks]

State whether the following question is true or false. Support your answer with brief explanation.
If a firm with marginal cost equal to \$2 faces a demand curve defined as Q_d = 100 - 5P, then profit is at a maximum when price is \$10.   [3 marks]

If a firm with marginal cost equal to \$2 faces a demand curve defined as Q_d = 100 - 5P, then revenue is at a maximum when price is \$10.   [3 marks]

A firm should increase expenditures on marketing and product variation up to the point where an additional dollar spent generates a marginal revenue of no less than one dollar.                                   [3 marks]

If a firm is experiencing decreasing returns to scale, then a doubling of output will require more than a doubling of all inputs.               [3 marks]

The more price elastic is the demand for a good or service, the higher will be the price mark-up over the marginal cost of production.           [3 marks]

1. Demand : Q = 100 - 5P

Or, 5P = 100 - Q

Or, P = 20 - 0.2Q

Or, PQ = 20 Q - 0.2Q² = TR

Or, MR = d(TR)/dQ = 20 - 0.4Q

Profit will be maximized by producing at the point where MR=MC and profit maximizing price will be determined at the point where profit maximizing quantity lies on the demand curve.

Therefore, 20 - 0.4Q = 2

Or, 0.4Q = 18

Or, Q = (18/0.4)= 45

Now from demand equation we get, when Q = 45, P = 20 - (0.2*45) = 20 - 9 = 11

Therefore, profit maximizing price is \$11

Answer: the given statement is FALSE.

2. In the previous question, we found out that for this demand equation, MR = 20 - 0.4Q.

Revenue is maximized when d(TR)/dQ = MR = 0

Therefore, 20 - 0.4Q = 0

Or, 0.4Q = 20

Or, Q = 20/0.4 = 50

Now from the demand equation we get, when Q= 50, P = 20 - (0.2*50) = 20 - 10 = 10.

Therefore, the given statement is TRUE.

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