Question

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]

Answer #1

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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