Solution Found!
?(a) Show that if the profit ????(????) is a maximum, then the marginal revenue equals
Chapter 4, Problem 66(choose chapter or problem)
(a) Show that if the profit ๐(๐ฅ) is a maximum, then the marginal revenue equals the marginal cost.
(b) If ๐ถ(๐ฅ) ๏ผ 16,000 + 500๐ฅ โ 1.6x2ย + 0.004๐ฅ3ย is the cost function and ๐(๐ฅ) ๏ผ 1700 โ 7๐ฅ is the demand function, find the production level that will maximize profit.
Questions & Answers
QUESTION:
(a) Show that if the profit ๐(๐ฅ) is a maximum, then the marginal revenue equals the marginal cost.
(b) If ๐ถ(๐ฅ) ๏ผ 16,000 + 500๐ฅ โ 1.6x2ย + 0.004๐ฅ3ย is the cost function and ๐(๐ฅ) ๏ผ 1700 โ 7๐ฅ is the demand function, find the production level that will maximize profit.
ANSWER:
Step 1 of 2
a)
By definition, profit is the difference between revenue and cost, i.e.
If the profit ย is a maximum, then
Therefore if profit is maximum, then
By definition, ย is marginal revenue and ย is marginal cost.