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ECON-200 Lecture Notes - Lecture 10: Marginal Revenue, Marginal Cost, Marginal Product

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School
Diablo Valley College
Department
Economics
Course
ECON-200
Professor
Sorce

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Document Summary

Price (p) is defined as the cost of an item or product. Quantity (q) can be defined as the amount or number of an item produced or sold. Total revenue (tr) primarily consists of the amount a firm generates by selling its goods and services. Total revenue is defined as the price of the item times the number of items sold. Marginal revenue (mr) is the change in total revenue from an additional unit sold. mr= tr qmr= tr q. Total cost (tc) includes the payments made for the various factors of production. Marginal cost (mc) is the increase in total cost that arises from an extra unit of production. mc= tc q. Total profit (tp) is the difference between total revenue and total costs. tp=tr tctp=tr tc. The excess of marginal revenue over marginal cost or the change in total profit from each additional unit sold. mp= tp q=mr mc.

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Related Questions

A small firm faces an inverse demand function of P = 100 - Q. Its total cost function is given by TC = .5Q2. (You should see right away that marginal revenue is thus MR = 100 - 2Q, and it also happens that marginal cost is just MC = Q. Both MR and MC are the first derivatives of total revenue and total cost. And a quick comment on MC: unlike some marginal cost functions we've seen, this one is not constant, because marginal cost is getting $1 higher with each additional unit of output.)

The Chief Executive Officer will manage the firm, choosing output and price. Currently, the CEO is negotiating an incentive-based contract with the shareholders of the company.
(Hint: basing compensation on revenue will motivate revenue maximization rather than profit maximization!)

Hint: since the plan creates incentives for the CEO to maximize revenue rather than profit, you should not set MR = MC at this point. BIG hint: revenue is maximized when selling an additional unit won't increase your revenue, or in math terms, when MR = 0.)

Owners' proposal: CEO keeps 10% of TR.

Firm price:

 Ā 

Firm output:

 Ā 

Total revenue:

 Ā 

Firm profit:

 Ā 

CEO compensation:

 Ā 

Remaining profit for owners:

 Ā 

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Output (Q)

Price per Unit

(P)

Total Revenue (TR)

Marginal Revenue (MR)

Total Cost (TC)

Average Total Cost (ATC)

Marginal Cost (MC)

0

$10

$8

1

9

11

2

8

12

3

7

15

4

6

24

5

5

35

6

4

48

Does this data represent the revenues and costs of a perfect competitive firm or a firm with some degree of Ć¢Ā€Āœmonopoly powerĆ¢Ā€Ā? ______________________

How do you know? ________________________________________________

Fill in the blanks in the table above.

How much output should this firm produce to maximize itĆ¢Ā€Ā™s profit? _____units. What price should this firm charge for its product? $_____ per unit.

This choice of output and price will lead to an economic profit = $______

The average revenue (demand) for product Q is given by AR = 50 - Q and the total cost of Q by:

STC = 100-4Q+2Q^2

a. Find the price function and then the TR function. See Assignment 3 or 4 for an example. Hint: another name for price is average revenue (AR).

b. Write the MR and MC functions below. Remember: MR = dTR/dQ and MC = dSTC/dQ. See Assignment 5 for a review of derivatives.

c. What positive value of Q will maximize total profit? Remember, letting MR = MC signals the objective of total profit maximization. Solve MR = MC for Q. The value of Q you get should not be zero or negative.

d. Use the price function found in (a) to determine the price per unit that will need to be charged at the Q found in (c). This will be the price you should ask for the total profit maximizing quantity.

e. What total profit will result from selling the quantity found in (c) at the price found in (d)? Hint: the profit function is found as TR Ć¢Ā€Ā“ STC.