2. Announcements
• 150 People are enrolled
• As of last class, 50 had signed up to “follow” on
website. econ2ucsd.wordpress.com
• 45 had clickers. Today we have ___. (Freq. BB)
• Takeaway: I need to give you better incentives.
• Get a clicker and register by Monday, +5% extra
credit on Midterm.
• If you still haven’t registered by Monday, I will
give more positive incentives to those who have.
3. Last Class
• Finished our review of producer and
consumer surplus from Econ 1.
• Today, final Econ 1 review: The firm.
– Marginal Revenue
– Marginal Cost
– Profit Maximization
• Will make use of clickers to see if we are
following the material.
4. Learning Goals for Today
• Calculate marginal revenue equation for given
market demand
– Derive total revenue, and connection with
marginal revenue
• Discern what a firm’s marginal costs are, and
relate these to marginal revenue
– Derive total cost as a function of capital and wage
inputs, and connection with marginal revenue
5. Total Revenue (TR)
• The total income a firm receives for selling its
goods.
• Determined by Demand line: TR=PDQ.
• If PD=a-bQ, and we only know Q, can we
determine TR?
• YES. TR=PDQ=(a-BQ)Q
11. Marginal Revenue
• Added Revenue from immediate next unit of
goods sold
• MR(Q) = TR(Q) – TR(Q-1)
• For instance, if TR from 3 sold is 10, and TR
from 4 sold is 12, then MR(Q=4)=2.
18. Marginal Revenue Can Be Negative
P
Q PD TR MR
10
0 10 0 x PD=10-2Q
1 8 8 8
D
2 6 12 4 Q
1 2 3 4 5
3 4 12 0
-8
4 2 8 -4
5 0 0 -8
19. Why Does This Make Sense?
If PD=a-bQ, TR=PDQ=aQ-bQ2, inverse quadratic equation.
TR=PDQ
TR TR
Increasing Decreasing (1) When TR is
increasing, MR is
positive.
(2) When TR is
decreasing, MR is
negative.
P
PD=a-bQ (3) However, Be
careful to notice
that MR is always
decreasing.
Q
20. Theorem for when MR=0
• If PD=a-bQ, then MR=0 when Q=(1/2)*(a/b).
TR=PDQ
Q
P
a
PD=a-bQ
Q
(1/2)* b/a
b/a
21. Putting it all together.
TR=PDQ
Q
P
a
PD=a-bQ
Q
(1/2)* b/a
b/a
MR
-a
22. PD=8-1/8Q. For which Q is MR
positive?
A. Q= 0 to 8
B. Q= 8 to 16
C. Q = 0 to 64
D. Q = 0 to 32
23. Answer: D
• Theorem: If PD=a-bQ, MR intersects Q axis at
(1/2)*a/b.
• Here, PD=8-1/8Q.
• So, (1/2)*a/b=(1/2)*8/(1/8)
• Recall, 8/(1/8) = 8 * 8.
• So, MR intersects Q axis at Q=1/2*64=32.
• Correct answer: Positive on [0,32).
24. Total Cost
• Total cost is the dollar value of inputs
necessary to produce some amount Q.
• Say I use one unit of labor to produce Q units
of output and the wage rate is w. Total cost of
producing Q units is w.
• Say I use one unit of capital to produce Q units
of output and the rental rate is r. Total cost of
producing Q units is r.
25. Example
We consider a business that takes labor as the only input.
Say the wage rate is w=$10/hr, and there is diminishing marginal product of labor
Producing Q Requires how many labor hours? TC MC
0 0 0 0
1 0.2 (+0.2 hrs)
2 0.6 (+0.4 hrs)
3 1.2 (+0.6 hrs)
4 2 (+0.8 hrs)
5 3 (+1 hrs)
26. Example
We consider a business that takes labor as the only input.
Say the wage rate is w=$10/hr, and there is diminishing marginal product of labor
Producing Q Requires how many labor hours? TC MC
0 0 0 0
1 0.2 (+0.2 hrs) 2
2 0.6 (+0.4 hrs) 6
3 1.2 (+0.6 hrs) 12
4 2 (+0.8 hrs) 20
5 3 (+1 hrs) 30
27. Example
We consider a business that takes labor as the only input.
Say the wage rate is w=$10/hr, and there is diminishing marginal product of labor
Producing Q Requires how many labor hours? TC MC
0 0 0 0
1 0.2 (+0.2 hrs) 2 2
2 0.6 (+0.4 hrs) 6 4
3 1.2 (+0.6 hrs) 12 6
4 2 (+0.8 hrs) 20 8
5 3 (+1 hrs) 30 10
28. Think
• How does the marginal cost of a unit of
production relate to the minimum amount
you would be willing to accept for a unit of
that good?
29. Marginal Cost is Also
A. The supply line
B. The demand line
C. The marginal revenue line
D. The marginal product line
30. Answer: A
• The supply line is the schedule of reservation
prices, i.e., the minimum the seller is willing to
accept for a given Q.
• Surely, the seller will never accept less than
MC.
31. MR and MC. Putting the Two
Examples together: Profits.
Q PD MR MC=PS Profit
0 10 x 0
1 8 8 2
2 6 4 4
3 4 0 6
4 2 -4 8
5 0 -8 10
33. Under perfect competition, P* is the
market price. What price would a
profit-maximizing firm charge if there
were no competition?
P
A. PA PA PS=MC
B. PB
PB
C. PC P*
D. PD(=0) PC
E. P* PD
PD
Q
MR
34. Answer: Save for Next Class
• We will begin our discussion here on Monday.
• Make sure to bring Problem Set 1!
• Check website for updates.
