Marginal Revenue & Marginal Cost

April 5, 2013

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.

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.

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

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

Total Revenue (TR)Q PD TR

0 10 0

1 8

2 6

3 4

4 2

5 0 0

P

Q

10

8

6

4

2

1 2 3 4 5

PD=10-2Q

D

Total Revenue (TR)Q PD TR

0 10 0

1 8 8

2 6

3 4

4 2

5 0 0

P

Q

10

8

6

4

2

1 2 3 4 5

PD=10-2Q

D

Total Revenue (TR)Q PD TR

0 10 0

1 8 8

2 6 12

3 4

4 2

5 0 0

P

Q

10

8

6

4

2

1 2 3 4 5

PD=10-2Q

D

Total Revenue (TR)Q PD TR

0 10 0

1 8 8

2 6 12

3 4 12

4 2

5 0 0

P

Q

10

8

6

4

2

1 2 3 4 5

PD=10-2Q

D

Total Revenue (TR)Q PD TR

0 10 0

1 8 8

2 6 12

3 4 12

4 2 8

5 0 0

P

Q

10

8

6

4

2

1 2 3 4 5

PD=10-2Q

D

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.

Marginal Revenue (MR)Q PD TR MR Graphical

0 10 0 x x

1 8 8

2 6 12

3 4 12

4 2 8

5 0 0

Marginal Revenue (MR)Q PD TR MR Graphical

0 10 0 x x

1 8 8 8-0=8

2 6 12

3 4 12

4 2 8

5 0 0

Marginal Revenue (MR)Q PD TR MR Graphical

0 10 0 x x

1 8 8 8-0=8

2 6 12 12-8=4

3 4 12

4 2 8

5 0 0

-

Marginal Revenue (MR)Q PD TR MR Graphical

0 10 0 x x

1 8 8 8-0=8

2 6 12 12-8=4

3 4 12 12-12=0

4 2 8

5 0 0

-

-

Marginal Revenue (MR)Q PD TR MR Graphical

0 10 0 x x

1 8 8 8-0=8

2 6 12 12-8=4

3 4 12 12-12=0

4 2 8 8-12=-4

5 0 0

-

-

-

Marginal Revenue (MR)Q PD TR MR Graphical

0 10 0 x x

1 8 8 8-0=8

2 6 12 12-8=4

3 4 12 12-12=0

4 2 8 8-12=-4

5 0 0 0-8=-8

-

-

-

-

Marginal Revenue Can Be NegativeQ PD TR MR

0 10 0 x

1 8 8 8

2 6 12 4

3 4 12 0

4 2 8 -4

5 0 0 -8

P

Q

10

5

PD=10-2Q

D

1 42

-8

3

Why Does This Make Sense?

If PD=a-bQ, TR=PDQ=aQ-bQ2, inverse quadratic equation.

TR=PDQ

TR Increasing

TR Decreasing

PD=a-bQP

Q

(1) When TR is increasing, MR is positive.(2) When TR is decreasing, MR is negative.(3) However, Be careful to notice that MR is always decreasing.

Theorem for when MR=0

• If PD=a-bQ, then MR=0 when Q=(1/2)*(a/b).TR=PDQ

a

b/a(1/2)*b/a

P

Q

Q

PD=a-bQ

TR=PDQ

a

b/a

-a

P

Q

Q

(1/2)*b/a

Putting it all together.

PD=a-bQ

MR

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

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).

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.

Example

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)

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

Example

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

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

Example

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

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

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?

Marginal Cost is Also

A. The supply line

B. The demand line

C. The marginal revenue line

D. The marginal product line

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.

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

MR and MC. Putting the Two Examples together: Profits.

Q PD MR MC=PS Profit

0 10 x 0

1 8 8 2 6

2 6 4 4 0

3 4 0 6 -6

4 2 -4 8 -12

5 0 -8 10 -18

Under perfect competition, P* is the market price. What price would a

profit-maximizing firm charge if there were no competition?

A. PA

B. PB

C. PC

D. PD(=0)

E. P*

P

PA

PB

PC

PD

Q

PS=MC

PD

MR

P*

Answer: Save for Next Class

• We will begin our discussion here on Monday.

• Make sure to bring Problem Set 1!

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