170925 entrepreneurial economics2

Entrepreneurial Economics

A supplemental lecture on BMA5001

Organized by NUS MBA Entrepreneurship Club

29th September, 2017

2

Ryo’s Part

• Competitive Market • In the short run

• In the long run

• Individual company and market

• Monopoly

Competitive Market in the Short Run

Perfect Competition• Firms are price taker

• Firms have no power to decide the price to sell.

• Both buyers and sellers have complete information about price, costs,…

• Firms are selling identical(homogeneous) products.

Competitive market

𝑃

𝑞

𝑞 𝑞 + 1

𝑃1

𝐴 𝐵

Demand curve = uniform price in every quantity.

Consumers in perfect Competitive market isPerfect price elastic. Because if you charge $1 more,No one buy from you.

Short-runWhat is Short-run?

In short run,

- no entry, no exit

- k(capital) = fixed. (You cannot build new plants)

So, companies could change only quantity 𝑞

(We use 𝑞 as individual firm and 𝑄 for market)

Company aims maximize their profit.What is Economic profit(𝜋)?

Profit is Total Revenue – Total (opportunity) Cost𝜋 𝑞 = 𝑇𝑅 𝑞 − 𝑇𝐶 𝑞

In Economics, cost is excluding sunk cost

(sunk cost do not always equals to fixed cost)

Total Revenue is Price × quantity, so:𝑇𝑅 𝑞 = 𝑃𝑞

Do you draw “Revenue” graph properly?

Before draw graph….You can download worksheet here

https://www.dropbox.com/s/ydlnvacb2kchxve/170925_Entrepreneurial%20Economics2_final%20-%20Worksheet.pdf?dl=0

• 𝑇𝑅(𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒) = 𝑃 × 𝑞

• 𝑀𝑅(𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒) =

• 𝑇𝐶(𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡) =

• 𝑀𝐶(𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐶𝑜𝑠𝑡) =

• 𝜋(𝑃𝑟𝑜𝑓𝑖𝑡) =

• 𝐴𝑇𝐶 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 =

• 𝐴𝑉𝐶(𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝐶𝑜𝑠𝑡) =

Worksheet 1

https://www.dropbox.com/s/ydlnvacb2kchxve/170925_Entrepreneurial Economics2_final - Worksheet.pdf?dl=0

Before draw graph….

• 𝑇𝑅(𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒) = 𝑃 × 𝑞

• 𝑀𝑅 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 =𝜕𝑇𝑅

𝜕𝑞= 𝑃 in competitive market

• TC(𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡) = 𝐹𝐶(𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡) + 𝑉𝐶(𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝐶𝑜𝑠𝑡)

• 𝑀𝐶 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐶𝑜𝑠𝑡 =𝜕𝑇𝐶

𝜕𝑞

• 𝜋 𝑃𝑟𝑜𝑓𝑖𝑡 = 𝑇𝑅 − 𝑇𝐶

• 𝐴𝑇𝐶 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 =𝑇𝐶

𝑞

• 𝐴𝑉𝐶 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝐶𝑜𝑠𝑡 =𝑉𝐶

𝑞

I will explain it later, graphically and mathematically.

𝑃𝑟𝑖𝑐𝑒 = 50, 𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡 = 100, 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝐶𝑜𝑠𝑡 = 50𝑞 − 11𝑞2 + 𝑞3

0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

Worksheet 2


0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

Revenue

𝑇𝑅(𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒) = 𝑃𝑟𝑖𝑐𝑒 × 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑦 = 50𝑞

𝑞

Marginal – the key concept of economics.

Δ𝑋

Δ𝑞, 𝑜𝑟

𝜕𝑋

𝜕𝑞

𝑋

𝑞

𝑞 𝑞 + 1

Δ𝑞

𝑋(𝑞)

𝑋(𝑞 + 1)Δ𝑋

If I change quantity, how X changes?

Why Marginal is important?

𝑀𝐶 < 𝑀𝑅

We can decide change quantity or not.

If 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐶𝑜𝑠𝑡 < 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒,We should produce more.

While 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐶𝑜𝑠𝑡 > 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒,We shouldn’t produce more.

So, in general, when MC = MR, 𝜋𝑚𝑎𝑥Do you draw “MR” graph?

𝑀𝐶 > 𝑀𝑅


0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

Revenue MR

𝑀𝑅 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 =

𝜕𝑇𝑅

𝜕𝑞=

𝜕(𝑃 × 𝑞)

𝜕𝑞= 𝑃𝑟𝑖𝑐𝑒

𝑀𝑅 = 𝑡𝑎𝑛𝑔𝑒𝑛𝑡 𝑜𝑓 𝑇𝑅

𝑞

In Competitive Market, firms are price takerSo, 𝑀𝑅 = 𝑃𝑟𝑖𝑐𝑒. Which means, consumers are perfectly price elastic(𝒆 = ∞).

Why?If you charge $1 more in competitive market,Consumers buy things from another firm.Remember Amazon Market Place.

Remember, Marginal is: if I change quantity, how X is changed.So, if you sell +1, you got +P revenue.


0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

Revenue TotalCost MR Profit

Do you draw “Total Cost”

and“MC (Marginal Cost)”

graph properly?


0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

TotalCost

TotalCost = 𝐹𝐶 + 𝑉𝐶= 100 + 50𝑞 − 11𝑞2 + 𝑞3

𝑞


0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

TotalCost MC

𝑀𝐶 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝐶ost =𝜕𝑇𝐶

𝜕𝑞= 50 − 22𝑞 + 3𝑞2

MC = Tangent of Total Cost

𝑞

Next, Profit graph!


0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

Revenue TotalCost Profit

𝑃𝑟𝑜𝑓𝑖𝑡: 𝜋(𝑞) = 𝑇𝑅 − 𝑇𝐶= 𝑃𝑞 − 100 + 50𝑞 − 11𝑞2 + 𝑞3

= −100 + 11𝑞2 − 𝑞3

𝑞


0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20



= −100 + 11𝑞2 − 𝑞3

At Point A and C, 𝜋(𝑞) = 0At Point B 𝜋(𝑞) = 𝑀𝐴𝑋

A C

B


0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20



= −100 + 11𝑞2 − 𝑞3

B

This Point B is exactly same as…


0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

MC MR

B

𝑀𝐶(𝑞𝐵) = 𝑀𝑅 (= 𝑃𝑟𝑖𝑐𝑒)

50 − 22𝑞 + 3𝑞2 = 50

𝑞 =22

3



0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

Revenue TotalCost MC MR Profit

B


50 − 22𝑞 + 3𝑞2 = 50

𝑞 =22

3



0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

Revenue TotalCost MC MR Profit

B

These are mathematically same:1)

𝜋(𝑞) = 𝑇𝑅 − 𝑇𝐶When 𝜋 𝑞 = 𝑚𝑎𝑥,

𝜕𝜋 𝑞

𝜕𝑞= 0

2)Profit is max when𝜕𝑇𝑅

𝜕𝑞=

𝜕𝑇𝐶

𝜕𝑞↔ 𝑀𝑅 = 𝑀𝐶

The latter is simpler because We know MR = Price.


0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

AVC ATC


ATC(Average Total Cost) =𝑇𝐶

𝑞= 50 − 11𝑞 + 𝑞2 +

100

𝑞

AVC(Average Variable Cost) =𝑉𝐶

𝑞= 50 − 11𝑞 + 𝑞2

0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

ATC MC


ATC is MINWhere ATC = MC

0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

AVC MC


AVC is MINWhere AVC = MC

0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

AVC ATC MC MR


MIN AVC and MIN ATC is notMC=MR(=P)In general.

0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

Revenue TotalCost VC AVC ATC MC MR


If the companyseek maximum profit,

Where is revenue?Where is profit?

Worksheet 3

𝑅

𝑇𝐶 𝑉𝐶 𝑀𝐶

𝐴𝑇𝐶

𝐴𝑉𝐶

0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20



Step1: Find

𝑀𝐶 𝑞𝑜𝑝𝑡 = 𝑀𝑅

𝑞𝑜𝑝𝑡

0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20



Step1: Find


Step2:This 𝑇𝑅(𝑞𝑜𝑝𝑡) or

The area 𝑃 × 𝑞𝑜𝑝𝑡 is

a Revenue

𝑞𝑜𝑝𝑡

𝑇𝑅(𝑞𝑜𝑝𝑡)

𝑞 =22

3

𝑇𝑅 = 𝑃𝑞 =1100

3

0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20



Step1: Find


Step2:This T𝑅(𝑞𝑜𝑝𝑡) or


a Revenue

Step3:Total Cost is 𝑇𝐶(𝑞𝑜𝑝𝑡)

Or The area 𝐴𝑇𝐶(𝑞𝑜𝑝𝑡) × 𝑞𝑜𝑝𝑡

𝑞𝑜𝑝𝑡


𝑇𝐶(𝑞𝑜𝑝𝑡)

0

50

100

150

200

250

300

350

400

450

500

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20



Step1: Find


Step2:This 𝑇𝑅(𝑞𝑜𝑝𝑡) or


a Revenue

Step3:Total Cost is 𝑇𝐶(𝑞𝑜𝑝𝑡)

Or The area 𝐴𝑇𝐶 × 𝑞𝑜𝑝𝑡

Step4:The profit is 𝑇𝑅 − 𝑇𝐶

OrThe Area (𝑃 − 𝐴𝑇𝐶(𝑞𝑜𝑝𝑡)) × 𝑞𝑜𝑝𝑡

𝑞𝑜𝑝𝑡


𝑇𝐶(𝑞𝑜𝑝𝑡)

profit

0

50

100

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

VC AVC ATC MC MR


Pick up:



a Total Revenue

The area 𝐴𝑇𝐶 × 𝑞𝑜𝑝𝑡

is a Cost

The Area (𝑃 − 𝐴𝑇𝐶(𝑞𝑜𝑝𝑡)) × 𝑞𝑜𝑝𝑡

Is a Profit

𝑞𝑜𝑝𝑡

For explanation purpose,I changed the scale of P-axis

𝐶𝑜𝑠𝑡 =𝐴𝑇𝐶(𝑞𝑜𝑝𝑡) × 𝑞𝑜𝑝𝑡

𝑃𝑟𝑜𝑓𝑖𝑡

0

50

100

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

ATC MC MR


𝑞𝑜𝑝𝑡

Pick up:



a Total Revenue

The area 𝐴𝑇𝐶 × 𝑞𝑜𝑝𝑡

is a Cost

The Area (𝑃 − 𝐴𝑇𝐶(𝑞𝑜𝑝𝑡)) × 𝑞𝑜𝑝𝑡

Is a Profit

We only need these3 curves.

Check every equation:For 𝑃(𝑃𝑟𝑖𝑐𝑒) = 50, 𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡 = 100, 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝐶𝑜𝑠𝑡 = 50𝑞 − 11𝑞2 + 𝑞3

• 𝑇𝑅(𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒) = 𝑃 × 𝑞 = 50𝑞

• 𝑀𝑅(𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒) = 𝑃

• TC(𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡) = 𝐹𝐶 + 𝑉𝐶 = 100 + 50𝑞 − 11𝑞2 + 𝑞3


𝜕𝑞= 50 − 22𝑞 + 3𝑞2

• 𝜋 𝑃𝑟𝑜𝑓𝑖𝑡 = 𝑇𝑅 − 𝑇𝐶 = −100 + 11𝑞2 − 𝑞3


𝑞=

100

𝑞+ 50 − 11𝑞 + 𝑞2


𝑞= 50 − 11𝑞 + 𝑞2

Download and Check Excel

• https://www.dropbox.com/s/7w91ks1jiyvrprz/eshipVC3%20-%20forhandout.xlsx?dl=0

• Sheet Competitive Market

• In group 3-5 ppl, let’s share your finding in 3-5min.

https://www.dropbox.com/s/7w91ks1jiyvrprz/eshipVC3 - forhandout.xlsx?dl=0

0

50

100

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

VC AVC ATC MC

𝑆ℎ𝑢𝑡𝑑𝑜𝑤𝑛 𝑅𝑢𝑙𝑒

I𝐟𝑃 < 𝐴𝑉𝐶,

Company couldn’t Make profit norReduce loss of FC.

So, shutdown.

So, where is the firm’sSupply curve?

𝑞𝑜𝑝𝑡

0

50

100

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

VC AVC ATC MC

𝑆ℎ𝑢𝑡𝑑𝑜𝑤𝑛 𝑅𝑢𝑙𝑒

I𝐟𝑃 < 𝐴𝑉𝐶,

Company couldn’t Make profit norReduce loss of FC.

So, shutdown.

So, where is the firm’sSupply curve?

Here!

Because MC=Price.

𝑞𝑜𝑝𝑡

0

50

100

00

.5 11

.5 22

.5 33

.5 44

.5 55

.5 66

.5 77

.5 88

.5 99

.5 10

10

.5 11

11

.5 12

12

.5 13

13

.5 14

14

.5 15

15

.5 16

16

.5 17

17

.5 18

18

.5 19

19

.5 20

VC AVC ATC MC

Imagine, suddenly the price drops𝑃 = $26

(1)How many you should produce?(2)What is your revenue?(3)What is your profit?(4)Should you shut down?

(5)if you compare the profit with𝑞 = 0,5, 𝑎𝑛𝑑 7

what do you think?

𝑞𝑜𝑝𝑡

𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑠𝑡 = 100, 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝐶𝑜𝑠𝑡 = 50𝑞 − 11𝑞2 + 𝑞3 Worksheet 4

Imagine, suddenly the price drops 𝑃 = $26.

(1) How many you should produce?𝑀𝐶 = 𝑃, so 50 − 22𝑞 + 3𝑞2 = 26 ↔ 𝒒 = 𝟔

(2) What is your revenue?𝑇𝑅 = 𝑃 × 𝑞 = $26 × 6 = $𝟏𝟓6

(3) What is your profit?𝜋 = 𝑇𝑅 − 𝑇𝐶 = $156 − 100 + 50𝑞 − 11𝑞2 + 𝑞3 = $156 − $220 = −$𝟔𝟒You lose money.

(4)Should you shut down? No. because 𝐴𝑉𝐶(𝑞 = 6) = 50 − 11𝑞 + 𝑞2 = $20 and 𝑃 = $26 > 𝐴𝑉𝐶(𝑞 = 6)

(5) if you compare the profit with 𝑞 = 0 and 𝑞 = 5,7 what do you think?

Imagine, suddenly the price drops 𝑃 = $26.

(1) How many you should produce?𝑀𝐶 = 𝑃, so 50 − 22𝑞 + 3𝑞2 = 26 ↔ 𝒒 = 𝟔

(2) What is your revenue?𝑇𝑅 = 𝑃 × 𝑞 = $26 × 6 = $𝟏𝟓6

(3) What is your profit?𝜋 = 𝑇𝑅 − 𝑇𝐶 = $156 − 100 + 50𝑞 − 11𝑞2 + 𝑞3 = $156 − $220 = −$𝟔𝟒You lose money.

(4)Should you shut down? No. because 𝐴𝑉𝐶(𝑞 = 6) = 50 − 11𝑞 + 𝑞2 = $20 and 𝑃 = $26 > 𝐴𝑉𝐶(𝑞 = 6)

(5) if you compare the profit with 𝑞 = 0 and 𝑞 = 5 what do you think?If 𝑞 = 0, T𝑅 = $26 × 0 = 0, so 𝜋 = 𝑇𝑅 − 𝑇𝐶 = 0 − 𝑇𝐶 = −$𝟏𝟎𝟎If 𝑞 = 5, T𝑅 = $26 × 5 = 130, so 𝜋 = 𝑇𝑅 − 𝑇𝐶 = 130 − (100 + 50𝑞 − 11𝑞2 + 𝑞3) = −$𝟕𝟎If 𝑞 = 7, T𝑅 = $26 × 7 = 182, so 𝜋 = 𝑇𝑅 − 𝑇𝐶 = 182 − (100 + 50𝑞 − 11𝑞2 + 𝑞3) = −$𝟕𝟐

So, if we produce 𝑞 = 6, we lose money $64, But this is still better off than other quantity.This is why we should not shut down if 𝑷 > 𝑨𝑽𝑪(𝒔𝒉𝒖𝒕𝒅𝒐𝒘𝒏 𝒓𝒖𝒍𝒆)

𝒃𝒆𝒕𝒕𝒆𝒓 𝒕𝒉𝒂𝒏 𝒅𝒐 𝒏𝒐𝒕𝒉𝒊𝒏𝒈!

Individual firm and market supplyQ=1 Q=2 Q=3 Q=4

David 40 50 80 100

Joe - 40 50 80

Imagine, there are only two producers in the world.And they could produce following Marginal Cost(=individual supply curve)Could you draw a individual supply curve?

𝑄

𝑃

$100

80

5040

1 2 3 4 5 6 7 8

𝑃

$100

80

5040

1 2 3 4𝑞

individual

Worksheet 5

𝑃

$100

80

5040

1 2 3 4𝑞

Individual firm and market supplyMC Q=1 Q=2 Q=3 Q=4

David 40 50 80 100

Joe - 40 50 80

Imagine, there are only two producers in the world.And they could produce following Marginal Cost(=individual supply curve)Could you draw a Market supply curve?

𝑄

𝑃

$100

80

5040

1 2 3 4 5 6 7 8

Market

individual

𝑃

$100

80

5040

1 2 3 4𝑞

Individual firm and market supplyQ=1 Q=2 Q=3 Q=4

David 40 50 80 100

Joe - 40 50 80

Imagine, there are only two producers in the world.And they could produce following Marginal Cost(=individual supply curve)Could you draw a Market supply curve?

𝑄

𝑃

$100

80

5040

1 2 3 4 5 6 7 8

1 + 2 = 3

3 + 4 = 7

2 + 3 = 5

Market

Just horizontal (where same price) sum over the quantity!

Exercise

Let’s draw graph: AVC, ATC, MC when 𝐹𝐶 = 10, 𝑉𝐶 = 0.75𝑞2

Average Variable Cost, Average Total Cost, and Marginal Cost.

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

𝐴𝑇𝐶 =𝑇𝐶

𝑞

𝑀𝐶 =𝜕𝐶

𝜕𝑞

𝐴𝑉𝐶 =𝑉𝐶

𝑞

Ex1

When 𝐹𝐶 = 10, 𝑉𝐶 = 0.75𝑞2

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

AVC ATC MC

𝐴𝑇𝐶 =𝐹𝐶 + 𝑉𝐶

𝑞=

10

𝑞+ 0.75𝑞

𝑀𝐶 =𝜕𝐶

𝜕𝑞= 1.5𝑞


𝑞= 0.75𝑞

Ex1

Let’s write down graph: AVC, ATC, MC when 𝐹𝐶 = 10, 𝑉𝐶 = 4𝑞 − 𝑞2 + 0.1𝑞3

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15


𝑞

𝑀𝐶 =𝜕𝐶

𝜕𝑞


𝑞

Ex2

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15

AVC ATC MC𝐴𝑇𝐶 =𝐹𝐶 + 𝑉𝐶

𝑞=

10

𝑞+ 4 − 𝑞 + 0.1𝑞2

𝑀𝐶 =𝜕𝐶

𝜕𝑞= 4 − 2𝑞 + 0.3𝑞3


𝑞= 4 − 𝑞 + 0.1𝑞2

Let’s write down graph: AVC, ATC, MC when 𝐹𝐶 = 10, 𝑉𝐶 = 4𝑞 − 𝑞2 + 0.1𝑞3

Ex2

Competitive Market in the Long Run

Short Run: Shut down condition𝑃𝑟𝑖𝑐𝑒 < 𝐴𝑉𝐶(𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝐶𝑜𝑠𝑡)

Long Run: Shut down condition

𝑃𝑟𝑖𝑐𝑒 < 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑜𝑠𝑡

Because there are no fixed cost in the long run.

(sell and buy fixed asset in the long run)

Long Run: There are entry and exitIn competitive market, in the long run,

it drives profit to zero.

Cite: https://courses.edx.org/courses/course-v1:MITx+14.100x+3T2016/courseware/65ca1e8e024b4e0aae5d764b31942021/510230ecf173432786c678ab0591cf5d/?activate_block_id=block-v1%3AMITx%2B14.100x%2B3T2016%2Btype%40sequential%2Bblock%40510230ecf173432786c678ab0591cf5d

If firms making profit,

Another company will enter into the market in the long run. So the supply curve become flatten(𝑆𝑅1 → 𝑆𝑅2).

The Price will decrease (𝑃1 → 𝑃2)

And Individual firm lose quantity(𝑞1 → 𝑞2)

Long Run: There are entry and exitIn competitive market, in the long run,

it drives profit to zero.

Cite: https://courses.edx.org/courses/course-v1:MITx+14.100x+3T2016/courseware/65ca1e8e024b4e0aae5d764b31942021/510230ecf173432786c678ab0591cf5d/?activate_block_id=block-v1%3AMITx%2B14.100x%2B3T2016%2Btype%40sequential%2Bblock%40510230ecf173432786c678ab0591cf5d

𝑆𝑅3

𝑄3𝑞3

𝜋3 = 0

More entry till the profit=0

This point is most efficient to produce because ATC is MIN.

Short Run Cost VS Long Run CostIn the short run, your Average Total Cost is like this:

Heavy fixed cost Over Capacity

- Overtime rate charge- Diminishing Productivity

Your work is digging a hole.Your company has only 1 scoop.Due to high demand, your firmdecide to hire +1 worker.But there are no scoop.

Short Run Cost VS Long Run CostIn the Long run, your firm could build new plant

Because you could use Capital(K)

Huge plant needs More cost at first.

They are more productive.

But still have limitation.

Short Run Cost VS Long Run CostIf we made 3 plants in the long run, our cost curve is

Yellow dotted line.

Short Run Cost VS Long Run CostBut in the long run, managers could decide build a plant with target quantity in every K(capital) level. Which means there are infinite option. So the Yellow dotted line is LRMC.In general this is more efficient (low price same quantity) for firms than SRMC.

Monopoly

Monopolistic Market

• Government sometimes allows monopoly to infrastructure companies.• Ex: Electric Power Company, Telecom

Company, Post Office,…

• Only one seller and many buyers.

• No close substitutes

• Barriers to entry

• Monopolistic Company is Price Maker.

Monopolistic Market

The firm is price maker, but they are not almighty.

Because consumers could react. If you set $100 for an ordinal candy,no one want to buy it so company couldn’t make profit.

• 𝜋 = 𝑇𝑅 − 𝑇𝐶

•𝜕𝜋

𝜕𝑄= 𝑀𝑅 − 𝑀𝐶 = 0 ⇒ 𝜋𝑚𝑎𝑥

• This when 𝜋𝑚𝑎𝑥 ⇒ 𝑀𝑅 = 𝑀𝐶 rule is still same as monopoly.

Competitive market VS Monopolistic Market

𝑃

𝑞

𝑞 𝑞 + 1

𝑃1

𝐴 𝐵

Demand curve

Consumers in Competitive market isPerfect price elastic.So, 𝑀𝑅 = 𝑃1 (𝑞 + 1) − 𝑞 = 𝐵

𝑃

𝑄

Q 𝑄 + 1

𝑃1

𝐴 𝐵

Demand curve

𝐶𝑃2

Consumers in Monopolistic market ismoderate price elastic.

So, 𝑀𝑅 =Δ𝑅

Δ𝑄=

(𝑃2 𝑄+1 −𝑃1𝑄)

𝑄+1 −𝑄= 𝐵 − 𝐶

So, monopolist lose revenue sometimes when they produce and sell more.

Monopolistic Market Example

• Demand Curve is 𝑄𝐷 𝑃 = 20 − 𝑃

(1)What is MR for monopolist?

(2)Draw MR and Demand Curve

𝑃

𝑄

20

20

10

10

Worksheet 6


• Demand Curve is 𝑄𝐷 𝑃 : 𝑃 = 20 − 𝑄↔ 𝑃 = 20 − 𝑄

• 𝑇𝑅 = 𝑃𝑄

• 𝑀𝑅 =𝜕𝑃𝑄

𝜕𝑄you can rewrite it if you like: (= 𝑃 + 𝑄

𝜕𝑃

𝜕𝑄)

• here, we differentiate by Q. so, we would like to re-write TR by TR(Q)

• 𝑇𝑅 = 𝑃𝑄 = 20 − 𝑄 × 𝑄 = 20𝑄 − 𝑄2


𝜕𝑄=

𝜕(20𝑄−𝑄2)

𝜕𝑄= 20 − 2𝑄

𝑃

𝑄

20

Demand curve

20

10

10

MR

Worksheet 6

[advanced] Monopolistic and competitive


𝜕𝑄you can rewrite it if you like: (= 𝑃 + 𝑄

𝜕𝑃

𝜕𝑄)


𝜕𝑄= 𝑃 + 𝑄

𝜕𝑃

𝜕𝑄

If competitive market,This term is 0

So, 𝑀𝑅 = 𝑃

Worksheet 6

[advanced] Monopolistic and competitive • In addition to that, we know

Elasticity 𝑒 =Δ𝑄/𝑄

Δ𝑃/𝑃=

P

Q

ΔQ

ΔP

So, transform MR to this form:


𝜕𝑄= 𝑃 + 𝑄

𝜕𝑃

𝜕𝑄= 𝑃 + 𝑄

𝑃

𝑃

𝜕𝑃

𝜕𝑄

• = 𝑃 + 𝑃𝑄

𝑃

𝜕𝑃

𝜕𝑄

• This is1

𝑒so, 𝑴𝑹 = 𝑷(𝟏 +

𝟏

𝒆)

• And if 𝑒 ⇒ ∞(Competitive Market),1

𝑒⇒ 0 𝑠𝑜 𝑀𝑅 ⇒ 𝑃

Monopolistic Market

The firm is price maker, but they are not almighty.

Because consumers could react. If you set $100 for an ordinal candy,no one want to buy it so company couldn’t make profit.

• 𝜋 = 𝑇𝑅 − 𝑇𝐶

•𝜕𝜋

𝜕𝑄= 𝑀𝑅 − 𝑀𝐶 = 0 ⇒ 𝜋𝑚𝑎𝑥

• 𝝅𝒎𝒂𝒙 ⇒ 𝑴𝑹 = 𝑴𝑪 rule is still same as monopoly.



• We know


𝜕𝑄=

𝜕(20𝑄−𝑄2)

𝜕𝑄= 20 − 2𝑄

So, If Cost function is 𝐓𝐂 = 𝟐 + 𝑸𝟐

• A monopolist will supply what quantity at what price?

𝑃

𝑄

20

Demand curve

20

10

10

MR

Worksheet 6-2



• We know


𝜕𝑄=

𝜕(20𝑄−𝑄2)

𝜕𝑄= 20 − 2𝑄

• TC = 2 + 𝑄2

• MC= 𝜕𝑇𝐶

𝜕𝑄= 2𝑄

• When MR=MC, that is 20 − 2𝑄＝2𝑄

• 𝑄 = 5, 𝑃 = 20 − 𝑄 = 15

𝑃

𝑄

20

Demand curve

20

10

10

MR

𝑀𝐶 = 2𝑄

5

15


We know

• Demand Curve is 𝑄𝐷 𝑃 : 𝑃 = 20 − 𝑄and 𝑇𝐶 = 2 + 𝑄2

What is the Revenue, Cost, and Profit?

• If we produce Q=3,4,…7How our Revenue /Profit Changes?

• What is DWL(Deadweight Loss)?

𝑃

𝑄

20

Demand curve

20

10

10

MR

𝑀𝐶 = 2𝑄

5

15Q TR TC 𝜋

3

4

5

6

7

Worksheet 6-3



• 𝑇𝑅 = 𝑃𝑄 = 20𝑄 − 𝑄2

• TC = 2 + 𝑄2

𝑃

𝑄

20

Demand curve

20

10

10

MR

𝑀𝐶 = 2𝑄

5

15

Q TR TC 𝜋

3 51 11 40

4 64 18 46

5 75 27 48

6 84 38 46

7 91 51 40

Worksheet 6-3

𝐷𝑊𝐿

Exercise

Monopolistic Market Example 2

• Demand Curve is 𝑄𝐷 𝑃 : 𝑃 = 24 − 𝑄

• Cost Function is: TC = 12 + 𝑄2

1. A monopolist will supply what quantity at what price?

2. Draw, Demand Curve, MR, MC

3. Then Draw AVC, ATC

4. Show on the graph, Revenue and Profit

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

AVC ATC Demand MR MC𝑃

𝑄

Worksheet 7

Monopolistic Market Example 2• Demand Curve is 𝑄𝐷 𝑃 : 𝑃 = 24 − 𝑄

• Cost Function is: TC = 12 + 𝑄2

1. A monopolist will supply what quantity at what price?

2. Draw, Demand Curve, MR, MC

3. Then Draw AVC, ATC

4. Show on the graph, Revenue and Profit

HINT:

• 𝑇𝑅(𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒) = 𝑃 × 𝑄

• 𝑀𝑅(𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒) =𝜕𝑇𝑅

𝜕𝑄


𝜕𝑄

• 𝜋 𝑃𝑟𝑜𝑓𝑖𝑡 = 𝑇𝑅 − 𝑇𝐶


𝑄


𝑄 0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

AVC ATC Demand MR MC

Worksheet 7

Monopolistic Market Example 2Given, Demand Curve is 𝑸𝑫 𝑷 : 𝑷 = 𝟐𝟒 − 𝑸

Cost Function is: 𝑻𝑪 = 𝟏𝟐 + 𝑸𝟐

• 𝑇𝑅 𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 = 𝑃 × 𝑄 = 24𝑄 − 𝑄2


𝜕𝑄= 24 − 2𝑄


𝜕𝑄= 2𝑄

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25


Worksheet 7





𝜕𝑄= 24 − 2𝑄


𝜕𝑄= 2𝑄

𝜋𝑚𝑎𝑥 ⇒ 𝑀𝑅 = 𝑀𝐶24 − 2𝑄 = 2𝑄

↔ 𝑄 = 6

So, what’s next?How to figure out Price?

Remember, monopolist is not almighty.The firm should respect Demand curve.

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Demand MR MC

Worksheet 7





𝜕𝑄= 24 − 2𝑄


𝜕𝑄= 2𝑄

𝜋𝑚𝑎𝑥 ⇒ 𝑀𝑅 = 𝑀𝐶24 − 2𝑄 = 2𝑄

↔ 𝑄 = 6

So, what’s next?How to figure out Price?

Remember, monopolist is not almighty.The firm should respect Demand curve.

So, Graphically, here is a price!

Mathematically, assign Q=6 to Demand Curve 𝑷 = 𝟐𝟒 − 𝑸 so, 𝑃 = 18

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Demand MR MC

here

Worksheet 7




• 𝑃 = 18, 𝑄 = 6

• 𝜋 𝑃𝑟𝑜𝑓𝑖𝑡 = 𝑇𝑅 − 𝑇𝐶 = 60• 𝑇𝑅 = 144 − 36 = 108

• 𝑇𝐶 = 48

Next, ATC, AVC

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Demand MR MC

18

Worksheet 7

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25



Next, ATC

𝑇𝐶 = 12 + 𝑄2


𝑄=

12

𝑄+ 𝑄


𝑄= 𝑄

Next, Where is Revenue, Cost and Profit?

18

Variable Cost

Fixed Cost

Worksheet 7-2

0

5

10

15

20

25

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25



𝑃 = 1818

𝑇𝑅 = 𝑃 × 𝑄= 18 × 6 = 108

𝑇C =ATC × 𝑄

= 8 × 6 = 48

𝑄

Rest of them are profit.You can simulate on excel.

Worksheet 7-2


𝑄=

12

𝑄+ 𝑄

𝑎𝑠𝑠𝑖𝑔𝑛 𝑄 = 6

Download and Check Excel

• https://www.dropbox.com/s/7w91ks1jiyvrprz/eshipVC3%20-%20forhandout.xlsx?dl=0

(same excel as before)

• Sheet Monopoly

• In group 3-5 ppl, let’s share your finding in 3-5min.

https://www.dropbox.com/s/7w91ks1jiyvrprz/eshipVC3 - forhandout.xlsx?dl=0

Problem solving procedure.For Competitive Market For Monopoly Market

Step1: Find out optimal quantity, which means find 𝑞𝑜𝑝𝑡 where profit 𝜋 𝑞𝑜𝑝𝑡 = 𝑚𝑎𝑥.

• 𝑞𝑜𝑝𝑡 is where Marginal Revenue equals to Marginal Cost. Which is 𝑀𝑅 = 𝑀𝐶

• 𝑀𝐶 =𝜕𝑇𝐶

𝜕𝑞=

𝜕𝑉𝐶

𝜕𝑞, where TC=Total Cost, VC=Variable Cost.

𝑀𝑅 = 𝑃(price)

To know 𝑀𝑅 =𝜕𝑇𝑅

𝜕𝑄, We should calculate T𝑅 = 𝑃 × Q

We know Demand Curve 𝑃 𝑄 = 𝒂 − 𝒃𝑸 (or 𝑄2 or something)To differentiate by 𝑄, we use 𝒂 − 𝒃𝑸 as 𝑃 to earn TR. So T𝑅 = 𝑃 × Q = 𝒂 − 𝒃𝑸 × 𝑄 = 𝑎𝑄 − 𝑏𝑄2, so we’ll have MR.

Solve 𝑀𝑅 = 𝑀𝐶, we got optimal 𝑄𝑜𝑝𝑡

Step2: Find out optimal Total Revenue(TR), Total Cost(TC), and Profit (𝜋).

First of all, we need Price 𝑃.

We already know Price 𝑃Find out 𝑃𝑜𝑝𝑡 using Demand Curve.

Assign 𝑄𝑜𝑝𝑡 to 𝑃 𝑄 = 𝒂 − 𝒃𝑸, we got 𝑃𝑜𝑝𝑡

Using 𝑇𝑅𝑜𝑝𝑡 = 𝑃𝑜𝑝𝑡 × Qopt, 𝑇𝐶𝑜𝑝𝑡 = 𝑇𝐶(Qopt), we get TR and TC.

To know TC, we could use Average Total Cost 𝐴𝑇𝐶. 𝐴𝑇𝐶 𝑄𝑜𝑝𝑡 × 𝑄𝑜𝑝𝑡 = 𝑇𝐶𝑜𝑝𝑡

𝜋 𝑞𝑜𝑝𝑡 = 𝑇𝑅𝑜𝑝𝑡 − 𝑇𝐶𝑜𝑝𝑡.

If you want to know more, check Entrepreneurial Economics #1

• https://www.slideshare.net/ryouen/170902-entrepreneurial-economics-v4-80086316• Covered:

• Price Elasticity

• Demand / Supply curve shift

• Welfare and Deadweight Loss

• Marginal Rate of Substitute and indifference curve

https://www.slideshare.net/ryouen/170902-entrepreneurial-economics-v4-80086316

ReferenceNUS MBA BMA5001 Lecture Note 3, 6, 7

Principles of Microeconomics (Mankiw's Principles of Economics)

MITx: 14.100x Microeconomics

https://en.wikiquote.org/wiki/Greg_Mankiw#Ch._1._Ten_Principles_of_EconomicsAmazon.com

https://courses.edx.org/courses/course-v1:MITx+14.100x+3T2016/course/

https://en.wikiquote.org/wiki/Greg_Mankiw#Ch._1._Ten_Principles_of_Economics

Thank you !!

170925 entrepreneurial economics2

Economy & Finance