❊❝♦♥♦♠✐❝ ❢♦r❡❝❛st✐♥❣ ❛♥❞ ♣♦❧✐❝② ❛♥❛❧②s✐s ✇✐t❤ ❛♥ ❡♠♣✐r✐❝❛❧❧② ❡st✐♠❛t❡❞ ❛❣❡♥t✲❜❛s❡❞ ♠♦❞❡❧ ❢♦r ❆✉str✐❛

❊❝♦♥♦♠✐❝ ❢♦r❡❝❛st✐♥❣ ❛♥❞ ♣♦❧✐❝② ❛♥❛❧②s✐s ✇✐t❤

❛♥ ❡♠♣✐r✐❝❛❧❧② ❡st✐♠❛t❡❞ ❛❣❡♥t✲❜❛s❡❞ ♠♦❞❡❧ ❢♦r

❆✉str✐❛

❙❡❜❛st✐❛♥ P♦❧❡❞♥❛^✶ ▼✐❝❤❛❡❧ ▼✐❡ss^✷

✶■♥t❡r♥❛t✐♦♥❛❧ ■♥st✐t✉t❡ ❢♦r ❆❞✈❛♥❝❡❞ ❙②st❡♠s ❆♥❛❧②s✐s ✭■■❆❙❆✮✱ ▲❛①❡♥❜✉r❣

■♥st✐t✉t ❢ür ❍ö❤❡r❡ ❙t✉❞✐❡♥ ✭■❍❙✮✱ ❲✐❡♥

✷❊♥✈✐r♦♥♠❡♥t ❆❣❡♥❡♥❝② ❆✉str✐❛ ✭❯♠✇❡❧t❜✉♥❞❡s❛♠t✮✱ ❲✐❡♥

■♥st✐t✉t ❢ür ❍ö❤❡r❡ ❙t✉❞✐❡♥ ✭■❍❙✮✱ ❲✐❡♥

■♥st✐t✉t❡ ❢♦r ❊❝♦❧♦❣✐❝❛❧ ❊❝♦♥♦♠✐❝s✱ ❲❯ ❲✐❡♥

Pr❡s❡♥t❛t✐♦♥ ❝♦♥❢❡r❡♥❝❡ ✧❊❱■❉❊◆❈❊✲❇❆❙❊❉ P❖▲■❈❨ ▼❆❑■◆● ✭❲■❋❖✱ ■❍❙ ❛♥❞

❈❊❯✮✧✱ ▼❛② ✷✼^t❤ ✷✵✷✶

✶ ✴ ✺✵

INSTITUTE FOR ECOLOGICAL ECONOMICS

❖✉t❧✐♥❡ ♦❢ ♣r❡s❡♥t❛t✐♦♥

✶✳ ■♥tr♦❞✉❝❡ ✐♥t♦ ❆❇▼

✷✳ ❋♦❝✉s ♦♥ ❞❛t❛ s♦✉r❝❡s ❢♦r ❆❇▼

◮ ◆❛t✐♦♥❛❧ ❛❝❝♦✉♥t✐♥❣ ❞❛t❛

◮ ❆❞❞✲✐♥ ♦❢ ❙❛❜✐♥❛ ❞❛t❛

✸✳ ❋♦r❡❝❛st✐♥❣ ♦♥ ❞✐✛❡r❡♥t ❧❡✈❡❧s ♦❢ ❣r❛♥✉❧❛r✐t②

✹✳ ❆♣♣❧✐❝❛t✐♦♥ ♦❢ ❆❇▼ t♦ ❡st✐♠❛t✐♥❣ t❤❡ ❡❝♦♥♦♠✐❝ ✐♠♣❛❝ts ♦❢ ❈❖❱■❉✲✶✾ ✐♥ ❆✉str✐❛

✷ ✴ ✺✵

❖✈❡r❛r❝❤✐♥❣ ✐❞❡❛s ❛♥❞ r❡s❡❛r❝❤ ❛❣❡♥❞❛ ❢♦r ❆❇▼

◮ ❯s❡ ❉❛t❛ ❢r♦♠ ♥❛t✐♦♥❛❧ ❛❝❝♦✉♥ts t♦ ❡st✐♠❛t❡ ❆❇▼ t♦ ❛ ♥❛t✐♦♥❛❧ ❡❝♦♥♦♠②

✭❆✉str✐❛✮✳

◮ ❑❡❡♣ ❆❇▼ s✐♠♣❧❡ ✕ ♥♦ ❢r❡❡ ♣❛r❛♠❡t❡rs✳

◮ ❯s❡ P❛r❛♠❡t❡r✲❢r❡❡ ❛❞❛♣t✐✈❡ ❧❡❛r♥✐♥❣ ❢♦r ❡①♣❡❝t❛t✐♦♥ ❢♦r♠❛t✐♦♥✳

◮ ❈♦♥str✉❝t ❛♥ ❆❇▼ ✇✐t❤♦✉t ❛♥ ✐♥✐t✐❛❧ tr❛♥s✐❡♥t ✭❜✉r♥✲✐♥✮ ♣❤❛s❡✳

◮ ❱❛❧✐❞❛t✐♦♥✿ ❈♦♠♣❛r❡ ❢♦r❡❝❛st✐♥❣ ♣❡r❢♦r♠❛♥❝❡ ♦❢ ❆❇▼ t♦ t❤❛t ♦❢ st❛♥❞❛r❞

♠♦❞❡❧s✱ ❡✳❣✳ ✭s✐♠♣❧❡✮ t✐♠❡s s❡r✐❡s ♠♦❞❡❧s ❛♥❞ ❛ st❛♥❞❛r❞ ❉❙●❊ ♠♦❞❡❧✳

❖✉t❧♦♦❦✿ ❈❛♥ t❤❡ ❝♦♥str✉❝t✐♦♥ ♦❢ t❤✐s t②♣❡ ♦❢ ❡♠♣✐r✐❝❛❧❧② ❡st✐♠❛t❡❞ ❆❇▼s ❜❡ ❛ ✇❛② t♦

❛❞❞r❡ss t❤❡ ▲✉❝❛s ❝r✐t✐q✉❡ ❢r♦♠ ❛ ♥❡✇ ❛♥❣❧❡✱ ✐✳❡✳

◮ ■♥❝♦r♣♦r❛t❡ ❞❡t❛✐❧❡❞ ♠✐❝r♦✲❢♦✉♥❞❛t✐♦♥s✱ ❢♦r✇❛r❞ ❧♦♦❦✐♥❣ ❜❡❤❛✈✐♦✉r ✰ ❡♥❞♦❣❡♥♦✉s

♠♦❞❡❧ ❞②♥❛♠✐❝s ♦❢ ❡❝♦♥♦♠② ❛s ❛ ❝♦♠♣❧❡① s②st❡♠ ✭❡♠❡r❣❡♥❝❡✮✱

◮ ❈♦♠♣❡♥s❛t✐♥❣ ❢♦r ♣♦t❡♥t✐❛❧ ✇❡❛❦♥❡ss❡s ♦❢ ♠♦r❡ st❛♥❞❛r❞ ❛♣♣r♦❛❝❤❡s s✉❝❤ ❛s

❉❙●❊ ♠♦❞❡❧s✱ ❛♥❞ s❛t✐s❢②✐♥❣ t❤❡ ▲✉❝❛s ❝r✐t✐q✉❡ ❛t t❤❡ s❛♠❡ t✐♠❡❄

✸ ✴ ✺✵

INSTITUTE FOR ECOLOGICAL ECONOMICS

❊❝♦♥♦♠✐❝ ❢♦r❡❝❛st✐♥❣✿ ❆❇▼ ❢♦r ❛ s♠❛❧❧ ♦♣❡♥ ❡❝♦♥♦♠②

❆♥ ❡♠♣✐r✐❝❛❧ ❆❇▼ t❤❛t ❞❡♣✐❝ts t❤❡ ♥❛t✐♦♥❛❧ ❡❝♦♥♦♠② ♦❢ ❆✉str✐❛✳

◮ ■♥❝♦r♣♦r❛t❡s ❛❧❧ ❡❝♦♥♦♠✐❝ ❛❝t✐✈✐t✐❡s ✭♣r♦❞✉❝✐♥❣ ❛♥❞ ❞✐str✐❜✉t✐✈❡ tr❛♥s❛❝t✐♦♥s✮ ❛s

❝❧❛ss✐✜❡❞ ❜② t❤❡ ❊✉r♦♣❡❛♥ s②st❡♠ ♦❢ ❛❝❝♦✉♥ts ✭❊❙❆✮✳

◮ ■♥❝❧✉❞❡s ❛❧❧ ❡❝♦♥♦♠✐❝ ❡♥t✐t✐❡s✿ ❛❧❧ ❥✉r✐❞✐❝❛❧ ❛♥❞ ♥❛t✉r❛❧ ♣❡rs♦♥s ❛r❡ r❡♣r❡s❡♥t❡❞ ❜②

❛❣❡♥ts✳

◮ ■♥t❡❣r❛t❡s ❞❛t❛ ❢r♦♠ ✐♥♣✉t✲♦✉t♣✉t t❛❜❧❡s ✭■❖❚s✮✱ ♥❛t✐♦♥❛❧ ❛♥♥✉❛❧ s❡❝t♦r ❛❝❝♦✉♥ts

✭◆❆❙❆✮✱ ❣♦✈❡r♥♠❡♥t st❛t✐st✐❝s✱ ❝❡♥s✉s ❛♥❞ ❜✉s✐♥❡ss ❞❡♠♦❣r❛♣❤② ❞❛t❛✱ ❛♥❞

❜✉s✐♥❡ss s✉r✈❡②s✳

◮ ❇❡❤❛✈✐♦✉r❛❧ ❡q✉❛t✐♦♥s ✉s❡❞ ❛r❡ st❛♥❞❛r❞ ✐♥ ❧✐t❡r❛t✉r❡✱ ❡✳❣✳

❬❉❡❧❧✐ ●❛tt✐ ❡t ❛❧✳✱ ✷✵✶✶✱ ❆ss❡♥③❛ ❡t ❛❧✳✱ ✷✵✶✺❪

◮ P❛r❛♠❡t❡rs ❛r❡ ❡st✐♠❛t❡❞ r❛t❤❡r t❤❛♥ ❝❛❧✐❜r❛t❡❞✱ ♥♦ ❢r❡❡ ♣❛r❛♠❡t❡rs✱

◮ →◆♦ ✏❜✉r♥✲✐♥✑ ♣❤❛s❡✳

◮ ❊♠♣✐r✐❝❛❧ ✈❛❧✐❞❛t✐♦♥✿ ❝♦♠♣❛r❡ ♦✉t✲♦❢✲s❛♠♣❧❡ ♣r❡❞✐❝t✐♦♥ ♣❡r❢♦r♠❛♥❝❡ ♦❢ t❤❡ ❆❇▼

✇✐t❤ t❤❛t ♦❢ ❛✉t♦r❡❣r❡ss✐✈❡ ✭❆❘✮✱ ✈❡❝t♦r ❛✉t♦r❡❣r❡ss✐✈❡ ✭❱❆❘✮ ❛♥❞ ❉❙●❊ ♠♦❞❡❧s

❡st✐♠❛t❡❞ ♦♥ t❤❡ s❛♠❡ ♦❜s❡r✈❛❜❧❡ t✐♠❡ s❡r✐❡s✳

✹ ✴ ✺✵

❆❣❡♥ts ✫ ♠❛r❦❡ts

❆❣❡♥ts✿

◮ ◆♦♥✲✜♥❛♥❝✐❛❧ ❝♦r♣♦r❛t✐♦♥s ✭✜r♠ s❡❝t♦r✮✱ ❧✐♠✐t❡❞ ❝♦♠♣❛♥✐❡s ❛♥❞ s❡❧❢✲❡♠♣❧♦②❡❞ ✕ ❝❛✳

✻✵✵ ✵✵✵ ✜r♠ ❛❣❡♥ts✳

◮ ❋✐♥❛♥❝✐❛❧ ❝♦r♣♦r❛t✐♦♥s ✭❜❛♥❦✐♥❣ s❡❝t♦r✮✱ ♦♥❡ r❡♣r❡s❡♥t❛t✐✈❡ ❜❛♥❦✳

◮ ❍♦✉s❡❤♦❧❞s ✭✐♥❞✐✈✐❞✉❛❧ ♣❡rs♦♥s✮ ✲ ❝❛✳ ✽✳✷ ♠✐❧❧✐♦♥ ❤♦✉s❡❤♦❧❞ ❛❣❡♥ts✿

◮ ❊♠♣❧♦②❡❞ ✭❛❝t✐✈❡ ♦♥ ❧❛❜♦r ♠❛r❦❡t✮✱

◮ ❯♥❡♠♣❧♦②❡❞ ✭✐♥✈♦❧✉♥t❛r✐❧② ✐❞❧❡✮✱

◮ ■♥✈❡st♦r ✭♦✇♥ ✜r♠s✮✱

◮ ■♥❛❝t✐✈❡ ❤♦✉s❡❤♦❧❞s ✭♥♦t ❛❝t✐✈❡ ♦♥ ❧❛❜♦r ♠❛r❦❡t✱ r❡❝❡✐✈❡ s♦❝✐❛❧ ❜❡♥❡✜ts✮✳

◮ ●❡♥❡r❛❧ ❣♦✈❡r♥♠❡♥t✳

▼❛r❦❡ts✿ ❝❤❛r❛❝t❡r✐③❡❞ ❜② s❡❛r❝❤ ✫ ♠❛t❝❤✐♥❣

◮ ✻✹ ❞✐✛❡r❡♥t ♣r♦❞✉❝ts ❛❝❝♦r❞✐♥❣ t♦ s❡❝t♦r❛❧ str✉❝t✉r❡ ❛s ✐♥ ■❖❚✱

◮ ❚❤❡s❡ ♣r♦❞✉❝ts ❝❛♥ ❜❡ ✉s❡❞ ❢♦r ❝♦♥s✉♠♣t✐♦♥✱ ♦r ❢♦r ✐♥✈❡st♠❡♥t✴✐♥t❡r♠❡❞✐❛t❡

✐♥♣✉ts ✭❞✐✛❡r❡♥t ♠❛r❦❡ts✮✱

◮ ❆❞❞✐t✐♦♥❛❧ ♠❛r❦❡ts✿ ❧❛❜♦✉r✱ ❝r❡❞✐t ❛♥❞ ❞❡♣♦s✐ts✳

✺ ✴ ✺✵

INSTITUTE FOR ECOLOGICAL ECONOMICS

▼❛❥♦r ❊❝♦♥♦♠✐❝ ❆❣❡♥ts ❛♥❞ t❤❡✐r ■♥t❡r❛❝t✐♦♥s

✻ ✴ ✺✵

❆❣❡♥t ❜❡❤❛✈✐♦r

◮ ❊❛❝❤ ✜r♠ ❝❤♦♦s❡s ✐ts s✉♣♣❧②✱ ♣r✐❝❡s✱ ♣r♦❞✉❝t✐♦♥ ❛♥❞ ✐♥✈❡st♠❡♥t✿

◮ ❙✉♣♣❧② ❈❤♦✐❝❡ ❛❝❝♦r❞✐♥❣ t♦ ❡①♣❡❝t❡❞ ❞❡♠❛♥❞ ✭❡①♣❡❝t❡❞ r❡❛❧ ❡❝♦♥♦♠✐❝ ❣r♦✇t❤✮✱

◮ Pr✐❝✐♥❣ ❛❝❝♦r❞✐♥❣ t♦ ❡①♣❡❝t❡❞ ❝♦sts ✭❡①♣❡❝t❡❞ ✐♥✢❛t✐♦♥✮✱

◮ Pr♦❞✉❝t✐♦♥ ❜② ❧✐♠✐t❛t✐♦♥❛❧ ✭▲❡♦♥t✐❡❢✮ ♣r♦❞✉❝t✐♦♥ t❡❝❤♥♦❧♦❣②✱

◮ ■♥✈❡st♠❡♥t ❛❝❝♦✉♥t✐♥❣ ❢♦r ❡①♣❡❝t❡❞ ✇❡❛r ❛♥❞ t❡❛r ♦❢ ❝❛♣✐t❛❧✳

◮ ❘❡❛❧✐③❡❞ s❛❧❡s✿ ♠✐♥✐♠✉♠ ♦❢ s✉♣♣❧② ❝❤♦✐❝❡✱ ❞❡♠❛♥❞✱ ❛♥❞ ♣r♦❞✉❝t✐♦♥ ♣♦ss✐❜✐❧✐t✐❡s

✭s❡❛r❝❤ ✫ ♠❛t❝❤✐♥❣✮✳

◮ ❊❛❝❤ ❤♦✉s❡❤♦❧❞ ❡①♣❡❝ts ♥♦♠✐♥❛❧ ❞✐s♣♦s❛❜❧❡ ✐♥❝♦♠❡ Y_h^e(t) ❞❡♣❡♥❞✐♥❣ ♦♥ t❤❡

❛❝t✐✈✐t② st❛t✉s ❛♥❞ ❡①♣❡❝t❡❞ ✐♥✢❛t✐♦♥✳

◮ s♣❡♥❞s ❛ ✭✜①❡❞✮ ❢r❛❝t✐♦♥ ♦❢ t❤✐s ❡①♣❡❝t❡❞ ✐♥❝♦♠❡ ♦♥ ❝♦♥s✉♠♣t✐♦♥ ❛♥❞ ✐♥✈❡st♠❡♥t✳

◮ ❚❤❡ ❣❡♥❡r❛❧ ❣♦✈❡r♥♠❡♥t ♠❛✐♥❧② ❛❝ts ❛s ❛ ❝♦♥s✉♠❡r ✭❣♦✈❡r♥♠❡♥t ❝♦♥s✉♠♣t✐♦♥✮

❛♥❞ ❛s ❛ ✬r❡❞✐str✐❜✉t✐♦♥❛❧✬ ❡♥t✐t②✳

◮ ❚❤❡ ❜❛♥❦✐♥❣ s❡❝t♦r t❛❦❡s ❞❡♣♦s✐ts ❢r♦♠ ✜r♠s ❛♥❞ ❤♦✉s❡❤♦❧❞s✱ ❡①t❡♥❞s ❧♦❛♥s t♦

✜r♠s✱ ❛♥❞ r❡❝❡✐✈❡s ❛❞✈❛♥❝❡s ❢r♦♠ ♦r ❞❡♣♦s✐ts r❡s❡r✈❡s ❛t t❤❡ ❝❡♥tr❛❧ ❜❛♥❦✳

◮ ■♥t❡r❡st r❛t❡s r(t)❛r❡ ❞❡t❡r♠✐♥❡❞ ❜② ♠❡❛♥s ♦❢ ❛ ✜①❡❞ r✐s❦ ♣r❡♠✐✉♠ µ♦✈❡r t❤❡

♣♦❧✐❝② r❛t❡ r(t)¯ s❡t ❜② t❤❡ ❝❡♥tr❛❧ ❜❛♥❦ ❛❝❝♦r❞✐♥❣ t♦ ❛ ❚❛②❧♦r r✉❧❡✳

✼ ✴ ✺✵

INSTITUTE FOR ECOLOGICAL ECONOMICS

❊①♣❡❝t❛t✐♦♥s ✕ ♣❛r❛♠❡t❡r✲❢r❡❡ ❛❞❛♣t✐✈❡ ❧❡❛r♥✐♥❣

P❛r❛♠❡t❡r✲❢r❡❡ ❛❞❛♣t✐✈❡ ❧❡❛r♥✐♥❣✿ ❆❣❡♥ts ✭✜r♠s ❛♥❞ ❤♦✉s❡❤♦❧❞s✮ ❛❝t ❛s

❡❝♦♥♦♠❡tr✐❝✐❛♥s ✇❤♦ ❡st✐♠❛t❡ t❤❡ ♣❛r❛♠❡t❡rs ♦❢ t❤❡✐r ♠♦❞❡❧ t♦ ♠❛❦❡ ❢♦r❡❝❛sts ♦❢ ❦❡②

♠❛❝r♦❡❝♦♥♦♠✐❝ ❛❣❣r❡❣❛t❡s✳

❊①♣❡❝t❛t✐♦♥s✿ ❢♦r♠❡❞ ❛❝❝♦r❞✐♥❣ t♦ ❛♥ ❛✉t♦r❡❣r❡ss✐✈❡ ♠♦❞❡❧ ♦❢ ❧❛❣ ♦r❞❡r ♦♥❡ ✭❆❘✭✶✮✮✳

❆❘ ♠♦❞❡❧s✿ ❉❡♣❡♥❞❡♥t ✈❛r✐❛❜❧❡x(t) ❡①♣❧❛✐♥❡❞ ❜② ✐ts ❧❛❣✭s✮ ✉♣ t♦ ♦r❞❡r ♣✱ ❛♥❞ ❛♥ ❡rr♦r t❡r♠ǫ(t)✳

❚❤❡ ❡①♣❡❝t❡❞ r❡❛❧ ❣r♦✇t❤ r❛t❡γ^e(t) ❛♥❞ t❤❡ ❡①♣❡❝t❡❞ ✐♥✢❛t✐♦♥ r❛t❡ π^e(t) ❛r❡ ✐♥❢❡rr❡❞

❢r♦♠ ❛❣❡♥ts✬ ♣r❡❞✐❝t✐♦♥s ♦❢ ✭❡①♣❡❝t❡❞✮ ❣r♦ss ❞♦♠❡st✐❝ ♣r♦❞✉❝t ✭r❡❛❧ ●❉P✱ ✐♥ ❧♦❣ ❧❡✈❡❧s✮

❛♥❞ ✐♥✢❛t✐♦♥ ✭t❤❡ ●❉P ❞❡✢❛t♦rDEFL✱ ✷✵✶✵❂✶✵✵✮✱ ❧❛❣ ♦r❞❡r ♦♥❡✿

●❉P^e(t) =α^GDP●❉P(t−✶) +ǫ^GDP(t) ✭✶✮

DEFL^e(t) =α^DEFLDEFL(t−✶) +ǫ^π(t) ✭✷✮

❋♦r ❜♦t❤ ❡①♣❡❝t❛t✐♦♥ ❢♦r♠❛t✐♦♥ ❛♥❞ ❢♦r❡❝❛st✐♥❣ ❜❡❧♦✇✱ ✇❡ ✉s❡❞ t❤❡ ❆■❈ ❛♥❞ ❇■❈

❝r✐t❡r✐♦♥ t♦ ❞❡t❡r♠✐♥❡ t❤❡ ♦♣t✐♠❛❧ ❧❛❣ ❧❡♥❣t❤ ❢♦r t❤❡ ❆❘ ♠♦❞❡❧✳

✽ ✴ ✺✵

❋✐r♠s✿ ❙✉♣♣❧② ❈❤♦✐❝❡ ✫ Pr✐❝✐♥❣ ✭❆❞❛♣t✐✈❡ ▲❡❛r♥✐♥❣✮

❙✉♣♣❧② ❝❤♦✐❝❡✴❞❡♠❛♥❞ ❡①♣❡❝t❛t✐♦♥s✿

❋✐r♠s ❢♦r♠s ❡①♣❡❝t❛t✐♦♥s ❛❜♦✉t ❡❝♦♥♦♠✐❝ ❣r♦✇t❤ ✭γ^e(t)✮ ❛❝❝♦r❞✐♥❣ t♦ ❆❘✭✶✮ ♣r♦❝❡ss✱

✐✳❡✳ ❜② ♣❛r❛♠❡t❡r✲❢r❡❡ ❛❞❛♣t✐✈❡ ❧❡❛r♥✐♥❣✳ ❊❛❝❤ ✜r♠i ❛❞❛♣ts ❞❡s✐r❡❞ s❝❛❧❡ ♦❢ ❛❝t✐✈✐t②

✭Q_i^s(t)✮ ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ♣r❡✈✐♦✉s ♣❡r✐♦❞✬s ❞❡♠❛♥❞ ✭Q_i^d(t−✶)✮ ❛♥❞ t❤❡ ❛ss✉♠♣t✐♦♥s

❛❜♦✉t t❤❡ ❞❡✈❡❧♦♣♠❡♥t ♦❢ t❤❡ r❡❛❧ ❣r♦✇t❤ r❛t❡ ✭γ^e(t)✮

Q_i^s(t) =Q_i^e(t) =Q_i^d(t−✶)(✶+γ^e(t)) ✭✸✮

Pr✐❝✐♥❣✿ ❛❝❝♦r❞✐♥❣ t♦ ❡①♣❡❝t❡❞ ✐♥✢❛t✐♦♥ r❛t❡π^e(t)✱ ❝♦st✲str✉❝t✉r❡ ✭✬❝♦st✲♣✉s❤

✐♥✢❛t✐♦♥✬✮✱ ✉♥✐t t❛r❣❡t ♦♣❡r❛t✐♥❣ s✉r♣❧✉s✿

Pi(t) =

❯♥✐t ❧❛❜♦✉r ❝♦sts

z }| {

wi(t)(✶+τ^SIF) ¯P^HH(t−✶)(✶+π^e(t))

α_i(t) +

❯♥✐t ▼❛t❡r✐❛❧ ❝♦sts

z }| {

✶ β_i

X

g

asgP¯g(t−✶)(✶+π^e(t)) +

❯♥✐t ❝❛♣✐t❛❧ ❝♦sts

z }| {

δi

κ_iP¯^CF(t−✶)(✶+π^e(t))

+ τ_i^YP_i(t−✶)(✶+π^e(t))

| {z }

❯♥✐t ♥❡t t❛①❡s✴s✉❜s✐❞✐❡s ♣r♦❞✉❝ts

+ τ_i^K

κ_iωP¯^CF(t−✶)(✶+π^e(t))

| {z }

❯♥✐t ♥❡t t❛①❡s✴s✉❜s✐❞✐❡s ♣r♦❞✉❝t✐♦♥

+ ¯π_iP_i(t−✶)(✶+π^e(t))

| {z }

❚❛r❣❡t ✉♥✐t ♦♣❡r❛t✐♥❣ s✉r♣❧✉s

✭✹✮

✾ ✴ ✺✵

INSTITUTE FOR ECOLOGICAL ECONOMICS

❋✐r♠s✿ ❖✉t♣✉t ✫ ■♥✈❡st♠❡♥t

❖✉t♣✉tY_i(t) ♣r♦❞✉❝❡❞ ✈✐❛✿

✭✶✮ ✐♥t❡r♠❡❞✐❛t❡ ✐♥♣✉tsM_i(t)✱ ✭✷✮ ❧❛❜♦rN_i(t)✱ ✭✸✮ ❝❛♣✐t❛❧ st♦❝❦ K_i(t−✶)✱

✇✐t❤ ❛ ✜①❡❞ ❝♦❡✣❝✐❡♥t ✭▲❡♦♥t✐❡❢✮ t❡❝❤♥♦❧♦❣②✱ ✇❤❡r❡ t❤❡ ❝♦❡✣❝✐❡♥ts ❛r❡ ♦❜t❛✐♥❡❞ ❢r♦♠

■❖❚s✿

α_i(t)✱β_i ❛♥❞ κ_i ✕ ♣r♦❞✉❝t✐✈✐t② ❝♦❡✣❝✐❡♥ts✱

a_sg ✕ t❡❝❤♥♦❧♦❣✐❝❛❧❧② ❞❡t❡r♠✐♥❡❞ ✐♥♣✉t ✭✏t❡❝❤♥♦❧♦❣②✑✮ ❝♦❡✣❝✐❡♥ts✿

✭✺✮

Y_i(t) = min

Q_i^s(t), βi

a_s✶M_i✶(t−✶), βi

a_s✷M_i✷(t−✶), . . . , βi

a_sgM_ig(t−✶), αi(t)Ni(t), κiK_i(t−✶)

■♥✈❡st♠❡♥t ✕ ❛❝❝♦r❞✐♥❣ t♦✿

✭✶✮ ❞❡♣r❡❝✐❛t✐♦♥ r❛t❡ ♦❢ ❝❛♣✐t❛❧δ_i✱ ✭✷✮ ♣r♦❞✉❝t✐✈✐t② ♦❢ ❝❛♣✐t❛❧κ_i✱ ❛♥❞ ✭✸✮ ❞❡s✐r❡❞ s❝❛❧❡ ♦❢

❛❝t✐✈✐t②Q_i^s(t) ❜❛s❡❞ ♦♥ ❞❡♠❛♥❞ ❡①♣❡❝t❛t✐♦♥s✱

I_i^d(t) = δi

κ_iQ_i^s(t) = δi

κ_iQ_i^e(t) = δi

κ_iQ_i^d(t−✶)[✶+γ^e(t)] , ✭✻✮

✶✵ ✴ ✺✵

◆♦♥✲✜♥❛♥❝✐❛❧ ❛♥❞ ❋✐♥❛♥❝✐❛❧ ❈♦r♣♦r❛t✐♦♥s ✭❋✐r♠s✮✿ ❊❝♦♥♦♠✐❝ ❛❝t✐✈✐t✐❡s

◮ ❖✉t♣✉t ✭P✳✶✮^✶ → ♣❛rt ♦❢ ✇❤✐❝❤ r❡s✉❧ts ✐♥ r❡❛❧✐③❡❞ s❛❧❡s✿

◮ ✰P_iQ_i ✇❤❡r❡ P_i ✐s ♣r✐❝❡ ❝❤❛r❣❡❞✱ ❛♥❞Q_i ❛r❡ r❡❛❧✐③❡❞ s❛❧❡s ♦❢ ✜r♠ ✐

◮ ✲ ■♥t❡r♠❡❞✐❛t❡ ❝♦♥s✉♠♣t✐♦♥ ✭P✳✷✮

◮ ✲ ❈❛♣✐t❛❧ ❝♦♥s✉♠♣t✐♦♥ ✭P✳✺✶❈✮

◮ ✲ ❲❛❣❡s ❛♥❞ s❛❧❛r✐❡s ✭❉✳✶✶✮

◮ ✲ ❊♠♣❧♦②❡rs✬ s♦❝✐❛❧ ❝♦♥tr✐❜✉t✐♦♥s ✭❉✳✻✶✶✮

◮ ✲ ❚❛①❡s ♦♥ ♣r♦❞✉❝ts ✭❉✳✷✶✮

◮ ✲ ❖t❤❡r t❛①❡s ♦♥ ♣r♦❞✉❝t✐♦♥ ✭❉✳✷✾✮

◮ ✰ ❙✉❜s✐❞✐❡s ♦♥ ♣r♦❞✉❝ts ✭❉✳✸✶✮

◮ ✰ ❖t❤❡r s✉❜s✐❞✐❡s ♦♥ ♣r♦❞✉❝t✐♦♥ ✭❉✳✸✾✮

◮ ❂ ❖♣❡r❛t✐♥❣ s✉r♣❧✉s ✭❇✳✷❆✸◆✮

◮ ✲ ■♥t❡r❡st ✭❉✳✹✶✮

◮ ✲ ❚❛①❡s ♦♥ ✐♥❝♦♠❡ ✭❉✳✺✶✮

◮ ✲ ❞✐✈✐❞❡♥❞ ♣❛②♠❡♥ts ✭❉✳✹✷✮

✶❚❤❡ ❊❙❆ ❝♦❞❡ ✐s ❣✐✈❡♥ ✐♥ ❜r❛❝❦❡ts✳

✶✶ ✴ ✺✵

❍♦✉s❡❤♦❧❞s ✲ ✐♥❝♦♠❡✿ ❡❛❝❤ ❤♦✉s❡❤♦❧❞ ❢♦r♠s ❡①♣❡❝t❛t✐♦♥s ♦♥ ✐ts ❡①♣❡❝t❡❞ ♥♦♠✐♥❛❧ ❞✐s♣♦s❛❜❧❡

✐♥❝♦♠❡Y_h^e(t)✭✐✳❡✳ ❡①♣❡❝t❡❞ ♥❡t ✐♥❝♦♠❡ ❛❢t❡r t❛①❡s ❛♥❞ ✐♥❝❧✉❞✐♥❣ s♦❝✐❛❧ ♦r ✉♥❡♠♣❧♦②♠❡♥t ❜❡♥❡✜ts✮✿

Y_h^e(t) =















w_h(t)

✶−τ^SIW−τ^INC(✶−τ^SIW)

+sb^otherP¯^HH(t−✶)(✶+π^e(t)) ✐❢ ❡♠♣❧♦②❡❞

w_h(t) +sb^otherP¯^HH(t−✶)(✶+π^e(t)) ✐❢ ✉♥❡♠♣❧♦②❡❞

sb^inact+sb^otherP¯^HH(t−✶)(✶+π^e(t)) ✐❢ ♥♦t ❡❝♦♥♦♠✐❝❛❧❧② ❛❝t✐✈❡

θ^DIV(✶−τ^INC)(✶−τ^FIRM) max(✵,Π^ei(t)) +sb^otherP¯^HH(t−✶)(✶+π^e(t)) ✐❢ ❛♥ ✐♥✈❡st♦r θ^DIV(✶−τ^INC)(✶−τ^FIRM) max(✵,Π^ek(t)) +sb^otherP¯^HH(t−✶)(✶+π^e(t)) ✐❢ ❛ ❜❛♥❦ ✐♥✈❡st♦r

❍❡r❡✱ ✭✼✮

w_h(t) ✐s ✇❛❣❡ ✐♥❝♦♠❡ ♦r ✉♥❡♠♣❧♦②♠❡♥t ❜❡♥❡✜ts ✭✇❤✐❝❤ ❛r❡ ❛ ✜①❡❞ ❢r❛❝t✐♦♥ θ ♦❢ t❤❡ ✇❛❣❡ ❧❛st

❡❛r♥❡❞ ❜❡❢♦r❡ t❤❡ ✉♥❡♠♣❧♦②♠❡♥t✮ ♦❢ ❤♦✉s❡❤♦❧❞ h✱ P¯^HH(t−✶) ✐s ❧❛st ♣❡r✐♦❞✬s ❝♦♥s✉♠❡r ♣r✐❝❡ ✐♥❞❡①✱

Π^e_i(t)❛r❡ ❡①♣❡❝t❡❞ ♣r♦✜ts ♦❢ ✜r♠ i✱Π^e_k(t) ❛r❡ ❡①♣❡❝t❡❞ ❜❛♥❦ ♣r♦✜ts✱

sb^inact ❛r❡ s♦❝✐❛❧ ❜❡♥❡✜ts ❢♦r ✐♥❛❝t✐✈❡ ♣❡rs♦♥s ✭♠♦st❧② ♣❡♥s✐♦♥ ♣❛②♠❡♥ts✮✱ sb^other s♦❝✐❛❧ ❜❡♥❡✜ts

❞✐str✐❜✉t❡❞ ❡q✉❛❧❧② t♦ ❛❧❧ ❤♦✉s❡❤♦❧❞s

τ^INC ✐s t❤❡ ✐♥❝♦♠❡ t❛① r❛t❡✱ τ^SIW ✐s t❤❡ r❛t❡ ♦❢ s♦❝✐❛❧ ✐♥s✉r❛♥❝❡ ❝♦♥tr✐❜✉t✐♦♥s t♦ ❜❡ ♣❛✐❞ ❜② t❤❡

❡♠♣❧♦②❡❡✱ θ^DIV ✐s t❤❡ ❞✐✈✐❞❡♥❞ ♣❛②♦✉t r❛t✐♦✱ ❛♥❞τ^FIRM t❤❡ ❝♦r♣♦r❛t❡ t❛① r❛t❡✳

❍♦✉s❡❤♦❧❞s✿ ❈♦♥s✉♠♣t✐♦♥✱ ■♥✈❡st♠❡♥t ✫ ❙❛✈✐♥❣s

❍♦✉s❡❤♦❧❞s s♣❡♥❞ ❛ ❢r❛❝t✐♦♥ ♦❢ t❤❡✐r ❡①♣❡❝t❡❞ ✐♥❝♦♠❡ ♦♥ ❝♦♥s✉♠♣t✐♦♥✿

C_h^d(t) = ψY_h^e(t)

✶+τ^VAT ✭✽✮

❛♥❞ ♦♥ ✐♥✈❡st♠❡♥t✿

✭✾✮

I_h^d(t) = ψ^HY_h^e(t)

✶+τ^CF ✱

✇❤❡r❡ψ✱ψ^H ❛r❡ ♣r♦♣❡♥s✐t✐❡s t♦ ❝♦♥s✉♠❡✱✐♥✈❡st ♦✉t ♦❢ ❡①♣❡❝t❡❞ ✐♥❝♦♠❡❀τ^VAT✱τ^CF ❛r❡

✈❛❧✉❡ ❛❞❞❡❞✱ ✐♥✈❡st♠❡♥t t❛① r❛t❡s✳ ❚♦t❛❧ ❤♦✉s❡❤♦❧❞ ❝♦♥s✉♠♣t✐♦♥ ❛❧❧♦❝❛t❡❞ t♦ ❣♦♦❞sg

❛❝❝♦r❞✐♥❣ t♦ ✜①❡❞ ❝♦❡✣❝✐❡♥ts ❢r♦♠ ■❖❚s✱ ❛♥❛❧♦❣♦✉s t♦ ✜r♠ ✐♥✈❡st♠❡♥t ❛❜♦✈❡✳

❍♦✉s❡❤♦❧❞s✬ ❝♦♥s✉♠♣t✐♦♥✱ ✐♥✈❡st♠❡♥t ♣❧❛♥s ♥❡❡❞ ♥♦t ❜❡ r❡❛❧✐③❡❞ ✭❢✉♥❞❛♠❡♥t❛❧

✉♥❝❡rt❛✐♥t②✦✮✿ ❡①♣❡❝t❛t✐♦♥ ♠✐st❛❦❡s✱ s❡❛r❝❤ ❛♥❞ ♠❛t❝❤✐♥❣

❙❛✈✐♥❣s✿ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ r❡❛❧✐③❡❞ ❞✐s♣♦s❛❜❧❡ ✐♥❝♦♠❡Y_h(t)✱ r❡❛❧✐③❡❞ ❝♦♥s✉♠♣t✐♦♥

❡①♣❡♥❞✐t✉r❡Ch(t)✱ ✉s❡❞ t♦ ❛❝❝✉♠✉❧❛t❡ ✜♥❛♥❝✐❛❧ ✇❡❛❧t❤✿

D_h(t) =D_h(t−✶) +

❙❛✈✐♥❣s

z }| {

Y_h(t)−[(✶+τ^VAT)C_h(t) + (✶+τ^CF)I_h(t)] ✭✶✵✮

✳ ^{✶✸ ✴ ✺✵}

INSTITUTE FOR ECOLOGICAL ECONOMICS

❍♦✉s❡❤♦❧❞s✿ ❊❝♦♥♦♠✐❝ ❛❝t✐✈✐t✐❡s

◮ ✰ ❲❛❣❡s ❛♥❞ s❛❧❛r✐❡s ✭❉✳✶✶✮

◮ ✰ Pr♦♣❡rt② ■♥❝♦♠❡ ✭❉✳✹✮

◮ ✰ ▼✐①❡❞ ■♥❝♦♠❡ ❢r♦♠ ❙❡❧❢✲❊♠♣❧♦②♠❡♥t ✭❇✷❆✸◆✮

◮ ✰ ❙♦❝✐❛❧ ❜❡♥❡✜ts ♦t❤❡r t❤❛♥ s♦❝✐❛❧ tr❛♥s❢❡rs ✐♥ ❦✐♥❞ ✭❉✳✻✷✮

◮ ✰ ❖t❤❡r ❝✉rr❡♥t tr❛♥s❢❡rs ♥❡t ✭❉✼✱ ❉✽✱ ❉✳✾✮

◮ ✲ ❋✐♥❛❧ ❝♦♥s✉♠♣t✐♦♥ ❡①♣❡♥❞✐t✉r❡ ✭P✳✸✮

◮ ✲ ❚❛①❡s ♦♥ ♣r♦❞✉❝ts ✭❉✳✷✶✮

◮ ✲ ❚❛①❡s ♦♥ ✐♥❝♦♠❡ ✭❉✳✺✮

◮ ✲ ❊♠♣❧♦②❡❡s✬ s♦❝✐❛❧ ❝♦♥tr✐❜✉t✐♦♥s ✭❉✳✻✶✷✱ ❉✳✻✶✸✱ ❉✳✻✶✹✮

◮ ✲ ❈❛♣✐t❛❧ ❢♦r♠❛t✐♦♥ ✭❞✇❡❧❧✐♥❣s✮ ✭P✳✺✶✮

✶✹ ✴ ✺✵

●❡♥❡r❛❧ ●♦✈❡r♥♠❡♥t✿ ❊❝♦♥♦♠✐❝ ❛❝t✐✈✐t✐❡s

●♦✈❡r♥♠❡♥t ♠❛✐♥❧② ❛❝ts ❛s ❛ ❝♦♥s✉♠❡r ✭❣♦✈❡r♥♠❡♥t ❝♦♥s✉♠♣t✐♦♥✮ ❛♥❞ ❛s ❛

✬r❡❞✐str✐❜✉t✐♦♥❛❧✬ ❡♥t✐t②✿ ❝♦♥s✉♠❡s ♦♥ t❤❡ ❣♦♦❞s ♠❛r❦❡t t♦ ♣r♦✈✐❞❡ ❛ ♣✉❜❧✐❝ ❣♦♦❞✱

❝♦❧❧❡❝ts t❛①❡s✱ ♣r♦✈✐❞❡s tr❛♥s❢❡rs✳

◮ ✰ ❚❛①❡s ♦♥ ✐♥❝♦♠❡ ✭❉✳✺✱ ❉✳✾✶✮

◮ ✰ ❚❛①❡s ♦♥ ♣r♦❞✉❝ts ❛♥❞ ♣r♦❞✉❝t✐♦♥ ✭❉✳✷✮

◮ ✰ Pr♦♣❡rt② ■♥❝♦♠❡ ✭❉✳✹✮

◮ ✰ ❙♦❝✐❛❧ ❝♦♥tr✐❜✉t✐♦♥s ✭❉✳✻✶✮

◮ ✲ ❋✐♥❛❧ ❝♦♥s✉♠♣t✐♦♥ ✭P✳✸✮

◮ ✲ ❙✉❜s✐❞✐❡s ✭❉✳✸✮

◮ ✲ ■♥t❡r❡st ♣❛②♠❡♥ts ✭❉✳✹✶✮

◮ ✲ ❙♦❝✐❛❧ ❜❡♥❡✜ts ♦t❤❡r t❤❛♥ s♦❝✐❛❧ tr❛♥s❢❡rs ✐♥ ❦✐♥❞ ✭❉✳✻✷✮

◮ ✲ ❖t❤❡r ❝✉rr❡♥t ❡①♣❡♥❞✐t✉r❡s ✭❉✳✼✱ ❉✳✽✱ ❉✳✾✮

✶✺ ✴ ✺✵

INSTITUTE FOR ECOLOGICAL ECONOMICS

❊①♣♦rts✱ ■♠♣♦rts✱ ●♦✈❡r♥♠❡♥t ❈♦♥s✉♠♣t✐♦♥

❆❝❝♦r❞✐♥❣ t♦ t❤❡ s♠❛❧❧ ♦♣❡♥ ❡❝♦♥♦♠② ✭❙♦❊✮ ❛ss✉♠♣t✐♦♥ ❛s ❛♣♣r♦♣r✐❛t❡ ❢♦r t❤❡

❆✉str✐❛♥ ❡❝♦♥♦♠② ❛♥❞ ❡①♦❣❡♥♦✉s ♣♦❧✐❝② ❞❡❝✐s✐♦♥s✱ t❤❡s❡ ❡❝♦♥♦♠✐❝ ❛❣❣r❡❣❛t❡s ❛r❡ ❡✐t❤❡r

❛ss✉♠❡❞ t♦ ❜❡

◮ ❡①♦❣❡♥♦✉s❧② ❣✐✈❡♥ ❢r♦♠ ❞❛t❛ ✭❝♦♥❞✐t✐♦♥❛❧ ❢♦r❡❝❛sts✮✱

◮ ♦r t♦ ❢♦❧❧♦✇ ❛✉t♦r❡❣r❡ss✐✈❡ ✭❆❘✮ ♣r♦❝❡ss❡s ❛❝❝♦r❞✐♥❣ t♦ t❤❡ ❙♦❊ s❡tt✐♥❣ ❢♦r ❆✉str✐❛

❚❤✉s✱ ✐♠♣♦rtsY^I(t)✱ ❡①♣♦rtsC^E(t) ❛♥❞ ❣♦✈❡r♥♠❡♥t ❝♦♥s✉♠♣t✐♦♥C^G(t) ✭❛❧❧ r❡❛❧ ❛♥❞

✐♥ ❧♦❣ ❧❡✈❡❧s✮ ❡✐t❤❡r ❢♦❧❧♦✇ ❆❘✭✶✮ ♣r♦❝❡ss❡s ✭✉♥❝♦♥❞✐t✐♦♥❛❧ ❢♦r❡❝❛st✐♥❣ s❡t✉♣✮✿

Y^I(t) =α^IY^I(t−✶) +ǫ^I ✭✶✶✮

C^E(t) =α^EC^E(t−✶) +ǫ^E ✭✶✷✮

C^G(t) =α^GC^G(t−✶) +ǫ^G, ✭✶✸✮

♦r ❛r❡ ❣✐✈❡♥ ❡①♦❣❡♥♦✉s❧② ✐♥ t❤❡ ❝♦♥❞✐t✐♦♥❛❧ ❢♦r❡❝❛st✐♥❣ s❡t✉♣✳

✶✻ ✴ ✺✵

❉❛t❛ s♦✉r❝❡s ✲ ♥❛t✐♦♥❛❧ ❛❝❝♦✉♥t✐♥❣ ❞❛t❛

✶✼ ✴ ✺✵

●❉P=

❚♦t❛❧ s❛❧❡s ♦❢ ❣♦♦❞s ❛♥❞ s❡r✈✐❝❡s

z }| {

✻✶✶✷✼✽X

i=✶

(✶−τ_i^Y)P_i(t)Y_i(t) −

■♥t❡r♠❡❞✐❛t❡ ✐♥♣✉ts

z }| {

X

g,s,i∈I_s

P¯_g(t)a_sgYi(t)

βi ✭Pr♦❞✉❝t✐♦♥ ❛♣♣r♦❛❝❤✮

=

❍♦✉s❡❤♦❧❞ ❝♦♥s✉♠♣t✐♦♥

z }| {

✽✷✹✽✸✷✶

X

h=✶

C_h(t) +

●♦✈❡r♥♠❡♥t ❝♦♥s✉♠♣t✐♦♥

z }| { X

j

C_j(t) +

●r♦ss ✜①❡❞ ❝❛♣✐t❛❧ ❢♦r♠❛t✐♦♥

z }| {

✽✷✹✽✸✷✶

X

h=✶

I_h(t) +

✻✶✶✷✼✽

X

i=✶

P¯^CF(t)Ii(t)

+

❈❤❛♥❣❡s ✐♥ ✐♥✈❡♥t♦r✐❡s

z }| {

✻✶✶✷✼✽

X

i=✶

Pi(t)∆Si(t) + X

g,s,i∈Is

P¯g(t)

∆Mig(t)−asg

Y_i(t) βi

+

❊①♣♦rts z }| { X

l

(Cl(t)

−

■♠♣♦rts z }| { X

m

P_m(t)Q_m(t))−

◆❡t t❛①❡s ♦♥ ♣r♦❞✉❝ts z }| { X

i

τ_i^YP_i(t)Y_i(t) ✭❊①♣❡♥❞✐t✉r❡ ❛♣♣r♦❛❝❤✮

=(✶+τ^SIF) ¯P^HH(t)

✽✷✹✽✸✷✶

X

h=✶

w_h(t)

| {z }

❈♦♠♣❡♥s❛t✐♦♥ ♦❢ ❡♠♣❧♦②❡❡s

+

✻✶✶✷✼✽

X

i=✶

Πi(t) +r(t)L_i(t) + ¯P^CF(t)δi

κi

Y_i(t)

| {z }

●r♦ss ♦♣❡r❛t✐♥❣ s✉r♣❧✉s ❛♥❞ ♠✐①❡❞ ✐♥❝♦♠❡

+ ^X

i

τ_i^KP_i(t)Yi(t)

◆❡t t❛①❡s ♦♥ ♣r♦❞✉❝t✐♦♥

✭■♥❝♦♠❡ ❛♣♣r♦❛❝❤✮

P❛r❛♠❡t❡r s❡tt✐♥❣✿ ❊✉r♦♣❡❛♥ ❙②st❡♠ ♦❢ ❆❝❝♦✉♥ts

◮ ■♥♣✉t✲♦✉t♣✉t t❛❜❧❡s ✭■❖❚s✮

◮ ◆❛t✐♦♥❛❧ ❛♥♥✉❛❧ s❡❝t♦r ❛❝❝♦✉♥ts ✭◆❆❙❆✮

◮ ●♦✈❡r♥♠❡♥t st❛t✐st✐❝s

◮ ❉❡♠♦❣r❛♣❤✐❝ st❛t✐st✐❝s ❛♥❞ ❝❡♥s✉s ❞❛t❛

◮ ❇✉s✐♥❡ss s✉r✈❡②s

✶✾ ✴ ✺✵

❚❛❜❧❡✿

❊✉r♦st❛t ❞❛t❛ t❛❜❧❡s ✉s❡❞

◆❛♠❡ ❈♦❞❡

●❉P ❛♥❞ ♠❛✐♥ ❝♦♠♣♦♥❡♥ts ✲ ♦✉t♣✉t✱ ❡①♣❡♥❞✐t✉r❡ ❛♥❞ ✐♥❝♦♠❡ ✭q✉❛rt❡r❧②

t✐♠❡ s❡r✐❡s✮ ♥❛♠q❴✶✵❴❣❞♣

❙②♠♠❡tr✐❝ ✐♥♣✉t✲♦✉t♣✉t t❛❜❧❡ ✭■❖❚✮ ❛t ❜❛s✐❝ ♣r✐❝❡s ✭♣r♦❞✉❝t ❜② ♣r♦❞✉❝t✮ ♥❛✐♦❴✶✵❴❝♣✶✼✵✵

❈r♦ss✲❝❧❛ss✐✜❝❛t✐♦♥ ♦❢ ✜①❡❞ ❛ss❡ts ❜② ✐♥❞✉str② ❛♥❞ ❜② ❛ss❡t ✭st♦❝❦s✮ ♥❛♠❛❴✶✵❴♥❢❛❴st

❇❛❧❛♥❝❡ s❤❡❡ts ❢♦r ✜♥❛♥❝✐❛❧ ❛ss❡ts ♥❛s❛❴✶✵❴❢❴❜s

◆♦♥✲✜♥❛♥❝✐❛❧ tr❛♥s❛❝t✐♦♥s ♥❛s❛❴✶✵❴♥❢❴tr

❇✉s✐♥❡ss ❞❡♠♦❣r❛♣❤② ❜② ❧❡❣❛❧ ❢♦r♠ ✭❢r♦♠ ✷✵✵✹ ♦♥✇❛r❞s✱ ◆❆❈❊ ❘❡✈✳ ✷✮ ❜❞❴✾❛❝❴❧❴❢♦r♠❴r✷

●♦✈❡r♥♠❡♥t r❡✈❡♥✉❡✱ ❡①♣❡♥❞✐t✉r❡ ❛♥❞ ♠❛✐♥ ❛❣❣r❡❣❛t❡s ❣♦✈❴✶✵❛❴♠❛✐♥

●♦✈❡r♥♠❡♥t ❞❡✜❝✐t✴s✉r♣❧✉s✱ ❞❡❜t ❛♥❞ ❛ss♦❝✐❛t❡❞ ❞❛t❛ ❣♦✈❴✶✵❞❞❴❡❞♣t✶

●♦✈❡r♥♠❡♥t ❡①♣❡♥❞✐t✉r❡ ❜② ❢✉♥❝t✐♦♥ ✲ ❈❖❋❖● ❣♦✈❴✶✵❛❴❡①♣

P♦♣✉❧❛t✐♦♥ ❜② ❝✉rr❡♥t ❛❝t✐✈✐t② st❛t✉s✱ ◆❆❈❊ ❘❡✈✳ ✷ ❛❝t✐✈✐t② ❛♥❞ ◆❯❚❙ ✷

r❡❣✐♦♥ ❝❡♥s❴✶✶❛♥❴r✷

▼♦♥❡② ♠❛r❦❡t ✐♥t❡r❡st r❛t❡s ✲ ❛♥♥✉❛❧ ❞❛t❛ ✐rt❴st❴❛

▼♦♥❡② ♠❛r❦❡t ✐♥t❡r❡st r❛t❡s ✲ q✉❛rt❡r❧② ❞❛t❛ ✐rt❴st❴q

❈❤❛❧❧❡♥❣❡s ✇✐t❤ ♥❛t✐♦♥❛❧ ❛❝❝♦✉♥t✐♥❣ ❞❛t❛

◮ ❍❛r♠♦♥✐③❡ ■❖ t❛❜❧❡s ✇✐t❤ ❣♦✈❡r♥♠❡♥t st❛t✐st✐❝s

◮ ❍❛r♠♦♥✐③❡ ■❖ t❛❜❧❡s ❛♥❞ t✐♠❡ s❡r✐❡s ❞❛t❛

◮ ■♥❝♦♥s✐st❡♥❝✐❡s ❜❡t✇❡❡♥ ❞❛t❛s❡ts ❛r❡ ♠♦st ♣r♦❜❧❡♠❛t✐❝ ✐ss✉❡✿

◮ ❚✐♠❡ s❡r✐❡s ❞❛t❛ ❛r❡ ✉♣❞❛t❡❞✱ ■❖ ❞❛t❛ ❛r❡ ♥♦t

◮ ◆♦ ❝r♦ss✲❝❧❛ss✐✜❝❛t✐♦♥ t❛❜❧❡s ■❖ ❛♥❞ ◆❆❙❆ ❞❛t❛ ✭✜♥❛♥❝✐❛❧ ✈❛r✐❛❜❧❡s✮

◮ ❡t❝✳

✷✶ ✴ ✺✵

❋✐❣✉r❡✿ P❛r❛♠❡t❡r s❡tt✐♥❣✿ ■♥✐t✐❛❧ ❖✉t♣✉t✴❈♦st ❙tr✉❝t✉r❡

A01A02A03B C10-C12C13-C15

C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30 C31_C32

C33D E36 E37-E39

FG45G46G47H49H50H51H52H53 I

J58 J59_J60

J61 J62_J63

K64K65K66 L M69_M70

M71M72M73 M74_M75

N77N78N79 N80-N82

O PQ86 Q87_Q88R90-R92

R93S94S95S96 Sector

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Output [Euro]

×10¹⁰

intermediate consumption wages

social contributions taxes less subsidies capital consumption operating surplus

❋✐❣✉r❡✿❉✐str✐❜✉t✐♦♥ ♦❢ ♦✉t♣✉t ❛♥❞ ❝♦st str✉❝t✉r❡ ❜② s❡❝t♦r ✉s❡❞ ❛s ✐♥✐t✐❛❧ ✈❛❧✉❡s ❢♦r ♠♦❞❡❧

s✐♠✉❧❛t✐♦♥s ❢r♦♠ ♦❜s❡r✈❡❞ ❞❛t❛ ♦❢ ❆✉str✐❛

A01A02A03 B C10-C12C13-C15

C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30 C31_C32

C33D E36 E37-E39

F

G45G46G47H49H50H51H52H53 I J58 J59_J60

J61 J62_J63

K64K65K66 L M69_M70

M71M72M73 M74_M75

N77N78N79 N80-N82

O PQ86 Q87_Q88R90-R92

R93S94S95S96 Sector

0 1 2 3 4 5 6 7 8 9 10

Number firms

×10⁴

0 0.5 1 1.5 2 2.5 3 3.5 4

Number employees

×10⁵

firms employees

❋✐❣✉r❡✿❉✐str✐❜✉t✐♦♥ ♦❢ ♥✉♠❜❡r ♦❢ ✜r♠s ❛♥❞ ❡♠♣❧♦②❡❡s ❜② s❡❝t♦r ✉s❡❞ ❛s ✐♥✐t✐❛❧ ✈❛❧✉❡s ❢♦r ♠♦❞❡❧

s✐♠✉❧❛t✐♦♥s ❢r♦♠ ♦❜s❡r✈❡❞ ❞❛t❛ ♦❢ ❆✉str✐❛

❋✐❣✉r❡✿

❋✐r♠ ❙✐③❡ ❞✐str✐❜✉t✐♦♥

●❡♥❡r❛❧ ●♦✈❡r♥♠❡♥t✿ ❘❡✈❡♥✉❡s Y

( t )

✭✶✹✮

Y^G(t) =

❙♦❝✐❛❧ s❡❝✉r✐t② ❝♦♥tr✐❜✉t✐♦♥s

z }| {

(τ^SIF +τ^SIW) ¯P^HH(t) X

h∈H^E(t)

w_h(t) +

▲❛❜♦✉r ✐♥❝♦♠❡ t❛①❡s

z }| {

τ^INC(✶−τ^SIW) ¯P^HH(t) X

h∈H^E(t)

w_h(t)

+

❱❛❧✉❡ ❛❞❞❡❞ t❛①❡s

z }| { τ^VATX

h

C_h(t) +

❈❛♣✐t❛❧ ✐♥❝♦♠❡ t❛①❡s

z }| {

τ^INC(✶−τ^FIRM)θ^DIV X

i

max(✵,Πi(t)) + max(✵,Πk(t))

!

+

❈♦r♣♦r❛t❡ ✐♥❝♦♠❡ t❛①❡s

z }| {

τ^FIRM X

i

max(✵,Πi(t)) + max(✵,Πk(t))

!

+ τ^CFX

h

I_h(t)

| {z }

❚❛①❡s ♦♥ ❝❛♣✐t❛❧ ❢♦r♠❛t✐♦♥

+ X

s,i∈Is

τi^YP_i(t)Y_i(t)

| {z }

◆❡t t❛①❡s✴s✉❜s✐❞✐❡s ♦♥ ♣r♦❞✉❝ts

+ P¯^CF(t)X

i

τi^KK_i(t)

| {z }

◆❡t t❛①❡s✴s✉❜s✐❞✐❡s ♦♥ ♣r♦❞✉❝t✐♦♥

+τ^EXPORTX

l

C_l(t)

| {z }

❊①♣♦rt t❛①❡s

✳

✷✺ ✴ ✺✵

INSTITUTE FOR ECOLOGICAL ECONOMICS

●❡♥❡r❛❧ ●♦✈❡r♥♠❡♥t✿ ❉❡✜❝✐t ✫ ❉❡❜t

❚❤❡ ❣♦✈❡r♥♠❡♥t ❞❡✜❝✐t ✭♦r s✉r♣❧✉s✮ r❡s✉❧t✐♥❣ ❢r♦♠ ✐ts r❡❞✐str✐❜✉t✐✈❡ ❛❝t✐✈✐t✐❡s ✐s

✭✶✺✮

Π^G(t) =

●♦✈❡r♥♠❡♥t r❡✈❡♥✉❡s

z }| { Y^G(t) −

●♦✈❡r♥♠❡♥t ❝♦♥s✉♠♣t✐♦♥

z }| { X

j

C_j(t) −

■♥t❡r❡st ♣❛②♠❡♥ts

z }| { r^GL^G(t)

− X

h∈H^inact

P¯^HH(t)sb^inact+ X

h∈H^U(t)

P¯^HH(t)wh(t) +X

h

P¯^HH(t)sb^other

| {z }

❙♦❝✐❛❧ ❜❡♥❡✜ts ❛♥❞ tr❛♥s❢❡rs

❚❤❡ ❣♦✈❡r♥♠❡♥t ❞❡❜t ✐s ❞❡t❡r♠✐♥❡❞ ❜② t❤❡ ②❡❛r✲t♦✲②❡❛r ❞❡✜❝✐ts✴s✉r♣❧✉s❡s ♦❢ t❤❡

❣♦✈❡r♥♠❡♥t s❡❝t♦r✿

✭✶✻✮

L^G(t) =L^G(t−✶) + Π^G(t)

✷✻ ✴ ✺✵

❋♦r❡❝❛sts ✉s✐♥❣ ♥❛t✐♦♥❛❧ ❛❝❝♦✉♥t✐♥❣ ❞❛t❛

✷✼ ✴ ✺✵

❚❛❜❧❡✿

❯♥❝♦♥❞✐t✐♦♥❛❧ ❢♦r❡❝❛st✐♥❣ ♣❡r❢♦r♠❛♥❝❡

●❉P ❣r♦✇t❤ ●❉P ❞❡✢❛t♦r ❣r♦✇t❤ ❍♦✉s❡❤♦❧❞ ❝♦♥s✉♠♣t✐♦♥ ■♥✈❡st♠❡♥t ❊✉r✐❜♦r

❆❘✭✶✮ ❘▼❙❊✲st❛t✐st✐❝ ❢♦r ❞✐✛❡r❡♥t ❢♦r❡❝❛st ❤♦r✐③♦♥s

✶q ✵✳✻✷ ✵✳✸✼ ✵✳✻✻ ✶✳✹ ✵✳✵✺

✷q ✵✳✽✾ ✵✳✸✻ ✵✳✾✸ ✷✳✷✶ ✵✳✶

✹q ✶✳✸✸ ✵✳✸✹ ✶✳✸✷ ✸✳✺ ✵✳✶✻

✽q ✶✳✹✽ ✵✳✸✼ ✶✳✺✼ ✹✳✸✹ ✵✳✷✶

✶✷q ✶✳✸✶ ✵✳✸✸ ✷ ✻✳✵✾ ✵✳✷✻

❆❇▼ P❡r❝❡♥t❛❣❡ ❣❛✐♥s ✭✰✮ ♦r ❧♦ss❡s ✭✲✮ r❡❧❛t✐✈❡ t♦ ❆❘✭✶✮ ♠♦❞❡❧

✶q ✲✶✳✼ ✭✵✳✵✷✮ ✵ ✭✵✳✾✻✮ ✵✳✺ ✭✵✳✾✹✮ ✽✳✾ ✭✵✳✶✸✮ ✲✷✸✺✳✼ ✭✵✳✵✵✮

✷q ✲✶✳✽ ✭✵✳✸✵✮ ✲✶✳✷ ✭✵✳✷✾✮ ✵✳✺ ✭✵✳✾✻✮ ✶✵✳✷ ✭✵✳✷✵✮ ✲✾✵✳✸ ✭✵✳✶✾✮

✹q ✵✳✷ ✭✵✳✾✸✮ ✶✳✶ ✭✵✳✶✹✮ ✼✳✶ ✭✵✳✻✷✮ ✾✳✷ ✭✵✳✷✽✮ ✲✶✺✳✾ ✭✵✳✼✽✮

✽q ✺✳✾ ✭✵✳✶✸✮ ✵✳✹ ✭✵✳✼✽✮ ✷✶✳✻ ✭✵✳✵✹✮ ✷✾✳✽ ✭✵✳✵✵✮ ✺✽ ✭✵✳✵✵✮

✶✷q ✹✳✻ ✭✵✳✺✹✮ ✲✵✳✸ ✭✵✳✶✵✮ ✷✾✳✽ ✭✵✳✵✵✮ ✸✾✳✻ ✭✵✳✵✵✮ ✼✾✳✻ ✭✵✳✵✵✮

❉❙●❊ P❡r❝❡♥t❛❣❡ ❣❛✐♥s ✭✰✮ ♦r ❧♦ss❡s ✭✲✮ r❡❧❛t✐✈❡ t♦ ❆❘✭✶✮ ♠♦❞❡❧

✶q ✲✺✳✼ ✭✵✳✻✷✮ ✺✳✸ ✭✵✳✺✾✮ ✼✳✾ ✭✵✳✸✶✮ ✷✷✳✶ ✭✵✳✷✹✮ ✲✶✻ ✭✵✳✵✻✮

✷q ✲✸✳✹ ✭✵✳✽✵✮ ✲✷✵ ✭✵✳✶✼✮ ✼✳✷ ✭✵✳✹✸✮ ✸✶✳✹ ✭✵✳✷✽✮ ✲✸✾✳✶ ✭✵✳✵✶✮

✹q ✶✺✳✶ ✭✵✳✶✼✮ ✲✽✳✷ ✭✵✳✵✵✮ ✷✺✳✸ ✭✵✳✶✸✮ ✸✼✳✾ ✭✵✳✷✻✮ ✲✼✵✳✷ ✭✵✳✵✵✮

✽q ✸✾ ✭✵✳✵✽✮ ✶✳✼ ✭✵✳✹✸✮ ✶✵✳✾ ✭✵✳✸✷✮ ✸✻✳✶ ✭✵✳✶✻✮ ✲✶✸✷✳✷ ✭✵✳✵✵✮

✶✷q ✷✽✳✺ ✭✵✳✵✵✮ ✲✹✳✸ ✭✵✳✻✸✮ ✼✳✶ ✭✵✳✸✼✮ ✺✵✳✽ ✭✵✳✵✵✮ ✲✶✸✾✳✷ ✭✵✳✵✵✮

❚❛❜❧❡✿❘▼❙❊✲st❛t✐st✐❝ ❢♦r ❞✐✛❡r❡♥t ❢♦r❡❝❛st ❤♦r✐③♦♥s ❢r♦♠ ✷✵✶✵✿◗✷✲✷✵✶✻✿◗✹ ♦❢ ❆❇▼ ✐♥ ❝♦♠♣❛r✐s♦♥ t♦ ❆❘✭✶✮

❛♥❞ ❉❙●❊ ♠♦❞❡❧s ✭✉♥❝♦♥❞✐t✐♦♥❛❧ ❢♦r❡❝❛sts✮✳ ❱❛❧✉❡s ✐♥ ❜r❛❝❦❡ts ✐♥❞✐❝❛t❡ ♣✲✈❛❧✉❡s ♦❢ t❤❡

❬❉✐❡❜♦❧❞ ❛♥❞ ▼❛r✐❛♥♦✱ ✶✾✾✺❪ t❡st ♦♥ ♣r❡❞✐❝t✐✈❡ ❛❝❝✉r❛❝②✳

●❉P ❣r♦✇t❤ ●❉P ❞❡✢❛t♦r ❣r♦✇t❤ ❍♦✉s❡❤♦❧❞ ❝♦♥s✉♠♣t✐♦♥ ■♥✈❡st♠❡♥t

❆❘❳✭✶✮ ❘▼❙❊✲st❛t✐st✐❝ ❢♦r ❞✐✛❡r❡♥t ❢♦r❡❝❛st ❤♦r✐③♦♥s

✶q ✵✳✸✹ ✵✳✸✽ ✵✳✺✽ ✶✳✶✶

✷q ✵✳✸✼ ✵✳✸✹ ✵✳✼✺ ✶✳✹✾

✹q ✵✳✹✶ ✵✳✸✺ ✵✳✾✻ ✶✳✷✺

✽q ✵✳✺✸ ✵✳✸✺ ✶✳✷✷ ✶✳✵✼

✶✷q ✵✳✺✽ ✵✳✹✶ ✶✳✹✸ ✶✳✸✺

✏❆❇▼❳✑ ✭❝♦♥❞✳ ❢❝✳✮ P❡r❝❡♥t❛❣❡ ❣❛✐♥s ✭✰✮ ♦r ❧♦ss❡s ✭✲✮ r❡❧❛t✐✈❡ t♦ ❆❘❳✭✶✮ ♠♦❞❡❧

✶q ✸✳✸ ✭✵✳✶✷✮ ✲✵✳✾ ✭✵✳✷✶✮ ✲✷✷✳✶ ✭✵✳✶✾✮ ✲✶✳✽ ✭✵✳✾✹✮

✷q ✲✵✳✾ ✭✵✳✾✵✮ ✲✶✳✶ ✭✵✳✸✹✮ ✲✽✳✹ ✭✵✳✻✷✮ ✲✶✶✳✽ ✭✵✳✼✹✮

✹q ✲✷✸✳✶ ✭✵✳✺✶✮ ✵✳✽ ✭✵✳✺✶✮ ✲✶✷✳✽ ✭✵✳✺✺✮ ✲✶✵✼✳✶ ✭✵✳✶✵✮

✽q ✲✶ ✭✵✳✾✹✮ ✲✶ ✭✵✳✵✵✮ ✶✽✳✽ ✭✵✳✵✺✮ ✲✶✹✷✳✸ ✭✵✳✵✸✮

✶✷q ✶✽✳✺ ✭✵✳✵✵✮ ✲✶✳✻ ✭✵✳✵✵✮ ✻✳✻ ✭✵✳✸✸✮ ✲✶✷✵✳✺ ✭✵✳✵✻✮

✏❉❙●❊❳✑ ✭❝♦♥❞✳ ❢❝✳✮ P❡r❝❡♥t❛❣❡ ❣❛✐♥s ✭✰✮ ♦r ❧♦ss❡s ✭✲✮ r❡❧❛t✐✈❡ t♦ ❆❘❳✭✶✮ ♠♦❞❡❧

✶q ✲✻✵✳✼ ✭✵✳✵✺✮ ✶✳✹ ✭✵✳✾✶✮ ✲✷✵✵✳✸ ✭✵✳✵✽✮ ✲✶✳✶ ✭✵✳✾✻✮

✷q ✲✶✵✺✳✽ ✭✵✳✵✵✮ ✲✶✼✳✶ ✭✵✳✷✽✮ ✲✶✾✻✳✼ ✭✵✳✵✾✮ ✲✸✳✺ ✭✵✳✾✵✮

✹q ✲✶✵✺✳✹ ✭✵✳✵✵✮ ✲✶✷✳✹ ✭✵✳✺✾✮ ✲✷✹✷✳✷ ✭✵✳✶✷✮ ✲✽✻✳✷ ✭✵✳✵✵✮

✽q ✲✶✹✹✳✹ ✭✵✳✶✷✮ ✲✼✳✼ ✭✵✳✺✻✮ ✲✷✽✼✳✻ ✭✵✳✵✵✮ ✲✶✶✼✳✺ ✭✵✳✵✵✮

✶✷q ✲✶✻✵✳✷ ✭✵✳✵✵✮ ✲✸✸✳✾ ✭✵✳✵✵✮ ✲✸✺✹ ✭✵✳✵✵✮ ✲✼✶✳✾ ✭✵✳✵✵✮

❚❛❜❧❡✿❘▼❙❊✲st❛t✐st✐❝ ❢♦r ❞✐✛❡r❡♥t ❢♦r❡❝❛st ❤♦r✐③♦♥s ❢r♦♠ ✷✵✶✵✿◗✷✲✷✵✶✻✿◗✹ ♦❢ ❆❇▼ ✇✐t❤ ✻ ♣r❡❞✐❝t♦rs ✐♥

❝♦♠♣❛r✐s♦♥ t♦ ❆❘❳✭✶✮ ✇✐t❤ t❤❡ s❛♠❡ ♣r❡❞✐❝t♦rs✱ ❛s ✇❡❧❧ ❛s t♦ ❛ ❉❙●❊ ♠♦❞❡❧ ✇✐t❤ ❝♦♥❞✐t✐♦♥❛❧ ❢♦r❡❝❛sts✳

❱❛❧✉❡s ✐♥ ❜r❛❝❦❡ts ✐♥❞✐❝❛t❡ ♣✲✈❛❧✉❡s ♦❢ t❤❡ ❬❉✐❡❜♦❧❞ ❛♥❞ ▼❛r✐❛♥♦✱ ✶✾✾✺❪ t❡st ♦♥ ♣r❡❞✐❝t✐✈❡ ❛❝❝✉r❛❝②✳

INSTITUTE FOR ECOLOGICAL ECONOMICS

❈♦♥❞✐t✐♦♥❛❧ Pr❡❞✐❝t✐♦♥ P❡r❢♦r♠❛♥❝❡✱ ◗✉❛rt❡r❧② ❧❡✈❡❧s✿ ✷✵✶✵✿◗✹ ✲ ✷✵✶✸✿◗✹

2010 2011 2012 2013

7.4 7.5 7.6 7.7 7.8 7.9

8 10¹⁰ GDP (quarterly) DATA AR(1) DSGE ABM

2010 2011 2012 2013

3.9 4 4.1 4.2

4.3 10¹⁰Consumption (quarterly)

2010 2011 2012 2013

1.6 1.65 1.7 1.75 1.8 1.85

1.9 10¹⁰Investment (quarterly)

2010 2011 2012 2013

1.51 1.515 1.52 1.525 1.53 1.535

1.54 10⁶Government (quarterly)

2010 2011 2012 2013

3.85 3.9 3.95 4 4.05 4.1

4.15 10⁶ Exports (quarterly)

2010 2011 2012 2013

3.6 3.65 3.7 3.75 3.8 3.85

3.9 10⁶ Imports (quarterly)

❋✐❣✉r❡✿❆❇▼ ✭❜❧❛❝❦✮✱ ❆❘✭✶✮ ✭❜❧✉❡✮✱ ❉❙●❊ ✭r❡❞✮✱ ❊✉r♦st❛t ❞❛t❛ ✭❞❛s❤❡❞✮❀ ❤♦r✐③♦♥ ✶✷q ✸✵ ✴ ✺✵

❈♦♥❞✐t✐♦♥❛❧ Pr❡❞✐❝t✐♦♥ P❡r❢♦r♠❛♥❝❡✱ ●r♦✇t❤✿ ✷✵✶✵✿◗✹ ✲ ✷✵✶✸✿◗✹

2010 2011 2012 2013

-1 0 1 2 3

4 GDP growth (annual)

DATA AR(1) DSGE ABM

2010 2011 2012 2013

1 1.5 2 2.5 3 3.5

4 Inflation (annual)

2010 2011 2012 2013

-1 -0.5 0 0.5 1 1.5

2 GDP growth (quarterly)

2010 2011 2012 2013

0 0.5 1

1.5 Inflation (quarterly)

❋✐❣✉r❡✿❆❇▼ ✭❜❧❛❝❦✮✱ ❆❘✭✶✮ ✭❜❧✉❡✮✱ ❉❙●❊ ✭r❡❞✮✱ ❊✉r♦st❛t ❞❛t❛ ✭❞❛s❤❡❞✮❀ ❤♦r✐③♦♥ ✶✷q

✸✶ ✴ ✺✵