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Solving Circuit Theory Conundrums
Steve KeenUniversity of Western Sydney
Debunking Economicswww.debtdeflation.com/blogs
www.debunkingeconomics.com
1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 20100
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AustraliaUSAAustralia from 2006USA from 2010
Post WWII Debt to GDP Ratios
Year
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cent
of
GD
P
1926 1928 1930 1932 1934100
125
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100000
112500
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Debt to GDP RatioTotal Private Sector Debt (Right hand scale)
US debt ratio & debt level, Great Depression
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US
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illio
n
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Debt Financed DemandUnemployment (RHS)
Debt driven demand and unemployment, USA
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Circuit Theory Conundrums
• “If on the other hand, wage-earners decide to keep part of their savings in the form of liquid balances, firms will get back from the market less money than they have initially injected in it … firms will be unable to repay to the banks the whole of their debt.” (Graziani 1989)
• “For the sake of simplicity, we exclude the payment of interest to the banks.” (Bellofiore et al, 2000)
• “The existence of monetary profits … has always been a conundrum for theoreticians of the monetary circuit. If money is created from bank credit, how can we explain profits if firms borrow just enough to cover wages that are simply spent on consumption goods and returned to firms to extinguish their initial debt … In other words, how can M become M+?” (Rochon 2005)
Mathematical logic to the rescue...
• Circuit conundrums result from “thinking in statics”– Financial cycle too complex to follow verbally– Even “stock-flow consistent” modelling not
suitable• Solution is to think dynamically in continuous
time– Consider flows set in motion by a loan– See what the flows tell you
• Use appropriate mathematics to model– Problem with neoclassical economics not maths
per se• But “teleological mathematics”
– Work out what you want to believe – Torture common sense until you “prove” it
• Appropriate maths is a system of differential equations...
Consider simplest possible pure credit economy• As in Graziani 1989 & 2003:
– No Central Bank or fiat money– 3 sectors
• Firms/Capitalists• Workers/Households• Bankers/Banks
– Single loan of $L to Firm sector• Creates $L of debt and $L money
simultaneously– Initiates several flows between accounts
• Debt compounding• Loan and deposit interest payments• Wages• Consumption...
Accounting
Mathematical logic to the rescue...• Develop model from the flows alone
– Stocks (system states) derived from integrating flowsAccounts (Stocks) &
Operations (Flows)Firm Loan FL Firm Deposit FD Worker Deposit WD Bank Income BI
Loan interest A-A=0 -A +A
Deposit Interest +B -B
Wages -C +C
Deposit Interest +D -D
Consumption E+F -E -F
• Analysing the flows... Rates of change of accounts:Rate of change... Verbal descriptionOf FL = 0 Debt remains constantOf FD = B+E+F-(A+C) Deposit interest + consumption flows – (Debt interest + wages)Of WD = C+D-E Wages + Workers’ deposit interest - Workers' consumptionOf BI = A-(B+D+F) Loan interest – (Deposit interest + Bankers' consumption)
• Accounts stable if “flows in” equal “flows out”:
$ transfer
Mathematical logic to the rescue...• So system can be stable if:
Account Condition Verbal Description
FD B+E+F=A+C Deposit interest plus consumption flows = Debt interest plus wages
WD C+D=E Wages plus Workers’ deposit interest = Workers' consumption
BI A=B+D+F Loan interest = Deposit interest plus Bankers' consumption
• Not obviously onerous conditions... Exploring further:
• A is the loan interest rate (rL) times Firm debt (FL)
• B is the deposit interest rate (rD) times Firm savings (FD)
• C is some rate per year (say w) times FD
• D is the deposit interest rate on Worker savings (WD)• E is some consumption rate (say w) times Worker
savings• F is some consumption rate (say b) Banker savings
(BI)• Equilibrium values are:
Mathematical logic to the rescue...• Solved with symbolic algebra program:
Find
FL
FD
WD
BI
simplify
collect L
L
rL rD
rD rD w L
w rL
rD rD w L
rD rL
rD
L
• Two key conditions:• All accounts are positive if
• b > rL
• and w > rD
• Which means???
• If (for example)...• The (after inflation) interest rate on loans is
5%; • The interest rate on deposits is 1%; and• Bankers spend their account balance more
often than once every 20 years; and• Workers spend theirs more often than once
every century• Then the system can be stable
Common sense (and Marx) to the rescue...
• It’s actually very simple:– Capitalist borrows $100– Generates $400 (money turns over 4 times in a
year)– Pays $300 in wages + inputs, keeps $100 in profit– Uses $5 to pay interest on $100 debt– Pockets $75 (M+-M) after paying debt down by
$20• Expressed in terms of time lags, conditions under
which credit-financed business is profitable are quite broad– tS time lag from M to M+ (1/4th year standard
setting)– tW time lag in workers consumption (1/26th year)
– tB time lag in bankers consumption (1 year)• Positive bank balances (and hence incomes—shown
later) for broad range of parameter values...
Conditions for positive bank balances over time• Wide range of valid values:
0 5 10 15 200
20
40
60
80
100
FirmsWorkersBankers
Account Balances as a function of bankers consumption time lag
B from 0 to 20 years (given W=1/26, s=30%, S=1/4)
Acc
ount
bal
ance
s in
$
0 2 4 6 8 100
20
40
60
80
100
FirmsWorkersBankers
Account Balances as a function of production time lag
S from 0 to 10 years (given W=1/26, B=1, s=30%)
Acc
ount
bal
ance
s in
$
0 0.2 0.4 0.6 0.80
20
40
60
80
100
FirmsWorkersBankers
Account Balances as a function of surplus share
s from 0 to 1 (given W=1/26, B=1, S=1/4)
Acc
ount
bal
ance
s in
$
• Bank balances are positive if:• Surplus generated in
production• & workers consume• & bankers spend• Fairly basic conditions for
positive profits, wages, etc...
Viable even if turnover period is 7-10 years
Conditions for positive incomes over time
• Banker gross income easy to calculate– Interest on outstanding debt per year = rL.FL
• Worker gross income also easy– Wage flow per year = w.FD
– But what is w? Back to Marx & Sraffa:• Workers share of surplus (1-s)• Divided by time lag in going from M to M+ (tS )
• So w= (1-s)/tS
• What about capitalist profits?– Capitalists share of surplus (s)– Divided by time lag in going from M to M+ (tS )
– So Profits= FD.(1-s)/tS
– Also derivable from Price times Quantity minus Wages
rD
rL++
0.05s
tau_S
0.3
Capitalist share of surplus
0.25
Years from M to M+
omega
beta1
Banker A/C turnover p.a.
26
Worker A/C turnover p.a.
Bank Account Balances
Loan
100
05
101520253035404550556065707580859095
FD
100
05
101520253035404550556065707580859095
WD
25
0123456789
101112131415161718192021222324
BI
25
0123456789
101112131415161718192021222324
0.04
Loan minus deposit rate
0.01
Interest rate on deposits
Incomes per year
Wage
s
400
0
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375
GDP
400
0
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375
Profi
ts
400
020406080
100120140160180200220240260280300320340360380
Inte
rest
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Wages
FirmLoanAccount
BankIncomeAccount
FirmDepositAccount
WorkerDepositAccount
Profits
Interest
++
Firm Accounts
Years0 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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760
120115
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95
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Firm LoanFirm Deposit
Worker and Banker Accounts
Years0 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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760
2018
14
10
6
2
Worker DepositBank Income Account
Annual Incomes
Years0 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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760
30027023019015011070
Annual WagesAnnual Profits
Annual Income
Years0 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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760
109
7
5
3
1
Annual Gross Interest Income
Basic Circuit model without debt repayment. You can alter the simulation by varying the parameter values s (capitalist share of surplus), tau_S (turnover time), omega (No. of times workers turnover accounts per year), beta (ditto for bankers), deposit rate and spread between loan and deposit rates using the sliders above. Details of the model structure can be found by right-clicking on the blue boxes, which contain the flowchart mathematics for each of the accounts in the system.
Annual Income
Years0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 14 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 18 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 20 20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 21.9 22 22.1 22.2 22.3 22.4 22.5 22.6 22.7 22.8 22.9 23 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 23.9 24 24.1 24.2 24.3 24.4 24.5 24.6 24.7 24.8 24.9 25 25.1 25.2 25.3 25.4 25.5 25.6 25.7 25.8 25.9 26 26.1 26.2 26.3 26.4 26.5 26.6 26.7 26.8 26.9 27 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8 27.9 28 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 29 29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8 29.9 30 30.1 30.2 30.3 30.4 30.5 30.6 30.7 30.8 30.9 31 31.1 31.2 31.3 31.4 31.5 31.6 31.7 31.8 31.9 32 32.1 32.2 32.3 32.4 32.5 32.6 32.7 32.8 32.9 33 33.1 33.2 33.3 33.4 33.5 33.6 33.7 33.8 33.9 34 34.1 34.2 34.3 34.4 34.5 34.6 34.7 34.8 34.9 35 35.1 35.2 35.3 35.4 35.5 35.6 35.7 35.8 35.9 36 36.1 36.2 36.3 36.4 36.5 36.6 36.7 36.8 36.9 37 37.1 37.2 37.3 37.4 37.5 37.6 37.7 37.8 37.9 38 38.1 38.2 38.3 38.4 38.5 38.6 38.7 38.8 38.9 39 39.1 39.2 39.3 39.4 39.5 39.6 39.7 39.8 39.9 40 40.1 40.2 40.3 40.4 40.5 40.6 40.7 40.8 40.9 41 41.1 41.2 41.3 41.4 41.5 41.6 41.7 41.8 41.9 42 42.1 42.2 42.3 42.4 42.5 42.6 42.7 42.8 42.9 43 43.1 43.2 43.3 43.4 43.5 43.6 43.7 43.8 43.9 44 44.1 44.2 44.3 44.4 44.5 44.6 44.7 44.8 44.9 45 45.1 45.2 45.3 45.4 45.5 45.6 45.7 45.8 45.9 46 46.1 46.2 46.3 46.4 46.5 46.6 46.7 46.8 46.9 47 47.1 47.2 47.3 47.4 47.5 47.6 47.7 47.8 47.9 48 48.1 48.2 48.3 48.4 48.5 48.6 48.7 48.8 48.9 49 49.1 49.2 49.3 49.4 49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5 50.6 50.7 50.8 50.9 51
109
7
5
3
1
Annual Gross Interest Income
Annual Incomes
Years0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 14 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 18 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 20 20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 21.9 22 22.1 22.2 22.3 22.4 22.5 22.6 22.7 22.8 22.9 23 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 23.9 24 24.1 24.2 24.3 24.4 24.5 24.6 24.7 24.8 24.9 25 25.1 25.2 25.3 25.4 25.5 25.6 25.7 25.8 25.9 26 26.1 26.2 26.3 26.4 26.5 26.6 26.7 26.8 26.9 27 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8 27.9 28 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 29 29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8 29.9 30 30.1 30.2 30.3 30.4 30.5 30.6 30.7 30.8 30.9 31 31.1 31.2 31.3 31.4 31.5 31.6 31.7 31.8 31.9 32 32.1 32.2 32.3 32.4 32.5 32.6 32.7 32.8 32.9 33 33.1 33.2 33.3 33.4 33.5 33.6 33.7 33.8 33.9 34 34.1 34.2 34.3 34.4 34.5 34.6 34.7 34.8 34.9 35 35.1 35.2 35.3 35.4 35.5 35.6 35.7 35.8 35.9 36 36.1 36.2 36.3 36.4 36.5 36.6 36.7 36.8 36.9 37 37.1 37.2 37.3 37.4 37.5 37.6 37.7 37.8 37.9 38 38.1 38.2 38.3 38.4 38.5 38.6 38.7 38.8 38.9 39 39.1 39.2 39.3 39.4 39.5 39.6 39.7 39.8 39.9 40 40.1 40.2 40.3 40.4 40.5 40.6 40.7 40.8 40.9 41 41.1 41.2 41.3 41.4 41.5 41.6 41.7 41.8 41.9 42 42.1 42.2 42.3 42.4 42.5 42.6 42.7 42.8 42.9 43 43.1 43.2 43.3 43.4 43.5 43.6 43.7 43.8 43.9 44 44.1 44.2 44.3 44.4 44.5 44.6 44.7 44.8 44.9 45 45.1 45.2 45.3 45.4 45.5 45.6 45.7 45.8 45.9 46 46.1 46.2 46.3 46.4 46.5 46.6 46.7 46.8 46.9 47 47.1 47.2 47.3 47.4 47.5 47.6 47.7 47.8 47.9 48 48.1 48.2 48.3 48.4 48.5 48.6 48.7 48.8 48.9 49 49.1 49.2 49.3 49.4 49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5 50.6 50.7 50.8 50.9 51
30027023019015011070
Annual WagesAnnual Profits
Worker and Banker Accounts
Years0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 14 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 18 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 20 20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 21.9 22 22.1 22.2 22.3 22.4 22.5 22.6 22.7 22.8 22.9 23 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 23.9 24 24.1 24.2 24.3 24.4 24.5 24.6 24.7 24.8 24.9 25 25.1 25.2 25.3 25.4 25.5 25.6 25.7 25.8 25.9 26 26.1 26.2 26.3 26.4 26.5 26.6 26.7 26.8 26.9 27 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8 27.9 28 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 29 29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8 29.9 30 30.1 30.2 30.3 30.4 30.5 30.6 30.7 30.8 30.9 31 31.1 31.2 31.3 31.4 31.5 31.6 31.7 31.8 31.9 32 32.1 32.2 32.3 32.4 32.5 32.6 32.7 32.8 32.9 33 33.1 33.2 33.3 33.4 33.5 33.6 33.7 33.8 33.9 34 34.1 34.2 34.3 34.4 34.5 34.6 34.7 34.8 34.9 35 35.1 35.2 35.3 35.4 35.5 35.6 35.7 35.8 35.9 36 36.1 36.2 36.3 36.4 36.5 36.6 36.7 36.8 36.9 37 37.1 37.2 37.3 37.4 37.5 37.6 37.7 37.8 37.9 38 38.1 38.2 38.3 38.4 38.5 38.6 38.7 38.8 38.9 39 39.1 39.2 39.3 39.4 39.5 39.6 39.7 39.8 39.9 40 40.1 40.2 40.3 40.4 40.5 40.6 40.7 40.8 40.9 41 41.1 41.2 41.3 41.4 41.5 41.6 41.7 41.8 41.9 42 42.1 42.2 42.3 42.4 42.5 42.6 42.7 42.8 42.9 43 43.1 43.2 43.3 43.4 43.5 43.6 43.7 43.8 43.9 44 44.1 44.2 44.3 44.4 44.5 44.6 44.7 44.8 44.9 45 45.1 45.2 45.3 45.4 45.5 45.6 45.7 45.8 45.9 46 46.1 46.2 46.3 46.4 46.5 46.6 46.7 46.8 46.9 47 47.1 47.2 47.3 47.4 47.5 47.6 47.7 47.8 47.9 48 48.1 48.2 48.3 48.4 48.5 48.6 48.7 48.8 48.9 49 49.1 49.2 49.3 49.4 49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5 50.6 50.7 50.8 50.9 51
2018
14
10
6
2
Worker DepositBank Income Account
Firm Accounts
Years0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 13 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 14 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 15 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 18 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 19 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 20 20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9 21 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 21.9 22 22.1 22.2 22.3 22.4 22.5 22.6 22.7 22.8 22.9 23 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 23.9 24 24.1 24.2 24.3 24.4 24.5 24.6 24.7 24.8 24.9 25 25.1 25.2 25.3 25.4 25.5 25.6 25.7 25.8 25.9 26 26.1 26.2 26.3 26.4 26.5 26.6 26.7 26.8 26.9 27 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8 27.9 28 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 29 29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8 29.9 30 30.1 30.2 30.3 30.4 30.5 30.6 30.7 30.8 30.9 31 31.1 31.2 31.3 31.4 31.5 31.6 31.7 31.8 31.9 32 32.1 32.2 32.3 32.4 32.5 32.6 32.7 32.8 32.9 33 33.1 33.2 33.3 33.4 33.5 33.6 33.7 33.8 33.9 34 34.1 34.2 34.3 34.4 34.5 34.6 34.7 34.8 34.9 35 35.1 35.2 35.3 35.4 35.5 35.6 35.7 35.8 35.9 36 36.1 36.2 36.3 36.4 36.5 36.6 36.7 36.8 36.9 37 37.1 37.2 37.3 37.4 37.5 37.6 37.7 37.8 37.9 38 38.1 38.2 38.3 38.4 38.5 38.6 38.7 38.8 38.9 39 39.1 39.2 39.3 39.4 39.5 39.6 39.7 39.8 39.9 40 40.1 40.2 40.3 40.4 40.5 40.6 40.7 40.8 40.9 41 41.1 41.2 41.3 41.4 41.5 41.6 41.7 41.8 41.9 42 42.1 42.2 42.3 42.4 42.5 42.6 42.7 42.8 42.9 43 43.1 43.2 43.3 43.4 43.5 43.6 43.7 43.8 43.9 44 44.1 44.2 44.3 44.4 44.5 44.6 44.7 44.8 44.9 45 45.1 45.2 45.3 45.4 45.5 45.6 45.7 45.8 45.9 46 46.1 46.2 46.3 46.4 46.5 46.6 46.7 46.8 46.9 47 47.1 47.2 47.3 47.4 47.5 47.6 47.7 47.8 47.9 48 48.1 48.2 48.3 48.4 48.5 48.6 48.7 48.8 48.9 49 49.1 49.2 49.3 49.4 49.5 49.6 49.7 49.8 49.9 50 50.1 50.2 50.3 50.4 50.5 50.6 50.7 50.8 50.9 51
120115
105
95
85
Firm LoanFirm Deposit
V->S
2,1
3,1
4,1
5,1
6,1
7,1
S->V
2,1
3,1
4,1
5,1
6,1
7,1
These strip charts repeat the data in the main ones to the left, but show one year at a time to enable a closer look at rapid dynamics between variables.
Common sense (and Marx) to the rescue...• A Simulation (click here for
software)... BasicCircuitCompound.vsm
Conditions for positive incomes over time
• Banker gross income = rL.FL
• Worker gross income = FD.(1-s)/tS
• Capitalist gross income = FD.s/tS
• All positive so long as FD > 0.• System so far purely monetary
– Presumes physical system producing net surplus
• Easily linked with basic production system– Output = Labour times labour productivity
Q a L
– Labour = Wage flow/Wage
– What about prices?– Derive from equilibrium
conditions:
1h
d LW P
W dt N
1 D
S
FsL
W
– Wage set by “Phillips curve”
Cancel Cancel
CancelCancel
Basic financial and physical equilibrium conditions• In equilibrium, physical output Q = physical demand
D• Physical Output Q = a.L• Where L = Wage flow/Wage
1 D
S
FsL
W
So 1 D
S
FsQ a
W
• Equilibrium physical demand will be• Flow of monetary demand divided by Price
level• D = (Wages+Profits)/Price
• (net interest cancels out)• D = (FD.s/tS)/P• Equating D and Q:
1 D D
SS
F Fsa P
W
• Solve for
P: 11eq
WP
s a
• Surplus the source of profit• Price converts capitalist share of
surplus in production into monetary sum
CircuitProductionTimeLagsCompound.vsm
Variables
Q
0.0384615
Worker consumption lag
0.01
Interest rate on deposits0.04
Loan minus deposit rate0.25
Years from M to M+
0.3
Capitalist share of surplus
tau_S
s++
rL
rD
Parameters
tau_P
tau_B
tau_W
1
Banker consumption lag
1
Price setting lag
InitialConditions
FinancialSystem
*
Value of Output
Price Level
$/Unit of Output
Years0 20 40 60 80 100
1.00
1.25
1.50
1.75
2.00
Level of Output
Quantity
Years0 20 40 60 80 100
240
250
260
270
280
Value of Output
Price * Quantity
Years0 20 40 60 80 100
200
250
300
350
400
PriceSystem
ProductionSystem
P*Q
P*Q
Q
P
Tw o Measures of Profit
Years0 20 40 60 80 100
0
50
100
150
200 Price * Quantity - Wages (Sales-Cost)Financial Flow s
P*Q-Wages
Profit_$
Incomes
Years0 .2 .4 .6 .8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 7.8 8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.2 11.4 11.6 11.8 12 12.2 12.4 12.6 12.8 13 13.2 13.4 13.6 13.8 14 14.2 14.4 14.6 14.8 15 15.2 15.4 15.6 15.8 16 16.2 16.4 16.6 16.8 17 17.2 17.4 17.6 17.8 18 18.2 18.4 18.6 18.8 19 19.2 19.4 19.6 19.8 20 20.2 20.4 20.6 20.8 21 21.2 21.4 21.6 21.8 22 22.2 22.4 22.6 22.8 23 23.2 23.4 23.6 23.8 24 24.2 24.4 24.6 24.8 25 25.2 25.4 25.6 25.8 26
300260220
160120
60
0
Financial Flow sPrice * Quantity - Wages
Simulation:
Basic financial and physical equilibrium conditions• Dynamic price relation
is 1
1P
d WP P
dt a s
– Time-lagged convergence to equilibrium
value– Full monetary production model can now be
examined– Equilibrium conditions are (for given wage
W):FLe
FDe
WDe
BIe
Qe
Le
Pe
S rD W 1 rL B 1
rD B 1 1 rD W S W s 1( )
W rL B 1 s 1( )
rD B 1 1 rD W S W s 1( )
B rD rL
rD B 1
a rD W 1 rL B 1 s 1( )
W rD B 1 1 rD W S W s 1( )
rD W 1 rL B 1 s 1( )
W rD B 1 1 rD W S W s 1( )
W
a s 1( )
100
86.627
9.333
4.04
242.555
242.555
1.429
Common sense to the rescue...
• Capitalists can therefore– borrow money;– pay interest;– repay debt;– & still make a profit
• Aggregate profit exceeds zero– As do wages and interest income
• Price converts capitalist surplus in production into money– M becomes M+ via the price mechanism
• (if there is a surplus in production)• Fixed stock of money can finance constant output
– Rising M not needed to sustain constant output
Common sense (and Marx) to the rescue...• Contrary Circuit conclusions resulted from
– Confusion of stocks & flows:• Initial Loan (stock) is not the limit of financial
transactions the money it creates can cause (Flow/Year)
– Forgetting about surplus in production• Source of both physical and financial profit
– Forgetting about turnover period of capital:• “Let the period of turnover be 5 weeks, : the
working period 4 weeks... In a year of 50 weeks ... Capital I of £2,000, constantly employed in the working period, is therefore turned over 12½ times. 12½ times 2,000 makes £25,000.” (Capital II, Part II: The Turnover of Capital)
A new approach to dynamic modelling• Inspired by Godley/Lavoie Stock-Flow Consistent
tables– Plus comments by Scott Fullwiler at UMKC 2006
• Rendition of SAM tabular concept in continuous time– With bank account fundamental unit of analysis
• Far more suitable for asynchronous real-world– All investment does not occur at same time
• Discrete “t”, “t-1” period modelling imposes this– Does not require artificial time-delays– Allows processes to occur at different frequencies
• Consumption fortnightly, investment 2-yearly– See my Rossi-Ponsot 2009 chapter for more
details• Easily implemented in any symbolic algebra program
– (Mathcad—www.ptc.com/mathcad—shown here...)
Accounting
A new approach to dynamic modelling• Input table of accounts and flows between them:
• Substitute functions for placeholders A, B, etc.:Symbolic SubstitutionsInterest on outstanding debt A rL FL t( )rLDebt Service B AADeposit Interest C rD FD t( )rD
Wages D1 sS
FD t( )S
Workers Interest E rD WD t( )rD
Workers consumption FWD t( )
W
WD
Bankers consumption GBI t( )
B
BI
System S2
tFL t( )d
d0
tFD t( )d
drD FD t( ) rL FL t( )
BI t( )
B
WD t( )
W
FD t( ) s 1( )
S
tWD t( )d
drD WD t( )
WD t( )
W
FD t( ) s 1( )
S
tBI t( )d
drL FL t( ) rD FD t( ) rD WD t( )
BI t( )
B
• Automatically build “coupled ODE” model
$ transferS2
"Type"
"Account"
"Account"
"Compound Interest"
"Pay Interest on Loan"
"Interest on Deposit"
"Wages"
"Interest on Deposit"
"Consumption"
1
"Firm Loan"
FL t( )
A
B
0
0
0
0
1
"Firm Deposit"
FD t( )
0
B
C
D
0
F G
1
"Worker Deposit"
WD t( )
0
0
0
D
E
F
0
"Bank Income"
BI t( )
0
B
C
0
E
G
A
Conclusion: The Circuit “Works”
• Long-believed conundrums must be forgotten... But• Solving conundrums strengthens Circuit Theory
– Can explain where monetary profit comes from– System stable in the absence of Ponzi finance!– Model expands to growth, multiple sectors, fiat
money– Explains:
• Endogenous credit money creation;• Credit system’s desire to extend too credit;
– Bank surplus rises if Debt rises– Basis of “inherent instability” in Financial Instability
Theorem• Not just a Hypothesis!
• Model here merely start of modelling monetary dynamics...
The Circuit can be extended...• To general monetary dynamic disequilibrium model...
0 20 40 60 80 1005
0
5
10
15
Capital GoodsConsumer GoodsAgricultureEnergy
The Rate of Profit in a Monetary Multisectoral Model of Production
Years
Pro
fit/C
apita
(P
erce
nt)
20 25 30 35 402
0
2
4
6
8
Real Rate of Economic Growth
Per
cent
p.a
.
20 25 30 35 400
20
40
60
0
10
20
30
40
GDPDebt
Change in Nominal Credit and Nominal GDP
Per
cent
cha
nge
p.a.
94 96 98 100 102 10455
60
65
70
75
80
85
90
95
100
15
10
5
0
5
10
15
20
25
30
WagesProfitInterest
Income Distribution Limit Cycles
Employment RateW
ages
Sha
re o
f O
utpu
t
Cap
italis
t & B
anke
r S
hare
s
• Mixed credit-fiat money...
• Comparing different policies
30 40 50 600
5
10
15
20
No PolicyBank RescueBorrower Rescue
Years
Unem
plo
ym
ent (P
erc
ent of W
ork
forc
e)
0 2 4 6 8 10
4
2
0
2
4No StimulusQuantitative EasingFiscal Stimulus
Phase plot of unemployment & inflation
Unemployment
Infl
atio
n
