breed [employed an_employer] breed [unemployed an_unemployed] globals [initial-income income income-variation income-total-variation incomeE incomeE-variation public-expenditure public-expenditure-variation consumption initial-consumption consumption-total-variation investment-total-variation M TD TD-variation L r interest-rate interest-rate-variation] employed-own [Ce0 C1 consumption-variation consumptionE total-consumptionE] unemployed-own [Cu0 consumptionU total-consumptionU] patches-own [investment a investment-variation total-investment initial-investment incomeC incomeC-variation tax-rate] to setup clear-all ask one-of patches [ set pcolor green set public-expenditure (1000) set tax-rate (0.20)] create-employed (consumersnumber * (1 - unemployment-rate)) [setxy random-xcor random-ycor] ask employed [ set shape "facehappy" set color blue set incomeE ((random 50) + 5 + K) set Ce0 ((0.1 * incomeE) + 0.5) if incomeE < 10 [set C1 0.30 set size 1.2] if incomeE >= 10 and incomeE < 30 [set C1 0.50 set size 1.5] if incomeE >= 30 [set C1 0.80 set size 1.8] set consumptionE (Ce0 + C1 * (incomeE * (1 - tax-rate))) set total-consumptionE (sum [consumptionE] of employed)] create-unemployed (consumersnumber * unemployment-rate) [setxy random-xcor random-ycor] ask unemployed [ set size 1 set shape "face sad" set Cu0 (random 0.4) set color red set consumptionU (Cu0) set total-consumptionU (sum [consumptionU] of unemployed)] ask n-of 20 patches [ set pcolor yellow set incomeC (random 500) set a (0.80) set investment ((a - L) * incomeC) set total-investment (sum [investment] of patches with [pcolor = yellow]) set initial-investment (total-investment)] set consumption (sum [consumptionE] of employed + sum [consumptionU] of unemployed) set initial-consumption (consumption) set income (sum [consumptionE] of employed + sum [consumptionU] of unemployed + sum [investment] of patches with [pcolor = yellow] + public-expenditure) set initial-income (income) set r (10) set interest-rate ((income - total-supply) / (r * income)) set L (r * interest-rate) set TD ((1 - L) * income) do-plots end to work ask employed [move-to one-of patches with [pcolor = yellow] set color yellow] end to change-public-expenditure ask patches with [pcolor = green] [set public-expenditure-variation (public-expenditure * public-expenditure-variation-rate) set public-expenditure (public-expenditure + public-expenditure-variation) set income-variation (public-expenditure-variation) set income (income + income-variation) set income-total-variation (income - initial-income)] end to go change-consumption change-investment change-workforce-composition change-salary change-TD change-investment-i continue do-plots end to change-consumption ask employed [ifelse public-expenditure-variation-rate > 0 or public-expenditure-variation-rate < 0 [set incomeE-variation (public-expenditure-variation-rate * incomeE) set incomeE (incomeE + incomeE-variation) set consumption-variation (C1 * incomeE-variation) set consumptionE (consumptionE + consumption-variation) set total-consumptionE (sum [consumptionE] of employed) set consumption (consumption + sum[consumption-variation] of employed) set consumption-total-variation (consumption - initial-consumption) set income-variation (sum[consumption-variation] of employed) set income (income + income-variation) set income-total-variation (income - initial-income) set M (income-total-variation / (consumption-total-variation + investment-total-variation))] []] end to change-investment ask patches with [pcolor = yellow] [ifelse public-expenditure-variation-rate > 0 [set incomeC-variation (public-expenditure-variation-rate * incomeC) set incomeC (incomeC + incomeC-variation) set investment-variation ((a - L) * incomeC-variation) set investment (investment + investment-variation) set total-investment (sum [investment] of patches with [pcolor = yellow]) set investment-total-variation (total-investment - initial-investment) set income-variation (sum [investment-variation] of patches with [pcolor = yellow]) set income (income + income-variation) set income-total-variation (income - initial-income) set M (income-total-variation / (consumption-total-variation + investment-total-variation))] [ifelse public-expenditure-variation-rate < 0 [set incomeC-variation (public-expenditure-variation-rate * incomeC) set incomeC (incomeC + income-variation) set investment-variation (- investment) set investment (investment + investment-variation) set total-investment (sum [investment] of patches with [pcolor = yellow]) set investment-total-variation (total-investment - initial-investment) set income-variation (sum [investment-variation] of patches with [pcolor = yellow]) set income (income + income-variation) set income-total-variation (income - initial-income) set M (income-total-variation / (consumption-total-variation + investment-total-variation))] []]] end to change-workforce-composition if public-expenditure-variation-rate > 0 [ask n-of (0.02 * (consumersnumber * unemployment-rate)) unemployed [set breed employed]] if public-expenditure-variation-rate < 0 [ask n-of (0.02 * (consumersnumber * (1 - unemployment-rate))) employed [set breed unemployed]] end to change-salary ask patches with [pcolor = yellow] [ifelse public-expenditure-variation-rate > 0 or public-expenditure-variation-rate < 0 [set incomeE-variation ((public-expenditure-variation-rate / 2) * incomeC) set incomeE (incomeE + incomeE-variation)] []] ask employed [ifelse public-expenditure-variation-rate > 0 or public-expenditure-variation-rate < 0 [set consumption-variation (C1 * incomeE-variation) set consumptionE (consumptionE + consumption-variation) set total-consumptionE (sum [consumptionE] of employed) set consumption (consumption + sum[consumption-variation] of employed) set consumption-total-variation (consumption - initial-consumption) set income-variation (sum[consumption-variation] of employed) set income (income + income-variation) set income-total-variation (income - initial-income) set M (income-total-variation / (consumption-total-variation + investment-total-variation))] []] end to change-TD ask patches with [pcolor = green] [set TD-variation ((1 - L) * income-variation) set TD (TD + TD-variation) set interest-rate-variation ((total-supply * 10 ^ 5 * income-variation) / (r * (income - income-variation) * income)) set interest-rate (interest-rate + interest-rate-variation)] end to change-investment-i ask patches with [pcolor = yellow] [ifelse interest-rate-variation > 0 or interest-rate-variation < 0 [set investment-variation ((- r) * interest-rate-variation * incomeC) set investment (investment + investment-variation) set total-investment (sum [investment] of patches with [pcolor = yellow]) set investment-total-variation (total-investment - initial-investment) set income-variation (sum [investment-variation] of patches with [pcolor = yellow]) set income (income + income-variation) set income-total-variation (income - initial-income) set M (income-total-variation / (consumption-total-variation + investment-total-variation))] [ifelse Sensitivity [set investment-variation (0.1 * incomeC) set investment (investment + investment-variation) set total-investment (sum [investment] of patches with [pcolor = yellow]) set investment-total-variation (total-investment - initial-investment) set income-variation (sum [investment-variation] of patches with [pcolor = yellow]) set income (income + income-variation) set income-total-variation (income - initial-income) set M (income-total-variation / (consumption-total-variation + investment-total-variation))] []]] end to continue re-change-consumption re-change-investment re-change-TD change-investment-i do-plots end to re-change-consumption ask employed [ifelse income-variation > 0 or income-variation < 0 [set incomeE-variation (0.05 * income-variation) set incomeE (incomeE + incomeE-variation) set consumption-variation (C1 * incomeE-variation) set consumptionE (consumptionE + consumption-variation) set total-consumptionE (sum [consumptionE] of employed) set consumption (consumption + sum[consumption-variation] of employed) set consumption-total-variation (consumption - initial-consumption) set income-variation (sum[consumption-variation] of employed) set income (income + income-variation) set income-total-variation (income - initial-income) set M (income-total-variation / (consumption-total-variation + investment-total-variation))] []] end to re-change-investment ask patches with [pcolor = yellow] [ifelse income-variation > 0 [set incomeC-variation (0.05 * income-variation) set incomeC (incomeC + incomeC-variation) set investment-variation ((a - L) * incomeC-variation) set investment (investment + investment-variation) set total-investment (sum [investment] of patches with [pcolor = yellow]) set investment-total-variation (total-investment - initial-investment) set income-variation (sum [investment-variation] of patches with [pcolor = yellow]) set income (income + income-variation) set income-total-variation (income - initial-income) set M (income-total-variation / (consumption-total-variation + investment-total-variation))] []] end to re-change-TD ask patches with [pcolor = green] [set TD-variation ((1 - L) * income-variation) set TD (TD + TD-variation) set interest-rate-variation ((total-supply * 10 ^ 6.2 * r * income-variation) / ((r * (income - income-variation)) * (r * (income - income-variation)) + r * r * (income - income-variation) * income-variation)) set interest-rate (interest-rate + interest-rate-variation)] end to do-plots set-current-plot "Income" set-current-plot-pen "income" plot income set-current-plot "Investment" set-current-plot-pen "investment" ask patches with [pcolor = yellow] [plot total-investment] set-current-plot "Consumption" set-current-plot-pen "consumption" ask turtles [plot consumption] set-current-plot "Interest-rate" set-current-plot-pen "interest-rate" plot interest-rate end @#$#@#$#@ GRAPHICS-WINDOW 321 14 575 239 -1 -1 3.3 1 10 1 1 1 0 1 1 1 0 73 0 58 0 0 1 ticks CC-WINDOW 5 503 912 598 Command Center 0 BUTTON 35 58 98 91 NIL setup\n NIL 1 T OBSERVER NIL NIL NIL NIL SLIDER 31 268 184 301 consumersnumber consumersnumber 20 200 88 1 1 NIL HORIZONTAL SLIDER 28 314 191 347 public-expenditure-variation-rate public-expenditure-variation-rate -0.005 0.50 0.1 0.005 1 NIL HORIZONTAL SLIDER 27 355 189 388 unemployment-rate unemployment-rate 0.02 0.10 0.06 0.01 1 NIL HORIZONTAL BUTTON 34 174 97 207 NIL go NIL 1 T OBSERVER NIL NIL NIL NIL PLOT 686 10 893 173 Income time income 0.0 100.0 0.0 1.0E7 true false PENS "income" 1.0 0 -2674135 true PLOT 695 340 890 489 Consumption time Consumption 0.0 100.0 0.0 100.0 true false PENS "consumption" 1.0 0 -10899396 true BUTTON 36 97 99 130 NIL work NIL 1 T OBSERVER NIL NIL NIL NIL BUTTON 34 135 192 168 NIL change-public-expenditure NIL 1 T OBSERVER NIL NIL NIL NIL PLOT 688 176 903 326 Investment time investment 0.0 10.0 0.0 10.0 true false PENS "investment" 1.0 0 -13345367 true MONITOR 323 259 380 304 NIL M 4 1 11 BUTTON 34 217 113 250 NIL continue T 1 T OBSERVER NIL NIL NIL NIL SLIDER 25 396 197 429 total-supply total-supply 500 10000 5500 1000 1 NIL HORIZONTAL PLOT 349 332 549 482 Interest-rate NIL NIL 0.0 10.0 0.0 0.06 true false PENS "interest-rate" 1.0 0 -16777216 true SLIDER 25 436 197 469 K K -5 15 9 1 1 NIL HORIZONTAL MONITOR 385 260 470 305 Interest rate interest-rate 4 1 11 SWITCH 219 437 331 470 Sensitivity Sensitivity 1 1 -1000 MONITOR 476 259 612 304 Interest rate variation interest-rate-variation 10 1 11 @#$#@#$#@ WHAT IS IT? ----------- The model simulates the interaction between consumers, enterprises, the Government and the Central Bank in the short term. Consumers are divided into the employed and the unemployed. We assume that the Government lets the tax rate to be constant and changes only the amount of public expenditure. The Central Bank instead controls directly the money supply. In this model we can analyse the consequences generated by a variation of the public expenditure on the consumption of the employeed and on the investments of the enterprises but also on the interest rate. HOW IT WORKS ------------ A variation of the public expenditure varies the income of both the employed and the enterprises. The income of the unemployed is null so they consume only the amount Cu0 whereas the employed consume Ce0 + C1*(1-tax rate)*incomeE: consequently a variation of the income of the employed produces a variation of the consumption that depends only on the parameter C1. An increase of the income generates an increase of the consumption instead a decrease of the income generates a decrease of the consumption. The enterprises raises the level of their investments when their income increases whereas when their income decreases they set investments equal to zero. Moreover the level of investments is in inverse proportion to the interest rate. In addition, if the income rises (so the production too), the enterprises have to engage new workers to face up to the growth of the production: because of this, a fraction of the unemployed become employed. An opposite situation occurs if the income of the enterprises falls following a reduction of the public expenditure. Finally, a variation of the public expenditure and, consequently, of the income of the enterprises, produces a variation of the salary, and so of the income, of the employed generating in this way a variation of the consumption and so of the income, of the investment and so on. But a variation of the public expenditure has consequences also in the financial markets. In fact when income varies also the money demand varies but the money supply doesn't change so the interest rate varies too. Because of this there is a variation in the amount of investments in the opposite direction. Thanks to the appropriate switch we can also decide if the level of investments changes when the interest rate does not. A variation in the amount of investment generates a variation of the income and so of the consumption, of the investments of the enterprises, of the composition of the workforce, of the salary of the employed, of the consumption and so on. HOW TO USE IT ------------- The observer can decide the level of 5 parameters using the sliders: - the number of consumers - the unemployment rate - the public expenditure variation rate which represents the percentage variation of the public expenditure realized by the Government. In this way the Government always carries out a variation of the public expenditure but it is the observer who decides its amount - the total money-supply decided by the Central Bank in its monetary policy - K that represents the deviation from the mean, useful for the computation of the income of each employee. There are also 5 buttons in order to start the instructions: - to setup - to work - to change public expenditure - to go - to continue There is a switch "Sensitivity" that allows the observer to decide if investments may change (On) or not (Off) if the interest rate does not change. Finally there are 3 monitors. The first one is related to the variable M. This variable is the ratio of the total variation of the income and of the sum of the total variation of the consumption and of the investment. If it is greater than 1 then the income varies more than proportionally in comparison with the sum of the variation of the consumption and of the investment because of the effect of the multiplier. The second one shows the level of the equilibrium interest rate, that is the interest rate such that the total money supply (here fixed by using the slider) is equal to the total money demand. The last monitor shows the interest rate variation during the different cycles. We can observe the variation occured to the income, to the consumption, to the investment and to the interest rate following a variation of the public expenditure and of the income in the related graphs. THINGS TO NOTICE ---------------- The observer can analyse the effect of a variation in the public expenditure variation rate, in the level of the total supply and of the parameter K above all on the level of the interest rate and of the parameter M. Instead when we set the switch "Sensitivity" on, the effect is more evident on the level of the investments. THINGS TO TRY ------------- Try to change the total supply and the public-expenditure-variation-rate: what happens to the equilibrium interest rate? And what happens if you introduce the sensitivity of investments by using the switch? EXTENDING THE MODEL ------------------- It could be interesting to introduce another agent, the banks, in order to analyse in a better way the financial markets: in fact in this way consumers can allocate money also on deposits in an amount that depends proportionally on the level of the interest rate. CREDITS AND REFERENCES ---------------------- BLANCHARD, a cura di GIAVAZZI, AMIGHINI (2006), Macroeconomia, ed. 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