The supervolcano under Yellowstone Park erupts and all production ceases. This is shown in period 0. Since aggregate value added must equal aggregate labour the value of the ten physical units of opening stock must be negative. This is a circulating commodity capital model. There are no purchased non-wage inputs, no constant capital. It is not a one commodity model. Several agricultural commodities (wheat, barley, oats, rye) are produced using tradition agriculture where part of the harvest is retailed for sowing in the following period. One eleventh of the harvest is retained for every crop. Unit prices are held equal to 1 throughout. We work backwards from period 0 (see table below). The value of the closing stock of period -1 is equal to the value of opening stock of period 0. Let the unit value of sales in period -1 be v1. Then the value of the harvest is 100v1-100 and the value of the opening stock is 100v1-200. The value of this opening stock of commodity capital is equal to the value of the money for which it is eventually sold. A fraction 10/11 is sold at the end of period -1 and the remaining 1/11 is never sold. The value of the opening stock is therefore 100v1/11. So: 100v1-200 = 100v1/11 This gives v1=2.2, value of sales = 220, value of harvest = 120, value of opening stock 20. We repeat the calculation for period -2. The value of the closing stock of period -2 is equal to the value of opening stock of period -1. Let the unit value of sales in period -2 be v2. Then the value of the harvest is 100v2+20 and the value of the opening stock is 100v2-80. The value of this opening stock of commodity capital is equal to the value of the money for which it is eventually sold. A fraction 10/11 is sold at the end of period -2 and, of the remaining 1/11, 10/11 is sold at the end of period -1. The value of the opening stock is therefore 100v2/11 + 100v1/121 or 100v2/11 + 200/11. So: 100v2-80 = 100v2/11 + 200/11 This gives v2=0.9, value of sales = 90, value of harvest = 110, value of opening stock 10. We repeat the calculation for period -3. The value of the closing stock of period -3 is equal to the value of opening stock of period -2. Let the unit value of sales in period -3 be v3. Then the value of the harvest is 100v3+10 and the value of the opening stock is 100v3-90. The value of this opening stock of commodity capital is equal to the value of the money for which it is eventually sold. A fraction 10/11 is sold at the end of period -3 and, of the remaining 1/11, 10/11 is sold at the end of period -2 and, of the remaining 1/121, 10/11 is sold at the end of period -1. The value of the opening stock is therefore 100v3/11 + 100v2/121 + 100v1/1331 or 100v3/11 + 90/121 + 20/121 or 100v3/11 + 10/11. So: 100v3-90 = 100v3/11 + 10/11 This gives v3=1, value of sales = 110, value of harvest = 110, value of opening stock 10. Earlier periods are the same as period 3. Since unit prices are always = 1 the value of money has the same numerical value as the unit price of sales. The dollar value of stocks can be calculated. The dollar values under the "Labour" column are found, nominal money value added, are found using the value of money at the beginning of the period (labour goes in as a spike at the start of the period. Period 0 Opening Stock Labour Harvest Sales Closing Stock Physical 10 100 0 0 0 $ -45.45 45.45 0 0 0 Value (hrs) -100 100 0 0 0 Unit Value -10 Value of Money 2.2 2.2 Period -1 Opening Stock Labour Harvest Sales Closing Stock Physical 10 100 110 100 10 $ 22.22 111.11 54.55 100 -45.45 Value (hrs) 20 100 120 220 -100 Unit Value 2 1.02 2.2 -10 Value of Money 0.9 0.9 2.2 2.2 2.2 Period -2 Opening Stock Labour Harvest Sales Closing Stock Physical 10 100 110 100 10 $ 10 100 122.22 100 22.22 Value (hrs) 10 100 110 90 20 Unit Value 1 1 0.9 2 Value of Money 1 1 0.9 0.9 0.9 Period -3 Opening Stock Labour Harvest Sales Closing Stock Physical 10 100 110 100 10 $ 10 100 110 100 10 Value (hrs) 10 100 110 100 10 Unit Value 1 1 1 1 Value of Money 1 1 1 1 1