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To get a more general test of the shape of the supply curve in the early eighteenth century, before the potential onslaught of the flow of innovation, we employ information on the site rents per ton of coal extracted paid to the owners of the land under which the coal seams lay compared to the pithead price of coal. Table 5 shows average, minimum and maximum site rents per ton by decade for the north east as a percentage of the average pithead price of coal, calculated on the basis of a sample of 203 coal leases from the northeast from 1715 to 1864. Coal rents averaged only 10% of the selling price at the pithead over these years. But also there was little range in the site rents paid. The standard error of rents as a share of output costs averaged 3.4%, so that 95% of site rents would fall in the range 3-17%. The maximum site rent at any time was 31% of the estimated average pithead price of coal. In contrast in the modern world the mineral rent paid for some oil reserves in the Middle East is close to the whole of the wellhead price. That is why their were so few coal millionaires in eighteenth and nineteenth century England, in contrast to the oil billionaires of today.
Figure 5 shows the range of lease values across time. From 1715-1833 there was little trend in the level or the variation in lease values across time. But after 1833 there appears to be a break in the series, with both the level of rents relative to output prices and the variance dropping. But throughout both average coal rents and their variance remained small as a share of the pithead price.
For a given price of output, the variance in the rents at one time mainly reflected the variance in the extraction costs. In general, if we take the price at the Tyne as the same for all pits, then
where p is the price at the Tyne for a standard quality of coal, q is the quality of the coal, excost the cost of extraction and trancost the costs of getting the coal to the water, and i indexes the individual pit. Extraction costs, rather than transport costs, seem to dominate in the determination of rent. If transport costs to water were a substantial cost relative to rents then we would expect to see that after the introduction of rail travel c. 1830 there would be substantially greater dispersion of the pits from the Tyne. In fact average distances changed little. We calculated how close each pit was to the water, which varied from 0.25 miles to 18 miles. In 1727 to 1829 the average distance to the Tyne was 5.4 miles, in 1831-1864 6.4 miles. But this difference is not even close to statistically significant.
Presumably the existing network of wagon ways in the Tyne area was a fairly cost effective way of getting coal down to the Tyne. Second if transport costs to the Tyne were substantial we would expect to see lower rent at more distant pits, since there transport costs would absorb all the site rents. There was, however, no correlation between rent and distance to water, even before the arrival of the railroad. The implication of this is that the transport costs to the water were generally low, so that they did not have much impact on mineral rents. Thus the site rents measure mainly differences in extraction costs.
Accidental factors, such as the fact that large numbers of mines in the eighteenth century were leased for “dead rents” in order to be kept out of production, meant that at any time mine leases were for very varied points on the long run supply curve. Thus in 1770 while there were 31 collieries selling coal to the London market through the Tyne, another 11 collieries were being rented by the “Grand Allies” for a dead rent to keep their production out of the market. One, for example, was St Anthony’s colliery, close to the Tyne. The Grand Allies paid ₤300 a year to keep this colliery out of production for 42 years from 1734 to 1776. In another case the Grand Allies took Stanley colliery out of production in 1793, while paying the mineral owners again a rent of ₤300 per year until 1817 to keep it closed (Cromar, 1978). The variance of rents thus indicates the steepness of the slope of the supply curve.
If the advocates of significant technological advance in the industry in the years 1700are correct, there would be substantial variance in mineral rents in the early eighteenth century, reflecting differences in transport costs. As figure 5 shows, the variance was in fact small. From 1715 to 1749 90% of the site rents were between 5 and 14% of the average price of coal at the pithead.
A second test for a steeply sloped supply curve in the early eighteenth century would be the size of the average share of rents in the pithead price. If mine owners believed the curve was steeply sloped then rents would be a large share of the price for the pits currently worked. No one would want to lease coal land now for the very modest rents being paid if they believed that soon the cost of extracting coal on new seams would drive up prices substantially.
The owner of an exhaustible asset such as a coal seam can leave the coal in the ground and extract it later if prices are assumed likely to increase. The owner of a seam with extraction cost c per ton should delay mining as long as
where pt is the price of coal in year t, and r is the rate of return on capital. (pt – c) is the amount the seam can be leased for per ton in year t, and E(pt+1 – c) the expected site rent in year t+1. If coal seam owners expect site rents to increase at above the rate of return on capital they should just keep the coal underground and wait for more favorable prices. If real extraction costs from new mines and deeper seams were expected to be much higher in the early eighteenth century, then the market price of coal would be expected to rise also.
The incentive of the owners of the low cost seams would then be to conserve their assets for exploitation at a more favorable time unless the current coal price was already high enough to offer them large profits. Coal left in the ground would increase in value faster than the mineral rents obtained from its extraction could compound if invested in a mortgage or in landed property. What would persuade owners to exploit now would be a situation where enough owners deferred exploitation so that current prices rose sufficiently to make even current exploitation profitable. But this would imply that some owners received high site rents as long as extraction costs were expected to be increasing rapidly.
Figure 6 shows, for example, a simulated extraction path for the coal industry in the northeast, starting in 1700, where extraction costs then on the seams being exploited are assumed to be 4.5 s.
per ton (the actual costs in the 1730s for best coal). But costs were expected to rise as new seams were brought into production, with extraction costs per ton given by
where Q is cumulative output from 1700 on. With this specification the cost curve with cumulative output is as shown in figure 6. By 50 years from 1700, at the extraction rate of that decade, costs would be 23/- per ton with this assumption.
Assume that land owners have no market power and simply decide when to start working their seams. The price of coal at Newcastle is then the extraction cost plus the site rent. The price at London is the Newcastle price plus 17/- shipping and tax cost to the London market. The price in London (in shillings) is assumed to be
where qt is the million tons of the Newcastle reserves mined in that period. This demand curve is set so that at the actual annual output of the 1700s (q = 1.8 m tons per year) the price in London is close to the actual price that prevailed in that decade, 23/-. This implies that the maximum price that would be paid in London for coal is 40/-, and that demand for Newcastle coal in London was relatively elastic with respect to price (the price elasticity at the London price of the 1740s is 1.22 with this demand curve).11 The return on capital (r) is assumed to be 4.5%.
With just these specifications, we can calculate an implied extraction path (prices and quantities) for the decades following the 1700s, if the coal owners expected the technology and the demand to remain the same, and price path which meets condition (1) for the owners of the coal reserves. This is the path is shown in figure 6.
What is interesting for our purposes is that with these realistic specifications of initial costs the coal rents of the 1700s on the easily worked seams in use then are, at 3.5/- per ton, about 42 percent of the implied Newcastle price of 8.3/-. These rents are about 10 times as great as the rents per ton actually being charged in coal leases in the 1710s-1740s (see table 2). Yet the history of this 11Thus at the point where Newcastle output was 1% of the total reserves per year the price elasticity for Newcastle coal in London would be 12.5.
period is that mineral rents in the north east were low despite persistent attempts to restrict production. The payment of dead rents to keep mines out of production made no sense if future coal production was expected to come from seams with inherently much higher costs. Coal owners in the eighteenth century behaved as though they believed their currently worked seams, generally those close to the surface, had little cost advantage on coal seams not yet worked. And among the seams being opened up in any decade there is little sign of much variation in the costs of production.
Thus both the low level of coal rents in the early eighteenth century, and their low variance, indicates that the cost curve at that time was only very modestly upward sloped.
Total Factor Productivity in Coal Mining, 1700-1869 The evidence from consideration of the technological barriers, and from coal rents, is that extraction costs rose only modestly with cumulative output. Here we use this result to establish upper and lower bound estimates of the gains in total factor productivity (TFP) in coal mining over the Industrial Revolution era.
Lower Bound Estimate on Productivity Gains If we assume that the long run supply curve was in fact flat, then the TFP of the coal mining industry can be estimated reasonably well using the ratio of average input costs (C) to average extraction costs (EXCOST). Costs at any time t we measure as
ωj is the factor price paid to input j, and θj is the share of input j in the total payments to inputs (other than the land owners). The extraction cost is just the pithead price minus rents paid to the land owners. That is
This is labeled as Amin since it is a lower bound on the estimated productivity gains, because it assumes that coal seams were of equivalent quality over time.
Upper Bound Estimate on Productivity Gains We can also derive an upper bound productivity estimate. Since depth was the obstacle to exploiting the huge reserves of the deeper seams in the coal field, we can include a specific allowance for costs that increased with depth in the productivity calculation. These costs were pit sinking, winding and pumping. This is done by increasing the cost factor of the productivity calculation by a factor dependent on depth so that
where h is the average depth of pits, and φ is the share of costs that were dependent on the depth of pits in 1700. This measure of productivity will be the same in 1700 as before, but will increase as h increases relative to average depths in 1700. This productivity measure will overstate the gains in productivity between 1700 and 1860, since again it assumes all coal seams were equivalent apart from their depth. But in reality deeper mining was undertaken only when the lower seams justified the extra costs by being thicker, or having higher quality coal (the thickness of the seams economical to exploit in the northeast coal field varied between 6.5 feet and 2 feet). The above formula does not take into account the potential improvement in working costs and coal quality with deeper mining, and thus overestimates productivity gains.
The share of costs that were proportionate to depth, φ, can be estimated from the studies of Sidney Pollard and Michael Flinn of coal mine accounts in the early eighteenth century at about 9 percent (6 percent of costs were for fuel for winding and pumping, and 16 percent of capital costs were devoted to shaft sinking and to engines for winding and pumping, both of which were depth dependent). Average depth of pits increased from about 150 feet circa 1700 to the 450 feet seen in table 2 by the late 1820s. We assume depth moved up in a linear fashion so that average depth by the 1860s was 550 feet, nearly four times the average depth of 1700. With these two assumptions we can generate a cost function for mining as a function not just of input costs, but also of average mine depth.
We take as our best estimate of the true gains in coal mining productivity between 1700 and 1860 the average of these two measures. Tables 1, and 5-9 show the data necessary to calculate TFP in coal mining in the north east on either assumption. While the north east was a minority of the English industry, it was the single most important coalfield throughout this period, so productivity growth in the industry as a whole was unlikely to have differed much for England as a whole from the north east. 12 Mining labor was the most important cost, being more than 45% of all costs including rents of capital. The royalties paid for access to the seams were about 9%, which is very much in line with our estimates for the northeast shown below in table 6. Returns on capital were about 20% of costs.
Coal used for pumping and winding operations was 4% of costs, horse fodder 5%. The final 17% was a miscellany of craftsmen’s wages, and supplies such as timber, rope, candles, and oil.
12 Pollard (1983) places the share of the Northumberland and Durham coalfields at one-third for the beginning of the period and one-fourth for its closing. McCord and Rowe (1971) report that the region supplied London with nearly 95% of its coal requirements as late as 1826.