This paper sheds new light on the estimation of the long-run elasticity of the demand for business capital--for a measure that includes both equipment and structure--to changes in its user cost using a quarterly panel of two-digit manufacturing industries from South Africa from 1970 to 2000. For a variety of regression specifications, we find highly significant estimates of the user cost elasticity in the vicinity of -1.0 as implied by a Cobb-Douglas production function. These estimates contrast sharply with many previous studies that obtained small and/or statistically insignificant estimates of the user cost elasticity. This difference in findings may owe to the fact that the capital demand curve is better identified in a small open economy because shocks to capital supply are more likely to be exogenous. The economic embargo imposed on South Africa from 1985 to early 1994 temporarily forced its economy to become more closed and therefore provides a unique opportunity to assess the importance of identification in the estimation of the user cost elasticity. We find that the estimated magnitude of the user cost elasticity is considerably smaller over the embargo period. These findings suggest that the true elasticity is in the vicinity of the Cobb-Douglas benchmark, and that identification is important to uncovering this estimate.