In a famous article (J. Viner, “Cost Curves and Supply Curves,” Zeitschrift fur Nationalokonomie 3 (Sept. 1931): 23–46), Jacob Viner criticized his draftsman who could not draw a family of short-run ATC curves whose points of tangency with the U-shaped LAC curve were also the minimum points on each SAC curve. The draftsman protested that such a drawing was impossible to construct. Whom would you support in this debate, and why? Include a diagram in your answer.

The draftsman could not prepare a family of short-run ATC curves tangent with the LAC, whose tangency points were their minimum points because he was a mathematician. Technically, he derived the SAC curves below the LAC curve.

However, there can be no SAC curve below the LAC curve in economics. The LAC curve envelops all the SAC curves.Thus, the LAC curve lies tangent to the SAC curves.The LAC curve is U-shaped because there exist economies of scale at medium levels of output in the long run and diseconomies at initial and higher levels of output. In the long run, the same firm can expand its production scale from smallest to largest.

However, the lowest point of all the SACs are not the tangency points of all the SAC curves that lie on the LAC curve. That is so because the minimum point represents a minimum cost that will be incurred at different levels of output for different plant sizes. Only the SAC curve for a medium-scale plant has the lowest point coinciding with its point of tangency on the LAC curve because that is the point of efficiency. If the lowest point of the small-scale SAC curve lies on the LAC curve, a large-scale firm might take advantage and produce a higher output at lower average cost.

Therefore, the draftsman was wrong in pointing out that its not possible to draw a LAC curve which envelops all the SAC curves. However, it is the fact that it is not possible that the lowest point of all the SAC cuves lie on the LAC curve.

Suppose a firm, in the short run, wants to produce q1 output. It will produce at the smallest scale because it incurs an average cost of $8. The same amount of output produced at a medium scale will incur a high average cost of $10. Thus, small-scale production will be suitable for production with an average cost curve SAC₁.

Similarly, the medium-scale production is represented by the curve SAC2, and that for the largest scale by the curve SAC3. The tangency points for all the SAC curves lie on the LAC curve.

However, the lowest point on SAC for only the medium-scale production coincides with its tangency point and lies on the LAC curve. This point is also the lowest point of the LAC curve. Thus, it shows that the medium-scale plant is the most efficient in the long run.

If the lowest point of curve SAC₁ and SAC₂ were same as their tangency points on LAC, then the large scale firm will q₃ amount at lower cost in the long run.