Although Lerner (1936) has derived an elegant symmetry theorem, this paper shows that he destroyed it subsequently. This paper also shows that Lerner is too ambitious in collecting taxation. His government may feel disappointed by the final result, for importers or exporters will react...

This paper discloses two mistakes in Lerner's symmetry theorem. He has confused the debit and credit of his accounting, for his export tax is actually a subsidy. He has confused the exchange relation. This paper also hints on the source of these mistakes

This paper shows how Scitovsky (1942) has abused Descartes' geometry. He manipulated between the first and the second quadrants. This paper corrects his mistake and reproduces his desired result, but such result is still not the desired offer curve

This paper unveils three dirty tricks exercised by Kemp and Shimomura (2000): 1. They play around with an ambiguous trade balance equation; 2. They change the convex social indifference curve into a concave one; 3. They think they can dictate market prices. Without these tricks, there is no...

This paper reviews the optimal tariff theory of Kahn (1947) and Graaff (1949), and finds that their solutions are not optimal. Indeed, their policy recommendations are welfare detrimental. Graaff's tariff is even uncertain, can be positive or negative

This paper proves that Shapley's value is an unfair calculation, for it undercuts the benefit of coalition members. This paper recommends profitable economic reasoning for truly fair distribution of coalition gain

Buchanan (1965) works out a model that solves both the usage frequency and the desired membership number of a club. Ng (1973) argues that Buchanan’s solution is not optimal, and proposes to use marginal benefit, instead of average benefit, to work out the solution. This paper proves that...