Consider the model given by ln Y = β1 + β2 ln X2 + β3 ln X3 + β4 ln X4 + u, where Y = per capita consumption of tea, X2 = real disposable per capita income (measured in dollars), X3 = price of sugar (measured in dollars per pound), X4 = price of coffee (measured in dollars per pound). Suppose that according to economic theory, sugar and tea are complementary products. What would be the sign of the coefficient β3?

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Consider the model given by ln Y = β<sub>1</sub> + β<sub>2</sub> ln X<sub>2</sub> - β<sub>3</sub> ln X<sub>3</sub> + β<sub>4</sub> ln X<sub>4</sub> + u, where Y= per capita consumption of tea, X<sub>2</sub> = real disposable per capita income (measured in dollars), X<sub>3</sub> = price of sugar (measured in dollars per pound), X<sub>4</sub> = price of coffee (measured in dollars per pound). If we want to test the hypothesis that coffee and tea are unrelated products, what is the null going to be?