Consider the Walrasian demands x*(p, I) and x*(p', I) where p' is a price vector where the price of good i increased relative to p and all other prices stayed the same. Let T E denote the total effect on the demand for good i in response to the price increase, that is the change from xi*(p, I) to xi*(p', I). We know that T E can be decomposed into two effects the substitution effect (SE) and the income effect (IE). Are the following necessarily true (i.e, answer True if the expression is always true for every possible demand function, and False if there is some demand function such that the expression if false): 1. T E < 0 2. If SE < 0 then IE < 0 3. If SE < 0 then T E < 0 4. If T E < 0 then IE < 0 5. If IE < 0 then T E < 0
Consider the Walrasian demands x*(p, I) and x*(p', I) where p' is a
Are the following necessarily true (i.e, answer True if the expression is always true for every possible demand function, and False if there is some demand function such that the expression if false):
1. T E < 0
2. If SE < 0 then IE < 0
3. If SE < 0 then T E < 0
4. If T E < 0 then IE < 0
5. If IE < 0 then T E < 0
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