Problem
Consider an individual whose utility function has three goods: X1, X2, and X3. Assume that X1, and X2 are weakly separable from X3. Further assume that X3 is supplied by the government in the fixed amount X3*. The government collects a tax of t per unit of X3 that it supplies, hence disposable income is Y-tX3*. Demonstrate that the demand for X1, and X2 are a function only of Y and the prices of X1, and X2 (i.e., not P3).