A customer has a utility function of U(x,y)=xy+6x+6y
The price of good X is Px, customer income is I, hence constraint is x(Px)+y(Py)=I
1. Use Lagrange method to find demand function of x when I=20
2. Suppose Py=1, and Px can vary, I=20, what is the price-consumption curve?
3. Suppose Py=1, Px=2, customer income can change, what is the income-consumption curve?
4. Suppose I=20, Py=1, Px decreases from 2 to 1, what is the total effect of the price change on demand of x? Decompose the total effect into income and substitution effect.