Assume the utility function from two goods (x and y) given by: U(x,y)=2x+xy+4 suppose that x and y are purchased in the market at a constant unit price of birr 3 and birr 2 respectively and the consumer has a money income of birr 104, which he spend on the two goods.
a. Formulate the consumer maximization problem?
b. Compute and interpret MRSx,y at x=2 and y=8?
c. Use lagrangian method to find the values of x and y that maximize utility?
2. Maximize U(x,y) = xy+x+2y subjected to Px=2, Py=5, and M=51?
3. Maximize U(x,y) = xy subjected to Px=2, Py=8, and M=160?
4. Mx U(x,y) = x.0.4 y0.6 subjected to Px = 6, Py=8, and M=60