Consider Gaby's utility function u(X1, X2 ) = 4x1 + x2, where x1 is the consumption of rice and x2 is "everything else". Assuming the income is m and the prices are p1 and p2, repectively.

Is this preference homothetic? Justify your answer.

Derive the ordinary demand function for both x1 and x2 .(Consider all possible situations)

Suppose m = 30, p1 = 1, and p2 = 2, compute her optimal consumption bundle.

Now it cost p'1 = 4 to buy a unit of rice, what is his new consumption bundle?

Draw Engel curves for both x1 and x2.