1. (30 marks) The utility function is given by: u(x, y) = (xy)¹⁰ and the original budget is x+2y=100, where Px=1 and Py=2. Then the price of x goes up to 4.

(a)Find the demand function of x.

(b)Find demand elasticity when Px changes from 1 to 4.

(c)Find the substitution effect, income effect, and total change in demand for good x as defined in the lectures.

(d)Illustrate the changes in (c) with a graph.

(e)Find the EV.

1. {30 marks] The utility function is given by: ohm, 3r} = {xm and the original budget is x+2y=l, where Px=1 and Pv=2. Then the price of it goes up to 4. {a} Find the demand function of x. [b] Find demand elasticity when PX changes from 1 to 4. {c} Find the substitution effect. income effect. and total change in demand for good a: as dened in the lectures. [d] Iliustrate the changes in [c] with a graph. [e] Find the EU