Sophie has $50 to spend on goods 1 and 2 The unit prices of these goods are $1 and $2, respectively Her utility function is given by U x 1 x 2 2x 1 2x 2 (a) Write down Sophies budgetary constraint and deduce that U 48x 2 2x 2 2 100 (b) Hence work out Sophies optimal consumption of these goods ...

Sophie has $50 to spend on goods 1 and 2. The unit prices of these goods are

Question:

Sophie has $50 to spend on goods 1 and 2. The unit prices of these goods are $1 and $2, respectively. Her utility function is given by U = x₁x₂ + 2x₁ + 2x₂
(a) Write down Sophie’s budgetary constraint and deduce that U = 48x₂ − 2x²₂+ 100.
(b) Hence work out Sophie’s optimal consumption of these goods.