Assume the utility function is (1, 2 ) = 1^2 2. If the consumer has income I = 240 and faces prices 1 = $8 and 2 = $2.

a) Determine the optimal consumption basket given these prices and income using substitution and the Lagrange method.

b) Determine the change in the optimal basket if the price of good x2 increases to $8. Use both methods as in a) above.