a) Partially differentiate the utility function to find expressions for the marginal utility of x and y.
b) What is the marginal rate of substitution when x = 2 and y = 16
c) The consumer has a budget of $96 to spend. The price of x is $12 and the price of y is $6. Write the equation for the budget constraint.
d) What is the slope of the budget line, dy/dx?
The answer I got is 4x.
I've actually figured out how to do the remaining questions, but now I have some extension questions I could use some help with.
e) Set up the Lagrangian function.
f) Partially differentiate the Lagrangian function with respect to first x, then y and λ. Set each of the partial differentials you obtain equal to zero.
g) Solve the three simultaneous equations you got in f) to find the consumer's optimal bundle of x and y, and to find the marginal utility of an extra dollar of income, λ.