In: Economics
U = x^2y^4 with prices and Income . constraint 1 pxX+pyY=m
- Use the Lagrangian method to find demand function and the Lagrange Multiplier. Interpret the Lagrange multiplier. additionally, if an additional constraint is added that x ≥ 20. Use the Lagrangian method to find the demand function ( Marshallian demand) and the Lagrange Multiplier(s). Show details. Interpret the multiplier(s). Draw a diagram to illustrate.
Lagrangian method gives the optimal values of demand of good x and good y. The utility function given in the question is the monotonic transformation of Cobb Douglas utility function (xy = U(x,y)). Therefore indifference curve is convex to the origin as utility function is a concave function.