Q Ambrose's utility function is U(x; y) = x+ 4y^1/2. The price of x is 1 and the price of y is 2. If
his income rises from 100 to 150, his consumption of y increases by more than 10% but less than
What's the utility function, btw? Is it U(x,y)=4x+y?
This could be solved by using the Lagrangean Optimization method by optimizing the utility functions with respect to the budget constraint and by proceeding to solve for x and y. The percentage change in the value of y gives you the result.
the ICs of the given utility function are concave, and if you plot one its IC with y-intercept = (M/Py) then x-intercept of that IC has to be (4M^2/Py^2) and the slope of the line connecting these two points is (Py/4M). Now you can find the condition for different corner solutions.
How come the utility function is concave? I am getting hessian to be positive semi-definite, so, it should be convex. And in that case, Y should not change at all. Also, isn't this is a quasilinear utility function with linear in x, so, consumption of Y should not change at all.