Question

Thembi’s utility function is U X Y 2  10 . The price of X is Px = K10, the price of Y is Py = K5, and her income is Y = K150. Show thembi's consumption bundle ina grapgh. (Hint: use the Langrangian method).

Answer 1

To show Thembi's consumption bundle on a graph using the Lagrangian method, set up the Lagrangian function and find optimal consumption values for X and Y. Plugging these values into the budget constraint equation gives the quantities of X and Y that Thembi will consume.

Step-by-step explanation:

To show Thembi's consumption bundle on a graph, we can use the Lagrangian method. With Thembi's utility function U(X,Y^2)=10, the price of X (Px) is K10, price of Y (Py) is K5, and her income is Y = K150. We can set up the Lagrangian function as L = U(X,Y^2) + λ(Y - PxX - PyY^2). By taking the partial derivatives with respect to X, Y, and λ, we can find the optimal consumption bundle.

After solving for the partial derivatives and equating them to 0, we can find the optimal values of X and Y. Plugging these values into the budget constraint equation, we can determine the quantities of X and Y that Thembi will consume. The consumption bundle can be represented on a graph by plotting the quantities of X and Y on the X and Y axes, respectively.