Not sure if this is the correct board for this problem but here goes:
An agent with budget m > 0 lives in a world of two goods, good X and good Y, and is faced with positive prices Px and Py. Her preferences are represented by the utility function
U(x,y) := x^3y
where the symbol := stands for the expression "by definition equal."
a. Obtain the marginal utilities MUx and MUy of the two goods and the marginal rate of substitution of X for Y (MRSxy) at a typical positive bundle (x,y). Does this utility function exhibit positive marginal utilities and diminishing MRSxy for all positive consumption bundles? Explain.
b. Derive the agent's demand funtions for X and Y.
Well that's the assignment. I think that I'm pretty lost. Only thing I think that I'm sure about is the marginal rate of substitution will be equal to the Marginal Utility of X divided by Marginal Utility of Y. To obtain what those marginal utilities are is beyond me.
An agent with budget m > 0 lives in a world of two goods, good X and good Y, and is faced with positive prices Px and Py. Her preferences are represented by the utility function
U(x,y) := x^3y
where the symbol := stands for the expression "by definition equal."
a. Obtain the marginal utilities MUx and MUy of the two goods and the marginal rate of substitution of X for Y (MRSxy) at a typical positive bundle (x,y). Does this utility function exhibit positive marginal utilities and diminishing MRSxy for all positive consumption bundles? Explain.
b. Derive the agent's demand funtions for X and Y.
Well that's the assignment. I think that I'm pretty lost. Only thing I think that I'm sure about is the marginal rate of substitution will be equal to the Marginal Utility of X divided by Marginal Utility of Y. To obtain what those marginal utilities are is beyond me.