Short answer questions:

1. A consumer has the utility function over goods x and y, u(x, y) =12x³y⁴.

a.What is the slope of the consumer's indifference curve at the consumption bundle, (1,2) ?

b. What is the optimal choice if the price of x is $1 and price of y is $2 and m is $98.

1. Consider the utility function U(X, Y) = ln(X)+2ln(Y).
2. What is the marginal utility of X? What is the marginal utility of Y?
3. What is MRS_xy? That is, how many units of X do I need to make up for a loss of one unit of Y?
4. Consider next the utility function U(X, Y) = XY². What is MRS_xy for this utility function.?
5. Do these two utility functions represent the same preferences ?

1. Consumer's optimum choice always lies at the tangency between the budget line and an indifference curve. State if true or false.

1. Max has a utility functionU(x,y) = 2xy + 1. The prices ofx andy are both $1 and Max has an income of $20. How much of each good will he demand?