Suppose there are two goods, x and y. If one good has a negative price, and the other good has a positive price, then the slope of the budget constraint will be positive. is this true or false?

Suppose your utility for goods x1 and x2 is represented by the following utility function:  U(x1,x2)= x11/5  x24/5 a) What is your marginal rate of substitution, MRS12? b)  If the price for good x1 is p1 = 2, the price for good x2 is p2 = 4, and your available income is m = 20, write down your budget constraint. c) Using the prices and income given at b) above, find your optimal consumption choice bundle (Marshallian demand) and its corresponding utility level. d) Illustrate your optimal consumption choice on a graph. e) For the prices given in b), what income would you need to achieve a utility level of 25?   PLEASE ONLY ANSWER PART C, D AND E

Consider the single-good utility function u(x) = 3x². du(x) a) Find the marginal utility of x, MUx = dx b) Plot the utility function and marginal utility function on two separate graphs. c) Does this utility function satisfy the law of diminishing marginal utility? Explain.

Describe and graph your own example of a budget constraint using two goods (don’t forget to label your axes). In your example, make sure to state what the budget is, the price of the two goods, what the slope of the budget constraint equals (make sure to include the correct sign), and interpret what the slope represents.