Suppose we have the following utility function: U(x,y)=x^0.25 y^0.75

1. Calculate the marginal rate of substitution and comment on what you know about the shape of the indifference curve.
2. Suppose we have a budget constraint that may be written as 4x+2y=100. What are prices and income? Draw the budget constraint.
3. What is your optimal level of x and y with the above information?
4. Now suppose you have a new utility function and budget constraint and at your highest level of utility the marginal rate of substitution is greater than the price ratio. Draw a graph that shows this and comment on which good you prefer more.
5. Draw both an income expansion path and two Engel curves if x is a normal good, and y is a normal good at low income levels and become inferior at high income levels.