1. Adam consumes two goods: housing and food. Suppose we are given Adams marginal utility of housing and his marginal utility of food at the basket he currently consumes. Can we determine his marginal rate of substitution of housing for food at that basket?

2. Jimmy has the following utility function for hot dogs: U(H) = 10H H², with MU_H = 10 2H
   1. Plot the utility and marginal utility functions on two separate graphs.
   2. Suppose that Jimmy is allowed to consume as many hot dogs as he likes and that hot dogs cost him nothing. Show, both algebraically and graphically, the value of H at which he would stop consuming hot dogs.

3. Consider the utility function U(x, y) = yx with the marginal utilities MUx = y/(2x) and MUy = x.
   1. Does the consumer believe that more is better for each good?
   2. Do the consumers preferences exhibit a diminishing marginal utility of x? Is the marginal utility of y diminishing?

4.For the following sets of goods draw two indifference curves, U1 and U2, with U2 > U1. Draw each graph placing the amount of the first good on the horizontal axis