microeconomics & mathematics

2. Sofia will consume hot dogs, but only with whipped cream. Draw her preference map (Indifference Curves) for hotdogs and whipped cream. Explain.

3. For each of the following utility functions derive the Marginal Utility of X, the Marginal Utility of Y and the MRS for X and Y. In each case what type of goods are X and Y?

a. U(X,Y) = AXaYb

b. U(X,Y) = ln(XY)

c. U(X,Y) = 6x + 4Y

d. U(X,Y) = max(X,3Y)

4. Ryan has the utility function U(Pizza, Robots) = 10(Pizza)2(Robots).

a. If the price of robots is 10 and the price of a pizza is 5, and Ryan's total income is 150. What is his optimal consumption bundle of pizza's and robots?

b. Suppose the price of pizza increases to 10. What is the new optimal bundle?

c. Using your answers to a and b derive Ryan's likely demand curve for pizza.

d. Using your answer to a and b and c derive an estimate of Ryan's elasticity of demand for Pizza.

e. Suppose you are a monopoly provider of pizza in Ryan's life. At a price of 5, is it a good idea for you to raise the price of Pizza for Ryan?

5. Read this article: