NAME ________________________

Economics 331: Consumer Theory Problem Set

Dr. R. Horn

Note: All of these questions have appeared in various forms on previous exams:

  1. The theory of consumer behavior predicts that a consumer will buy more units of a good at a lower price unless the good is an inferior good. Do you agree? Explain?
  2. A consumer always buys 5 units of Y for every one unit of X. The slope of the consumer’s demand function for X can have a positive slope at lower prices but will have a negative slope at higher prices. Do you agree? Explain?
  3. Important: Explain carefully the income and substitution effects of a change in the price of a good. Show them on a diagram when the good in question is a normal good, an inferior good and finally a Giffen good. Are all Giffen goods inferior goods? Are all inferior goods Giffen goods?
  4. Important: Be able to explain the relationship between price, demand, expenditure and elasticity of demand. What is the relationship between the shape of the price consumption curve and the price elasticity of demand?
  5. Explain the derivation of Engel Curves.
  6. Assume a consumer's utility function is given by:

        U= 2 X2Y

                    a. For I = 45, Px = 2, and Py = 3; find the utility maximizing values of X and Y.

b. Suppose the price of X falls to 1. Find the new utility maximizing values of X and Y.

                    c. You now have two points of the demand curve for x. What is the price elasticity of demand for x ?

d. Draw a graph of the situation and identify (graphically) the income and substitution effects of the change in the price of X.

e. If for any change in the price of X, the consumer's expenditure on X remained constant what would the demand curve for X look like?
  1. Draw a price consumption curve for a good whose price elasticity of demand is less

          than one (or negative one). Is it possible for the price consumption curve for x to extend above the vertical intercept of the budget line?

8. Given the following utility function and values for income and prices, determine the amounts of X and Y that will maximize utility.

            U = X Y;    I = 1000 Px = 10 Py = 20

Suppose now consumer income declines to 500. What will be the new utility max values of X and Y? Draw a graph of the situation and include an income consumption curve. Use your income consumption curve to draw an Engel curve for X.

9. Mr. Worm's demand function for books has the form: Q = 20 - 2P, where Q represents quantity and represents price. He is currently paying $6 apiece for    books. What is his consumers surplus?