Consumer Behavior & Utility: Practice Questions

Consumer Theory: Practice Questions

1. Marginal Rate of Substitution and Optimal Choice

   A consumer has an MRS = 2. If the relationship between the prices is: Px = 3Py, the optimal choice will be found in:

   • a) Any bundle on the budget constraint.
   • b) The consumer will spend all income on X.
   • c) The consumer will spend all income on Y.
   • d) None of the above.

2. Utility Maximization with Cobb-Douglas Function

   A consumer has an income of 100€. Prices are Px = 10 and Py = 5. If the utility function is u(x, y) = x²y, the optimal choice will be:

   • a) X* = 6.66, Y* = 6.66
   • b) X* = 1, Y* = 18
   • c) The utility at the optimal choice is 245.
   • d) None of the above.

3. Characteristics of Utility Functions

   Which of the following options is correct:

   • a) In a Cobb-Douglas function, the equilibrium will be where MRSyx < Px/Py.
   • b) If goods are perfect complements: MRS is undefined, and the consumer will only demand Y.
   • c) If goods are perfect complements: the consumer will only demand X.
   • d) None of the above.

4. Cobb-Douglas Indifference Curve Slope

   Consider a Cobb-Douglas function. The slope of the indifference curve is 2 when X1=3 and X2=4. What is the value of the slope if X2=2?

   • a) The slope is higher than 2.
   • b) The slope is lower than 2.
   • c) We cannot determine it without knowing the value of X1.
   • d) We cannot determine anything without knowing the utility function.

5. Linear Utility Function and Preferences

   The utility function is u(x,y) = 2x + 5y. The prices are Px=1 and Py=3. We can affirm that:

   • a) The consumer prefers X less than Y.
   • b) The consumer prefers X more than Y.
   • c) The consumer likes both X and Y.
   • d) None of the above.

6. Optimal Consumption with Quasi-Linear Utility

   If a consumer has M=100 and the utility function u(X1,X2) = X1X2 + X1. The consumer will buy 3 units of X1 and 2 units of X2 if the prices are:

   • a) P1=20, P2=20.
   • b) P1=10, P2=5.
   • c) P1=20, P2=10.
   • d) None of the above.

7. Perfect Complements and Optimal Bundle

   Consider a consumer with the preferences u(x,y) = min(2x, 4y). If income is 24 euros and prices are Px=5 and Py=2, mark the incorrect answer:

   • a) The optimal consumption for this consumer is X*=4 and Y*=2.
   • b) The utility of the optimal bundle is 8.
   • c) Goods are perfect complements. This means the consumer will consume them together according to the rate X = (1/2)Y.
   • d) None of the above. All are correct.

8. Utility Maximization with Non-Standard Utility

   Suppose a consumer has an income of 30 euros. The utility function is u(x,y) = 2x² - y, and prices are Px=3 and Py=2. Mark the correct answer:

   • a) The consumer maximizes utility at X*=0.375 and Y*=14.43.
   • b) The consumer maximizes utility at X*=10 and Y*=0.
   • c) The indifference curves are convex with respect to the origin.
   • d) None of the above.

9. Cobb-Douglas Optimal Point Calculation

   Consider a consumer with the utility function u(x,y) = x^1/4y^1/4. If prices are Px=2 and Py=1 and income is M=60, the optimal point is:

   • a) X*=20, Y*=20.
   • b) X*=10, Y*=40.
   • c) The utility of the optimal bundle is 9.45.
   • d) A and C are true.

10. Perfect Substitutes Utility Function Form

    Suppose a consumer always substitutes units of X for units of Y. The general form of the utility function will be:

    • a) U(x,y) = Ax + By, where A>0 and B>0.
    • b) U(x,y) = min(Ax, By), where A>0 and B>0.
    • c) U(x,y)=
    • d) None of the above.