Practical and challenging questions on consumer theory, budget constraints, indifference curves, equilibrium of a consumer in a single-commodity case, and the equi-marginal principle, along with detailed answers

Practical and challenging questions on consumer theory, budget constraints, indifference curves, equilibrium of a consumer in a single-commodity case, and the equi-marginal principle, along with detailed answers:

1. **Question**:

   Maria is a coffee enthusiast who has a monthly budget of $100 to spend on coffee (C) and pastries (P). The price of coffee is $5 per cup, and the price of pastries is $2 each. Calculate the equation for Maria's budget constraint and plot it on a graph.

2. **Question**:

   John consumes only two goods, pizza (P) and burgers (B). His utility function is \(U(P, B) = P^2B\), and he has a monthly budget of $200. If the price of pizza is $10 and the price of burgers is $5, how many units of each should John consume to maximize his utility?

3. **Question**:

   Sarah enjoys consuming apples (A) and oranges (O). Her utility function is \(U(A, O) = 3A^{0.5}O^{0.5}\). If the price of apples is $1 per pound and the price of oranges is $2 per pound, and Sarah has a budget of $30, how many pounds of each fruit should she buy to maximize her utility?

4. **Question**:

   Mark consumes two goods: books (B) and movies (M). His utility function is \(U(B, M) = 2B^{0.3}M^{0.7}\). If the price of books is $20 each and the price of movies is $10 each, and Mark's monthly budget is $100, what quantities of books and movies should he purchase to maximize his utility?

5. **Question**:

   Emily consumes only tea (T) and coffee (C). Her utility function is \(U(T, C) = T^0.5C^0.5\), and her monthly budget is $60. If the price of tea is $2 per cup and the price of coffee is $4 per cup, how many cups of each should Emily consume to maximize her utility?

6. **Question**:

   Alex loves both ice cream (I) and cake (C). His utility function is \(U(I, C) = I^{0.6}C^{0.4}\). If the price of ice cream is $5 per scoop, the price of cake is $8 per slice, and Alex's weekly budget is $50, what quantities of ice cream and cake should he buy to maximize his utility?

7. **Question**:

   Lisa has a monthly budget of $200 to spend on wine (W) and cheese (Ch). The price of wine is $15 per bottle, and the price of cheese is $10 per pound. Lisa's utility function is \(U(W, Ch) = 2W^{0.3}Ch^{0.7}\). Determine the quantities of wine and cheese she should buy to maximize her utility.

8. **Question**:

   Ben enjoys consuming strawberries (S) and cream (Cr). His utility function is (U(S, Cr) = S^{0.4}Cr^{0.6}). If the price of strawberries is $3 per pint and the price of cream is $2 per pint, and Ben's weekly budget is $30, calculate the quantities of strawberries and cream he should purchase to maximize his utility.

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9. **Question**:

   Emily enjoys consuming pizza (P) and soda (S). Her utility function is \(U(P, S) = P^{0.6}S^{0.4}\). If the price of pizza is $12 per pie, and the price of soda is $2 per can, and Emily's monthly budget is $200, determine the quantities of pizza and soda she should purchase to maximize her utility.

10. **Question**:

    Jacob enjoys consuming both hamburgers (H) and hot dogs (HD). His utility function is \(U(H, HD) = H^{0.5}HD^{0.5}\). If the price of hamburgers is $4 each, and the price of hot dogs is $2 each, and Jacob's weekly budget is $24, calculate the quantities of hamburgers and hot dogs he should purchase to maximize his utility.

20 practical and challenging questions on consumer theory, budget constraints, indifference curves, equilibrium of a consumer in a single-commodity case, and the equi-marginal principle

1. Sarah has a monthly budget of $200 to spend on two goods, X and Y. The price of X is $10 per unit, and the price of Y is $5 per unit. Draw Sarah's budget constraint and indicate the feasible consumption bundles.

2. Tom's utility function is \(U(X, Y) = X^0.5Y^0.5\). If the price of X is $4 per unit and the price of Y is $2 per unit, how many units of X and Y should Tom consume to maximize his utility, given a budget of $64?

3. Mary consumes only two goods, A and B. Her utility function is \(U(A, B) = A^{0.3}B^{0.7}\). If the price of A is $6 per unit and the price of B is $3 per unit, what combination of A and B should Mary buy to maximize her utility with a budget of $90?

4. Mark's monthly budget is $500, and he spends it on two goods, P and Q. The price of P is $25 per unit, and the price of Q is $10 per unit. Calculate the equation for Mark's budget constraint and plot it on a graph.

5. Alice loves eating chocolate (C) and ice cream (I). Her utility function is \(U(C, I) = C^{0.6}I^{0.4}\). If the price of chocolate is $2 per bar, and the price of ice cream is $4 per scoop, and Alice's weekly budget is $40, determine the quantities of chocolate and ice cream she should buy.

6. John's utility function is \(U(X, Y) = X^0.4Y^0.6\). If the price of X is $8 per unit and the price of Y is $6 per unit, how much of X and Y should John purchase to maximize his utility with a budget of $240?

7. Calculate the consumer surplus for a consumer who is willing to pay $30 for a pair of shoes but buys them for $20.

8. If a consumer has a budget of $80 and the price of good X is $10 and the price of good Y is $5, determine the combination of X and Y that maximizes the consumer's utility with the utility function \(U(X, Y) = X^0.3Y^0.7\).

9. Jane's monthly budget is $300, and she spends it on two goods, A and B. The price of A is $12 per unit, and the price of B is $8 per unit. Calculate the equation for Jane's budget constraint and plot it on a graph.

10. Calculate the marginal rate of substitution (MRS) for a consumer whose indifference curve is represented by the equation \(X^2 + Y^2 = 25\).

11. Susan has a utility function \(U(X, Y) = X^{0.5}Y^{0.5}\). If the price of X is $6 per unit and the price of Y is $4 per unit, determine the optimal combination of X and Y for Susan to maximize her utility with a monthly budget of $120.

12. Chris has a budget of $400 per month and consumes two goods, A and B. The price of A is $20 per unit, and the price of B is $10 per unit. Calculate the equation for Chris's budget constraint and graph it.

13. Calculate the consumer surplus for a consumer who is willing to pay $50 for a concert ticket but purchases it for $30.

14. If a consumer's utility function is \(U(X, Y) = XY\), and the price of X is $5 per unit and the price of Y is $10 per unit, find the optimal combination of X and Y for utility maximization with a budget of $100.

15. Sarah's utility function is \(U(X, Y) = 2X^{0.4}Y^{0.6}\). If the price of X is $8 per unit and the price of Y is $12 per unit, determine how much of X and Y she should consume with a monthly budget of $240.

16. Calculate the marginal rate of substitution (MRS) for a consumer whose indifference curve is represented by the equation \(3X^2 + 4Y^2 = 36\).

17. Calculate the consumer surplus for a consumer who is willing to pay $25 for a meal at a restaurant but pays $20.

18. If a consumer's utility function is \(U(X, Y) = 4X^{0.3}Y^{0.7}\), and the price of X is $5 per unit and the price of Y is $8 per unit, find the optimal combination of X and Y for utility maximization with a budget of $160.

19. Peter has a monthly budget of $500 to spend on two goods, M and N. The price of M is $15 per unit, and the price of N is $10 per unit. Calculate the equation for Peter's budget constraint and illustrate it on a graph.

20. Calculate the marginal rate of substitution (MRS) for a consumer whose indifference curve is represented by the equation \(2X^2 + 3Y^2 = 36\).

Feel free to attempt these questions, and if you have any specific questions or need answers, please let me know!

These practical questions involve real-life budget constraints and utility functions, providing insight into how consumers make consumption decisions.