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Give step-by-step solution with explanation and final answer: also for all question give reason why other options are not correct Saul Goodman of “Better Call Saul” fame is a busy lawyer, capable of getting any client out of a legal mess. The problem is because he is always so busy trying to serve his (shady) clients, he does not get enough time to eat proper meals during the day. So, he mostly survives on coffee (X1) and donuts (X2) to get him through the day. Saul’s utility function reflecting his preference for coffee and donuts is given by: U(X1, X2) = 6X1X2. His daily allowance for his meals is $36. He must spend the entire amount each day to buy his coffee and donuts, i.e., he cannot save any of it. The price of a cup of coffee is $3 and the price of a donut is $2. Question 1: Given Saul’s utility function, what is Saul’s level of utility when he consumes 2 cups of coffee (X1) and 2 donuts (X2)? a) U = 6 b) U = 12 c) U = 24 d) U = 36 Question 2: If Saul’s consumption bundle now has one extra unit of X1 (i.e., X1 is now 3 units) but X2 remains unchanged (i.e., X2 is still 2 units), what is Saul’s total utility from consuming this bundle? a) U = 24 b) U = 36 c) U = 30 d) U = 18 Question 3: For Saul’s utility function, U = 6X1X2, what will be the change in Saul’s utility level when X1 increases by one unit from 2 to 3 (X2 still remaining unchanged at 2 units)? a) Change in utility level is 12. b) Change in utility level is 15. c) Change in utility level is 24. d) Change in utility level is 6. Question 4: What is Saul’s budget equation? a) 36 = 6X1 + 4X2 b) 36 = 2X1 + 3X2 c) 36 = 3X1 + 6X2 d) 36 = 3X1 + 2X2

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Give step-by-step solution with explanation and final answer: also for all question give reason why other options are not correct Saul Goodman of “Better Call Saul” fame is a busy lawyer, capable of getting any client out of a legal mess. The problem is because he is always so busy trying to serve his (shady) clients, he does not get enough time to eat proper meals during the day. So, he mostly survives on coffee (X1) and donuts (X2) to get him through the day. Saul’s utility function reflecting his preference for coffee and donuts is given by: U(X1, X2) = 6X1X2. His daily allowance for his meals is $36. He must spend the entire amount each day to buy his coffee and donuts, i.e., he cannot save any of it. The price of a cup of coffee is $3 and the price of a donut is $2. Question 1: Given Saul’s utility function, what is Saul’s level of utility when he consumes 2 cups of coffee (X1) and 2 donuts (X2)? a) U = 6 b) U = 12 c) U = 24 d) U = 36 Question 2: If Saul’s consumption bundle now has one extra unit of X1 (i.e., X1 is now 3 units) but X2 remains unchanged (i.e., X2 is still 2 units), what is Saul’s total utility from consuming this bundle? a) U = 24 b) U = 36 c) U = 30 d) U = 18 Question 3: For Saul’s utility function, U = 6X1X2, what will be the change in Saul’s utility level when X1 increases by one unit from 2 to 3 (X2 still remaining unchanged at 2 units)? a) Change in utility level is 12. b) Change in utility level is 15. c) Change in utility level is 24. d) Change in utility level is 6. Question 4: What is Saul’s budget equation? a) 36 = 6X1 + 4X2 b) 36 = 2X1 + 3X2 c) 36 = 3X1 + 6X2 d) 36 = 3X1 + 2X2

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Asked by: mayank
Created at: 2025-09-19 17:31:54

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# Saul Goodman Utility and Budget Problems Saul’s utility function: $$ U(X_1, X_2) = 6X_1X_2 $$ - \( X_1 \): Cups of coffee (\$3 each) - \( X_2 \): Donuts (\$2 each) - Daily allowance: \$36 --- ## Question 1 ### **What is Saul’s utility when he consumes 2 cups of coffee and 2 donuts?** **Plug values into the utility function:** \[ U = 6 \times X_1 \times X_2 = 6 \times 2 \times 2 = 6 \times 4 = 24 \] **Final Answer:** **c) U = 24** #### **Why other options are not correct:** - a) U = 6: \(6 \times 2 \times 2 = 24\), not 6. - b) U = 12: \(6 \times 2 \times 2 = 24\), not 12. - d) U = 36: \(6 \times 2 \times 2 = 24\), not 36. --- ## Question 2 ### **What is Saul’s utility if X1 = 3 and X2 = 2?** \[ U = 6 \times 3 \times 2 = 6 \times 6 = 36 \] **Final Answer:** **b) U = 36** #### **Why other options are not correct:** - a) U = 24: \(6 \times 3 \times 2 = 36\), not 24. - c) U = 30: \(6 \times 3 \times 2 = 36\), not 30. - d) U = 18: \(6 \times 3 \times 2 = 36\), not 18. --- ## Question 3 ### **What is the change in utility when X1 increases from 2 to 3 (X2 = 2)?** - Initial utility: \( U_1 = 6 \times 2 \times 2 = 24 \) - New utility: \( U_2 = 6 \times 3 \times 2 = 36 \) - Change: \( U_2 - U_1 = 36 - 24 = 12 \) **Final Answer:** **a) Change in utility level is 12.** #### **Why other options are not correct:** - b) 15: The actual change is 12, not 15. - c) 24: 24 is the initial utility, not the change. - d) 6: The change is 12, not 6. --- ## Question 4 ### **What is Saul’s budget equation?** - Total spending = Price of coffee × Quantity of coffee + Price of donut × Quantity of donut - \( 36 = 3X_1 + 2X_2 \) **Final Answer:** **d) 36 = 3X1 + 2X2** #### **Why other options are not correct:** - a) 36 = 6X1 + 4X2: Incorrect prices (coffee is \$3, donut is \$2). - b) 36 = 2X1 + 3X2: Prices swapped; coffee is not \$2, donut is not \$3. - c) 36 = 3X1 + 6X2: Donut price is not \$6, it's \$2. --- **Summary Table** | Q | Answer | Explanation | |---|--------|-------------| | 1 | c | \(6 \times 2 \times 2 = 24\) | | 2 | b | \(6 \times 3 \times 2 = 36\) | | 3 | a | \(36 - 24 = 12\) | | 4 | d | \(36 = 3X_1 + 2X_2\) |

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