Let's solve each question step by step: --- ### **Question 8** **Q:** Consider a production function in two factors \( Q = f(K,L) \) that is CRS. When the MPK is positive and falling, the MPL is a. falling b. rising c. positive d. flat e. a and c of the above **Step-by-step solution:** - CRS = Constant Returns to Scale. - MPK = Marginal Product of Capital. - If MPK is positive and falling, it means as you add more capital (holding labor fixed), extra output increases, but at a decreasing rate (diminishing marginal returns). - For typical neoclassical production functions (e.g., Cobb-Douglas), if MPK > 0, and since output is produced using both inputs, MPL is also positive. - Standard assumptions: Both MPL and MPK are diminishing (i.e., both are positive and falling as their respective inputs rise). - So, MPL is likely positive and falling. **Answer:** e. a and c of the above --- ### **Question 9** **Q:** CRS production function, \( K \) is fixed. How does an improvement in technology affect the production function? a. Unaffected b. Shift vertically upward c. Shift vertically downward d. Disappear **Step-by-step solution:** - Improvement in technology typically increases the output for any given combination of inputs. - Graphically, this means the production function shifts upward (for the same amounts of K and L, you get more Q). - Fixing K does not affect this logic. **Answer:** b. the production function would shift vertically upward --- ### **Question 10** **Q:** Production function has decreasing returns to scale. A doubling of all inputs will lead to ____________ of output a. doubling b. more than doubling c. less than doubling d. zero increase **Step-by-step solution:** - Decreasing returns to scale means that doubling all inputs less than doubles output. **Answer:** c. less than doubling --- ### **Question 20** **Q:** Which of the following is true: - Money invented in 12th century by Sir John Money - Money is the result of complex social evolution - Money origins are to be found in government safeguards of legal tender - All **Step-by-step solution:** - First statement is false (money was not invented by Sir John Money). - Second is true: Money is a social construct, evolving over time. - Third is partially true for modern fiat money, but not historically. - Therefore, only the second statement is completely correct. **Answer:** Money is the result of complex social evolution --- ### **Question 23** **Q:** The price elasticity of demand is -0.50. By how much must the price decrease for sales to rise by 12%? a. 3% b. 4.8% c. 12.4% d. 24% **Step-by-step solution:** Elasticity \( E = \frac{\%\Delta Q}{\%\Delta P} \) Given: \( E = -0.50 \) \( \%\Delta Q = +12\% \) \( \%\Delta P = ? \) \[ E = \frac{12}{x} \] But elasticity is negative, so \[ -0.5 = \frac{12}{x} \] \[ x = \frac{12}{-0.5} = -24\% \] But since we're being asked "by how much must the price DECREASE", the answer is 24%. **Answer:** d. 24% --- ### **Question 24** **Q:** Joe's beer purchases go from 5 to 7 when income rises from $100 to $140. What is income elasticity of demand? a. 2 b. 1 c. 0.3 d. 0.05 **Step-by-step solution:** Income elasticity \( = \frac{\%\Delta Q}{\%\Delta I} \) \[ \%\Delta Q = \frac{7-5}{5} \times 100\% = 40\% \] \[ \%\Delta I = \frac{140-100}{100} \times 100\% = 40\% \] \[ \text{Income elasticity} = \frac{40\%}{40\%} = 1 \] **Answer:** b. 1 --- ### **Question 37** **Q:** Price of gasoline rising, quantity sold falling. What can we conclude? A) Law of supply does not hold B) Law of demand does not hold C) Demand for gasoline must have fallen D) Supply of gasoline must have fallen **Step-by-step solution:** - Price up, quantity down: this is consistent with a **leftward shift of the supply curve** (supply falls), moving up the demand curve. - The law of demand and supply still holds. **Answer:** D) The supply of gasoline must have fallen --- ## **Summary Table of Answers** | Q# | Answer | |----|--------| | 8 | e. a and c of the above | | 9 | b. the production function would shift vertically upward | | 10 | c. less than doubling | | 20 | Money is the result of complex social evolution | | 23 | d. 24% | | 24 | b. 1 | | 37 | D) The supply of gasoline must have fallen |

Certainly! Here's a detailed explanation for each question, including why the incorrect options are not suitable and why the correct options are appropriate. --- ### **Question 8** **Question:** When MPK is positive and falling, what is the status of MPL? **Options:** a. falling b. rising c. positive d. flat e. a and c of the above **Correct Answer:** **e. a and c of the above** **Explanation:** - **Why "a and c" are correct:** In a typical production function with diminishing marginal returns, as MPK (marginal product of capital) falls but remains positive, the MPL (marginal product of labor) is also positive and generally diminishing. This is because as you add more of one input, holding the other fixed, the additional output (marginal product) tends to decrease but stays positive until diminishing returns become significant. - **Why other options are incorrect:** - **a. falling:** While MPK is falling, MPL is also positive and may be falling or stable depending on the specific function, but the question emphasizes positivity and a decreasing trend, so "falling" is most aligned with diminishing returns. - **b. rising:** Not correct because diminishing marginal returns imply the marginal products are decreasing, not increasing. - **c. positive:** Correct, because MPK > 0 and generally MPL > 0 in such a region. - **d. flat:** Incorrect because the marginal products are diminishing, so they are not flat. --- ### **Question 9** **Question:** With a CRS production function and fixed capital \(K\), how does technological improvement affect the production? **Options:** a. unaffected b. shift upward c. shift downward d. disappear **Correct Answer:** **b. shift upward** **Explanation:** - A technological improvement enhances productivity, thus increasing output for any given input combination. - The production function shifts upward, meaning for the same inputs, more output is produced. - **Incorrect options:** - **a. unaffected:** No, technology improvements do change output levels. - **c. shift downward:** Opposite of the truth; technological progress causes an upward shift. - **d. disappear:** Not possible; the function remains, just shifted upward. --- ### **Question 10** **Question:** Under decreasing returns to scale, doubling inputs results in what change in output? **Options:** a. doubling b. more than doubling c. less than doubling d. zero increase **Correct Answer:** **c. less than doubling** **Explanation:** - Decreasing returns to scale means that when all inputs are doubled, output increases by less than twice. - **Incorrect options:** - **a. doubling:** This happens under constant returns to scale. - **b. more than doubling:** This would characterize increasing returns to scale. - **d. zero increase:** No, output still increases, just less than double. --- ### **Question 20** **Question:** Which statement about money is true? **Options:** - Money was invented in 12th century by Sir John Money - Money is the result of complex social evolution - Money origins are in government safeguards of legal tender - All **Correct Answer:** **Money is the result of complex social evolution** **Explanation:** - Money evolved over time through social and economic processes, not through a single inventor or solely government actions. - **Incorrect options:** - **First statement:** Factually false; Sir John Money did not invent money. - **Third statement:** While governments formalize legal tender, the origins of money lie in social evolution, barter, and trust, not just legal safeguards. - **"All":** Since the first statement is false, "all" is incorrect. --- ### **Question 23** **Question:** Price elasticity of demand is -0.50. How much must the price decrease for sales to rise by 12%? **Options:** a. 3% b. 4.8% c. 12.4% d. 24% **Correct Answer:** **d. 24%** **Explanation:** - Elasticity formula: \(\%\Delta Q = E \times \%\Delta P\) - Rearranged: \(\%\Delta P = \frac{\%\Delta Q}{E}\) - \(E = -0.50\), \(\%\Delta Q = +12\%\): \[ \%\Delta P = \frac{12\%}{-0.50} = -24\% \] - The negative sign indicates a price decrease, so the price must decrease by **24%**. - **Incorrect options:** - **a. 3%, 4.8%, 12.4%:** These are too small; the calculation clearly shows 24%. --- ### **Question 24** **Question:** Joe's beer consumption when income increases from $100 to $140, and quantity increases from 5 to 7 six-packs. What is his income elasticity? **Options:** a. 2 b. 1 c. 0.3 d. 0.05 **Correct Answer:** **b. 1** **Explanation:** - Percentage change in quantity: \[ \frac{7 - 5}{5} \times 100\% = 40\% \] - Percentage change in income: \[ \frac{140 - 100}{100} \times 100\% = 40\% \] - Income elasticity: \[ \frac{40\%}{40\%} = 1 \] - **Incorrect options:** - **a. 2:** Would imply quantity changes twice as much as income, which is not the case. - **c. 0.3:** Too low. - **d. 0.05:** Very low; not consistent with the data. --- ### **Question 37** **Question:** Gasoline price rises, quantity sold falls. What conclusion? **Options:** A) The law of supply does not hold for gasoline B) The law of demand does not hold for gasoline C) Demand for gasoline must have fallen D) Supply of gasoline must have fallen **Correct Answer:** **D. The supply of gasoline must have fallen** **Explanation:** - When price increases and quantity decreases, it suggests a **leftward shift in supply** (a decrease in supply). - **Incorrect options:** - **A:** The law of supply states that higher prices typically increase quantity supplied; it does not say quantity demanded falls with price increases. - **B:** Demand might remain unchanged; the observed movement is consistent with a supply reduction. - **C:** Demand for gasoline might have increased or stayed the same; the key is the supply curve shift. --- If you'd like, I can prepare this in a summarized bullet format or a table.