MauryaHub PYQ Practice

ms3033_2026T1_Q1_NA.pdf

Managerial Economics · Quiz 1 · Jan 2026

← Course papers · Start practice / exam

Questions and published explanations below are available without starting a test. Some questions may not have a published solution yet.

Question 2 MCQ · 1.0 marks

For the production function **q = 4K**\(^{1/2}\) **+ 4L**
  1. Both MPL and MPK are constant
  2. MPK is decreasing but MPL is constant
  3. MPL is decreasing and MPK is constant
  4. Both MPL and MPK are decreasing

Published solution

**1. Given:** \(q=4K^{1/2}+4L\). **2. Concept:** MPL is the change in output from one more unit of labour. MPK is the change from one more unit of capital. **3. Calculate:** \[ MP_L=\frac{\partial q}{\partial L}=4\quad(\text{constant}) \] \[ MP_K=\frac{\partial q}{\partial K}=2K^{-1/2}\quad(\text{falls as }K\text{ rises}) \] **4. Conclude:** MPL is constant and MPK is decreasing. Answer: B — MPK is decreasing but MPL is constant. A: **Incorrect:** Wrong because MPK \(=2K^{-1/2}\) falls as K rises. B: **Correct:** MPL \(=4\) is constant and MPK \(=2K^{-1/2}\) is decreasing. C: **Incorrect:** MPL is not decreasing, and MPK is not constant. D: **Incorrect:** MPL is constant, not decreasing.

Question 3 MCQ · 1.0 marks

A firm can always trade three units of labour for one unit of capital and still keep output constant. The production technology for this firm can most suitably represented by
  1. Cobb-Douglas production function
  2. Leontief production function
  3. Linear production function
  4. None of these

Published solution

**1. Understand:** The firm can always swap 3 units of labour for 1 unit of capital and keep the same output. The rate of substitution is constant. **2. Concept:** A constant substitution rate means the inputs are perfect substitutes. Perfect substitutes are represented by a linear production function, for example \(q=L+3K\) (straight-line isoquants). **3. Conclude:** The technology is a linear production function. Answer: C — Linear production function. A: **Incorrect:** Cobb-Douglas has a changing rate of substitution along the isoquant. B: **Incorrect:** Leontief means inputs are used in fixed proportions, with no substitution. C: **Correct:** A constant rate of trade-off gives straight-line isoquants, which is linear. D: **Incorrect:** The technology matches the linear form.

Question 4 MCQ · 1.0 marks

A firm finds that it requires exactly two full-time workers to operate each piece of machinery in the factory. The production technology for this firm can most suitably represented by
  1. Cobb-Douglas production function
  2. Leontief production function
  3. Linear production function
  4. None of these

Published solution

**1. Understand:** Each machine needs exactly two workers. The inputs must be used in a fixed proportion, and extra workers or machines alone add no output. **2. Concept:** Fixed-proportion technology is represented by a Leontief production function, for example \(q=\min(L/2,K)\). **3. Conclude:** The technology is a Leontief production function. Answer: B — Leontief production function. A: **Incorrect:** Cobb-Douglas allows smooth substitution between inputs. B: **Correct:** Fixed 2:1 workers-to-machine proportions are Leontief. C: **Incorrect:** Linear functions allow perfect substitution, not fixed proportions. D: **Incorrect:** The technology matches the Leontief form.

Question 5 MCQ · 1.0 marks

The marginal product of capital is defined as
  1. a firm’s total output divided by total labour input
  2. the extra output produced by employing one more unit of labour while allowing other inputs to vary
  3. the extra output produced by employing one more unit of labour while holding other inputs constant
  4. the extra output produced by employing one more unit of capital while holding other input constant

Published solution

**1. Concept:** Marginal product of an input is the extra output from one more unit of that input while other inputs are held constant. **2. Apply:** For capital, it is the extra output from one more unit of capital, holding the other input constant. **3. Conclude:** The last option gives this definition. Answer: D — the extra output produced by employing one more unit of capital while holding other input constant. A: **Incorrect:** This is average product of labour. B: **Incorrect:** This describes labour and lets other inputs vary; it is not MPK. C: **Incorrect:** This is the definition of MPL, not MPK. D: **Correct:** This is the definition of the marginal product of capital.

Question 6 MCQ · 1.0 marks

If marginal costs equal average total costs
  1. average total costs are falling
  2. average total costs are maximized
  3. average total costs are rising
  4. average total costs are minimized

Published solution

**1. Concept:** When marginal cost is below average total cost, ATC falls. When MC is above ATC, ATC rises. **2. Apply:** If MC = ATC, ATC is neither rising nor falling. This happens at the bottom of the U-shaped ATC curve. **3. Conclude:** ATC is at its minimum. Answer: D — average total costs are minimized. A: **Incorrect:** ATC falls only when MC is below ATC. B: **Incorrect:** ATC is not at a maximum here; the MC curve cuts ATC from below at the minimum. C: **Incorrect:** ATC rises only when MC is above ATC. D: **Correct:** MC = ATC occurs at the minimum point of ATC.

Question 7 MCQ · 1.0 marks

When average product is decreasing in labor, marginal product is greater than average product.
  1. True
  2. False

Published solution

**1. Concept:** The average product and marginal product are linked. If MP is above AP, AP rises. If MP is below AP, AP falls. **2. Apply:** If AP is decreasing, MP must be less than AP, not greater. **3. Conclude:** The statement is false. Answer: B — False. A: **Incorrect:** If AP is falling, MP is below AP. B: **Correct:** The statement is reversed; MP < AP when AP is decreasing.

Question 8 MCQ · 1.0 marks

When average product is increasing in labor, marginal product is less than average product.
  1. True
  2. False

Published solution

**1. Concept:** AP rises when the marginal product is above it. **2. Apply:** When AP is increasing, MP > AP. The statement says MP is less than AP, which is the opposite. **3. Conclude:** The statement is false. Answer: B — False. A: **Incorrect:** If AP is rising, MP is above AP, not below. B: **Correct:** MP > AP when AP is increasing, so the statement is false.

Question 9 MCQ · 1.0 marks

When average product **APL** is at a maximum, then marginal product is equal to average product
  1. True
  2. False

Published solution

**1. Concept:** AP rises while MP > AP and falls while MP < AP. **2. Apply:** At the maximum of AP, it stops rising and has not yet started falling. So MP = AP there. (Formally, \(\frac{d}{dL}\frac{q}{L}=\frac{MP-AP}{L}=0\).) **3. Conclude:** The statement is true. Answer: A — True. A: **Correct:** At the maximum of AP, MP = AP. B: **Incorrect:** The statement is true, since MP crosses AP at AP's maximum.

Question 10 MCQ · 2.0 marks

[[IMAGE:49e716f71122effc_5_2]]
Source diagram or notation
  1. 5, 20
  2. 20, 5
  3. 20, 10
  4. 10, 20

Published solution

**1. Given:** \(q=10L^{1/2}K^{1/2}\), \(w=20\), \(r=80\), \(q=100\). **2. Cost-minimizing rule:** \(MRTS=\frac{w}{r}\). Here \(MRTS=\frac{MP_L}{MP_K}=\frac{K}{L}\). \[ \frac{K}{L}=\frac{20}{80}=\frac14\;\Rightarrow\;L=4K \] **3. Use the output constraint:** \[ 10\sqrt{(4K)K}=100\;\Rightarrow\;20K=100\;\Rightarrow\;K=5,\;L=20 \] **4. Conclude:** Labour = 20 and capital = 5. Answer: B — 20, 5. A: **Incorrect:** These are reversed; they give \(K/L=4\), not \(1/4\). B: **Correct:** L = 20 and K = 5 satisfy \(L=4K\) and \(10\sqrt{20\times5}=100\). C: **Incorrect:** L = 20, K = 10 gives output \(10\sqrt{200}\ne100\) and \(K/L\ne1/4\). D: **Incorrect:** L = 10, K = 20 gives \(K/L=2\), not \(1/4\).

Question 11 MCQ · 1.0 marks

A chair manufacturer hires its assembly-line labour for $15 an hour and calculates that the rental cost of its machinery is $30 per hour. Suppose that a chair can be produced using 4 hours of labour or machinery in any combination. Based on the above data, answer the given subquestions.
If the firm is currently using 3 hours of machine time for each hour of labour time, is it minimizing its costs of production? _____________
  1. Yes
  2. No

Published solution

**1. Given:** Labour costs $15 per hour and machines cost $30 per hour. A chair needs 4 hours of labour or 4 hours of machinery, in any combination. So labour and machine time are perfect substitutes with the same productivity. **2. Compare costs:** Labour is cheaper per hour. The cost of a chair is \(4\times15=\$60\) with only labour and \(4\times30=\$120\) with only machines. The current mix (3 machine hours per labour hour) is expensive. **3. Conclude:** The firm is not minimizing cost; it should use only labour. Answer: B — No. A: **Incorrect:** It uses too much of the costlier machine time, so cost is not minimized. B: **Correct:** Labour is cheaper, so using more machine time than labour is not cost-minimizing.

Question 12 NAT · 1.0 marks

A chair manufacturer hires its assembly-line labour for $15 an hour and calculates that the rental cost of its machinery is $30 per hour. Suppose that a chair can be produced using 4 hours of labour or machinery in any combination. Based on the above data, answer the given subquestions.
If not, what will be the optimal combination of labour and capital. L* = ________

    Published solution

    **1. Concept:** Labour and machinery are perfect substitutes with equal marginal products, but labour is cheaper (\(w=15<r=30\)). So the firm uses only labour. **2. Calculate:** One chair needs 4 hours of labour or machinery in any combination. Using all labour: \(L^*=4\), cost \(=4\times15=\$60\) (vs $120 with machines). Answer: \(L^*=4\).

    Question 13 NAT · 1.0 marks

    A chair manufacturer hires its assembly-line labour for $15 an hour and calculates that the rental cost of its machinery is $30 per hour. Suppose that a chair can be produced using 4 hours of labour or machinery in any combination. Based on the above data, answer the given subquestions.
    If not, what will be the optimal combination of labour and capital. K* = __________

      Published solution

      **1. Concept:** Since labour is cheaper ($15 vs $30) and perfectly substitutable with capital, the firm uses only labour. **2. Conclude:** \(K^*=0\) and \(L^*=4\) (cost $60). Answer: \(K^*=0\).

      Question 14 MCQ · 1.0 marks

      Consider two goods, coconut and fish with prices **Pc** **= 20** and **Pf** **= 10**. Robin has an income I= 1000 and he consumes only these two goods. With the help of the plot of his budget line taking fish on the Y-axis. Based on the above data, answer the given subquestions.
      The slope of the budget line is
      1. -2
      2. +2
      3. -1/2
      4. +1/2

      Published solution

      **1. Given:** \(P_c=20\), \(P_f=10\), \(I=1000\), fish on the Y-axis. **2. Budget line:** \(20C+10F=1000\), so \[ F=100-2C \] **3. Slope:** \(-\frac{P_c}{P_f}=-\frac{20}{10}=-2\). **4. Conclude:** The slope is \(-2\). Answer: A — -2. A: **Correct:** The slope is \(-P_c/P_f=-2\). B: **Incorrect:** The budget line slopes downward, so the slope is negative. C: **Incorrect:** \(-1/2\) would be \(-P_f/P_c\), which is inverted. D: **Incorrect:** The slope is negative and \(1/2\) is inverted.

      Question 15 MCQ · 1.0 marks

      Consider two goods, coconut and fish with prices **Pc** **= 20** and **Pf** **= 10**. Robin has an income I= 1000 and he consumes only these two goods. With the help of the plot of his budget line taking fish on the Y-axis. Based on the above data, answer the given subquestions.
      Intercepts on the axis are
      1. 50 on X-axis and 100 on Y-axis
      2. 100 on X-axis and 50 on Y-axis
      3. 50 on X-axis and 20 on Y-axis
      4. 20 on X-axis and 50 on Y-axis

      Published solution

      **1. Given:** Budget line \(20C+10F=1000\), coconut on X-axis and fish on Y-axis. **2. X-intercept (F=0):** \(C=\frac{1000}{20}=50\). **3. Y-intercept (C=0):** \(F=\frac{1000}{10}=100\). **4. Conclude:** 50 on the X-axis and 100 on the Y-axis. Answer: A — 50 on X-axis and 100 on Y-axis. A: **Correct:** \(1000/20=50\) on X and \(1000/10=100\) on Y. B: **Incorrect:** The intercepts are reversed. C: **Incorrect:** The Y-intercept should be 100, not 20. D: **Incorrect:** Neither intercept is correct.

      Question 16 MCQ · 1.0 marks

      Consider two goods, coconut and fish with prices **Pc** **= 20** and **Pf** **= 10**. Robin has an income I= 1000 and he consumes only these two goods. With the help of the plot of his budget line taking fish on the Y-axis. Based on the above data, answer the given subquestions.
      If keeping income unchanged, price of the coconut is halved, what will be the new slope of the budget line
      1. -2
      2. +1
      3. -1
      4. +2

      Published solution

      **1. Given:** The new coconut price is \(P_c=10\), income is 1000 and \(P_f=10\). **2. Slope:** \(-\frac{P_c}{P_f}=-\frac{10}{10}=-1\). **3. Conclude:** The new slope is \(-1\). Answer: C — -1. A: **Incorrect:** \(-2\) is the old slope. B: **Incorrect:** The slope of a budget line is negative. C: **Correct:** The new slope is \(-10/10=-1\). D: **Incorrect:** The slope of a budget line is negative.

      Question 17 MCQ · 1.0 marks

      Consider two goods, coconut and fish with prices **Pc** **= 20** and **Pf** **= 10**. Robin has an income I= 1000 and he consumes only these two goods. With the help of the plot of his budget line taking fish on the Y-axis. Based on the above data, answer the given subquestions.
      New intercepts on the axis are
      1. 50 on X-axis and 50 on Y-axis
      2. 100 on X-axis and 50 on Y-axis
      3. 100 on X-axis and 100 on Y-axis
      4. 10 on X-axis and 100 on Y-axis

      Published solution

      **1. Given:** New budget line \(10C+10F=1000\). **2. X-intercept (F=0):** \(C=1000/10=100\). **3. Y-intercept (C=0):** \(F=1000/10=100\). **4. Conclude:** 100 on the X-axis and 100 on the Y-axis. Answer: C — 100 on X-axis and 100 on Y-axis. A: **Incorrect:** The X-intercept should be 100, not 50. B: **Incorrect:** The Y-intercept should be 100, not 50. C: **Correct:** Both intercepts are \(1000/10=100\). D: **Incorrect:** The X-intercept should be 100, not 10.

      Question 18 MCQ · 1.0 marks

      Consider two goods, coconut and fish with prices **Pc** **= 20** and **Pf** **= 10**. Robin has an income I= 1000 and he consumes only these two goods. With the help of the plot of his budget line taking fish on the Y-axis. Based on the above data, answer the given subquestions.
      If income is halved keeping the original prices unchanged
      1. Slope remains same and both intercepts are doubled
      2. Slope remains same and both intercepts are halved
      3. Slope changes and both intercepts are doubled
      4. Slope changes and both intercepts remain same

      Published solution

      **1. Given:** Income becomes 500 with \(P_c=20\), \(P_f=10\). **2. Slope:** \(-P_c/P_f=-2\) (unchanged). **3. Intercepts:** \(C=500/20=25\) (was 50) and \(F=500/10=50\) (was 100). Both are halved. **4. Conclude:** The slope stays the same and both intercepts are halved. Answer: B — Slope remains same and both intercepts are halved. A: **Incorrect:** Intercepts fall when income falls; they are not doubled. B: **Correct:** The slope depends only on prices, and the intercepts are halved. C: **Incorrect:** The slope does not change, and intercepts fall. D: **Incorrect:** The slope does not change, and the intercepts change.

      Question 19 NAT · 1.0 marks

      The marginal product of labour in the production of chips is 50 kg chips per hour. The marginal rate of technical substitution of hours of labour for hours of machine capital is 1/4. What is the marginal product of capital in kg per hour? (only write the no.) __________

        Published solution

        **1. Given:** \(MP_L=50\) kg per hour and \(MRTS=\frac14\). **2. Formula:** \(MRTS=\frac{MP_L}{MP_K}\). **3. Substitute:** \[ \frac14=\frac{50}{MP_K}\;\Rightarrow\;MP_K=50\times4=200 \] Answer: \(200\).

        Question 20 NAT · 1.0 marks

        The short-run cost function of a company is given by the equation TC = 200 + 55q, where TC is the total cost and q is the total quantity of output. Based on the above data, answer the given subquestions.
        What is the company’s fixed cost? ________

          Published solution

          **1. Concept:** In \(TC=FC+VC\), fixed cost is the part that does not change with output. **2. Apply:** In \(TC=200+55q\), the constant is 200. Answer: \(200\).

          Question 21 NAT · 1.0 marks

          The short-run cost function of a company is given by the equation TC = 200 + 55q, where TC is the total cost and q is the total quantity of output. Based on the above data, answer the given subquestions.
          If the company produced 100 units of goods, what would be its average variable cost? ___________

            Published solution

            **1. Concept:** \(AVC=\frac{VC}{q}\), where \(VC=55q\). **2. Calculate at \(q=100\):** \[ VC=55\times100=5500,\quad AVC=\frac{5500}{100}=55 \] Answer: \(55\).

            Question 22 MCQ · 1.0 marks

            Imagine that you have started a snack food delivery business on your college campus. Students send you orders for snacks, such as potato chips and candy bars, via the Internet. You shop at local grocery stores to fill these orders and then deliver the orders. To operate this business, you pay $500 a month to lease computer time from a local Web-hosting company to use its server to host and maintain your website. You also own a sports utility vehicle (SUV) that you use to make deliveries. Your monthly car payment is $300, and you pay $100 a month in insurance costs. Each order that you fill takes, on average, a half hour and consumes $0.50 worth of gasoline. When you fill an order, you pay the grocer for the merchandise. You then collect a payment, including a delivery fee, from the students to whom you sell. If you did not operate this business, you could work at the campus dining hall, earning $6 an hour. Right now, you operate your business five days a week, Monday through Friday. On weekends, your business is idle, and you work in the campus dining hall. Based on the above data, answer the given subquestions.
            Your explicit costs include
            1. Leasing computer time
            2. Gasoline
            3. Money you pay grocers
            4. All of these

            Published solution

            **1. Concept:** Explicit costs are actual money payments to outsiders. **2. Check:** Computer leasing ($500), gasoline ($0.50 per order) and money paid to grocers are all payments made to others. **3. Conclude:** All of these are explicit costs. Answer: D — All of these. A: **Incorrect:** Leasing is a cash payment, but the other two are also explicit. B: **Incorrect:** Gasoline is a cash payment, but the others are also explicit. C: **Incorrect:** Paying grocers is a cash payment, but the others are also explicit. D: **Correct:** All three are cash payments to outsiders.

            Question 23 MCQ · 1.0 marks

            Imagine that you have started a snack food delivery business on your college campus. Students send you orders for snacks, such as potato chips and candy bars, via the Internet. You shop at local grocery stores to fill these orders and then deliver the orders. To operate this business, you pay $500 a month to lease computer time from a local Web-hosting company to use its server to host and maintain your website. You also own a sports utility vehicle (SUV) that you use to make deliveries. Your monthly car payment is $300, and you pay $100 a month in insurance costs. Each order that you fill takes, on average, a half hour and consumes $0.50 worth of gasoline. When you fill an order, you pay the grocer for the merchandise. You then collect a payment, including a delivery fee, from the students to whom you sell. If you did not operate this business, you could work at the campus dining hall, earning $6 an hour. Right now, you operate your business five days a week, Monday through Friday. On weekends, your business is idle, and you work in the campus dining hall. Based on the above data, answer the given subquestions.
            Our implicit cost will be
            1. $300 car payment
            2. $100 a month insurance cost
            3. Your wage at campus dining hall $6 an hour
            4. All of these

            Published solution

            **1. Concept:** Implicit costs are the opportunity costs of resources you own, with no cash payment. **2. Check:** The car payment and insurance are cash payments (explicit). The $6 per hour you could have earned at the dining hall is income you give up by using your own time. **3. Conclude:** The implicit cost is your dining hall wage of $6 an hour. Answer: C — Your wage at campus dining hall $6 an hour. A: **Incorrect:** This is a cash payment, so it is explicit. B: **Incorrect:** This is a cash payment, so it is explicit. C: **Correct:** It is the forgone income from your own time. D: **Incorrect:** Only the dining hall wage is implicit.

            Question 24 NAT · 1.0 marks

            Imagine that you have started a snack food delivery business on your college campus. Students send you orders for snacks, such as potato chips and candy bars, via the Internet. You shop at local grocery stores to fill these orders and then deliver the orders. To operate this business, you pay $500 a month to lease computer time from a local Web-hosting company to use its server to host and maintain your website. You also own a sports utility vehicle (SUV) that you use to make deliveries. Your monthly car payment is $300, and you pay $100 a month in insurance costs. Each order that you fill takes, on average, a half hour and consumes $0.50 worth of gasoline. When you fill an order, you pay the grocer for the merchandise. You then collect a payment, including a delivery fee, from the students to whom you sell. If you did not operate this business, you could work at the campus dining hall, earning $6 an hour. Right now, you operate your business five days a week, Monday through Friday. On weekends, your business is idle, and you work in the campus dining hall. Based on the above data, answer the given subquestions.
            Last week you purchased five large cases of Fritos for a customer who, as it turned out, did not accept delivery. You paid $200 for these cases. You have a deal with your grocers that they will pay you $0.5 for each dollar of returned merchandise. Just this week, you found a fraternity on campus that will buy the five cartons for $125 (and will pick them up from your apartment, relieving you of the need to deliver them to the frat house). What is the opportunity cost of filling this order in $ (i.e., selling these cartons to the fraternity)? __________

              Published solution

              **1. Concept:** Opportunity cost is the value of the best alternative given up. The $200 paid earlier is a sunk cost and is not counted. **2. Alternative:** The grocers will pay $0.50 for each dollar of returned merchandise: \[ 0.5\times200=\$100 \] **3. Conclude:** Selling to the fraternity means giving up the $100 refund. Answer: \(\$100\).

              Question 25 MCQ · 1.0 marks

              Imagine that you have started a snack food delivery business on your college campus. Students send you orders for snacks, such as potato chips and candy bars, via the Internet. You shop at local grocery stores to fill these orders and then deliver the orders. To operate this business, you pay $500 a month to lease computer time from a local Web-hosting company to use its server to host and maintain your website. You also own a sports utility vehicle (SUV) that you use to make deliveries. Your monthly car payment is $300, and you pay $100 a month in insurance costs. Each order that you fill takes, on average, a half hour and consumes $0.50 worth of gasoline. When you fill an order, you pay the grocer for the merchandise. You then collect a payment, including a delivery fee, from the students to whom you sell. If you did not operate this business, you could work at the campus dining hall, earning $6 an hour. Right now, you operate your business five days a week, Monday through Friday. On weekends, your business is idle, and you work in the campus dining hall. Based on the above data, answer the given subquestions.
              Last week you purchased five large cases of Fritos for a customer who, as it turned out, did not accept delivery. You paid $200 for these cases. You have a deal with your grocers that they will pay you $0.5 for each dollar of returned merchandise. Just this week, you found a fraternity on campus that will buy the five cartons for $125 (and will pick them up from your apartment, relieving you of the need to deliver them to the frat house). Should you sell the Fritos to the fraternity? ________
              1. Yes
              2. No

              Published solution

              **1. Compare:** Selling to the fraternity gives $125. The best alternative is returning the cartons to the grocers for \(0.5\times200=\$100\). The $200 already paid is sunk. **2. Decide:** \(125>100\), so selling gains $25 more. **3. Conclude:** Yes, sell the Fritos to the fraternity. Answer: A — Yes. A: **Correct:** The fraternity pays $125, which is more than the $100 refund. B: **Incorrect:** Rejecting $125 for a $100 refund loses $25.