Class 11 Economics (Mircoeconomics) Chapter 3 Production and Costs

Key Concept: Regional Cooperation, Geopolitical Dynamics

b) By creating competitive bilateral agreements with specific SAARC members

[Solution Description] China’s growing influence in South Asia through investments and infrastructure projects, such as those under the Belt and Road Initiative (BRI), can have a profound impact on regional economic dynamics. As China becomes a major investor and trade partner, SAARC countries might prioritize bilateral relations with China over multilateral cooperation within SAARC. This could lead to increased competition rather than cooperation within SAARC, affecting the organization’s ability to function effectively.

Key Concept: Short Run Cost Curves

c) Short Run Marginal Cost (SMC)

[Solution Description]

In the short run, both the Short Run Marginal Cost (SMC) and Average Variable Cost (AVC) curves are U-shaped. However, the U-shape arises primarily due to the law of diminishing returns affecting the variable costs as production scales up or down. Among the options provided, the SMC curve is distinctly recognized for this characteristic in textbooks under these conditions.

Key Concept: Basic Formula Application

c) \$150

[Solution Description] The total cost (TC) is calculated by adding the total fixed cost (TFC) to the total variable cost (TVC).

$$TC = TFC + TVC = 50 + 100 = 150$$

So, the total cost (TC) is \$150.

Key Concept: Advanced Curve Analysis, Mathematical Analysis

d) Assertion is false, but Reason is true.

[Solution Description] To analyze this situation, consider the nature of AP and MP curves. The AP increases as long as MP is greater than AP and decreases when MP is less than AP. Therefore, for AP to reach a maximum, MP must equal AP right at that peak. However, the MP does not necessarily need to start declining exactly when AP reaches its maximum; it only needs to be equal to AP at that point. The statement in Assertion is incorrect because AP reaching its maximum is dependent on MP equating AP, which can occur while MP is still rising or constant. The Reason correctly describes the situation where MP intersects AP at AP’s maximum point but doesn’t logically lead to the assertion’s claim. Hence, Assertion is false, but Reason is true.

Key Concept: Production Function Equation

b) 80

[Solution Description]

To find the output using the Cobb-Douglas production function, substitute $$K = 16$$ and $$L = 25$$ into the equation:

$$q = 4(16)^{0.5}(25)^{0.5}$$

Calculate $$(16)^{0.5} = 4$$ and $$(25)^{0.5} = 5$$. Thus, substitute these values back into the equation:

$$q = 4 \times 4 \times 5 = 80$$

Hence, the output is 80 units.

Key Concept: Curve Analysis

a) Downward sloping part

[Solution Description] The LRAC curve is U-shaped, and the downward sloping part corresponds to increasing returns to scale (IRS). During IRS, as output increases, the cost per unit decreases due to efficiencies gained.

Key Concept: Advanced Calculation, Theoretical Application

b) New AP = 36.67; AP is falling

[Solution Description]

Initially, the Average Product ($$AP_1$$) is given as 40, with 5 units of labor:

$$AP_1 = \frac{TP_1}{L_1} = 40 = \frac{200}{5}$$

With an increase in TP to 220 and labor to 6 units, the new Average Product ($$AP_2$$) is calculated as:

$$AP_2 = \frac{TP_2}{L_2} = \frac{220}{6} = 36.67$$

Since $$AP_2 < AP_1$$, it indicates that Marginal Product (MP) is less than the previous AP (40), hence causing AP to fall.

Key Concept: Basic Definition

b) U-shaped

[Solution Description] According to the syllabus, the Short Run Average Cost (SAC) is U-shaped due to the behavior of variable costs and fixed costs as output changes.

Key Concept: Returns to Scale

b) Increasing Returns to Scale

[Solution Description] To determine returns to scale, analyze the exponents’ sum in the production function $$q = L^{0.5}K^{0.7}$$. The sum of the exponents is $$0.5 + 0.7 = 1.2$$. Since this sum is greater than 1, the production function exhibits increasing returns to scale.

Key Concept: Comparative Analysis

a) It increases from 10 to 12

[Solution Description]

The marginal product (MP) can be calculated using the formula $$MP = \frac{\Delta TP}{\Delta L}$$. Here, $$\Delta TP = 72 – 60 = 12$$ and $$\Delta L = 5 – 4 = 1$$. Therefore, $$MP = \frac{12}{1} = 12$$.

Key Concept: AFC Curve Shape

c) Rectangular hyperbola

[Solution Description] The AFC curve is a rectangular hyperbola because as output increases, the AFC decreases at a diminishing rate, reflecting that fixed costs are distributed across an increasing number of units.

Key Concept: Critical Thinking, Application of SMC

b) Rs 4

[Solution Description]

To find the Short Run Marginal Cost (SMC), use the formula $$SMC = \frac{\Delta TC}{\Delta q}$$ where $$\Delta TC = \Delta TVC$$, as TFC does not change.

Given:

– TVC for 3 units = Rs 21

– TVC for 6 units = Rs 33

Calculate $$\Delta TVC$$:

$$\Delta TVC = TVC(6) – TVC(3) = 33 – 21 = 12$$

Change in quantity ($$\Delta q$$):

$$\Delta q = 6 – 3 = 3$$

Compute SMC:

$$SMC = \frac{\Delta TVC}{\Delta q} = \frac{12}{3} = 4$$

Hence, the SMC when output increases from 3 units to 6 units is Rs 4.

Key Concept: Input-Output Relation

a) Constant returns to scale

[Solution Description]

For the Cobb-Douglas production function $$q = x1^\alpha x2^\beta$$, the sum of the exponents $$(\alpha + \beta)$$ indicates the returns to scale:

– If $$\alpha + \beta = 1$$, it implies constant returns to scale, meaning if all inputs are doubled, the output will also double.

Key Concept: TP and Factor Proportions

a) Factor proportions become more suitable

[Solution Description]

Initially, when a variable input like labor is increased while keeping other inputs constant, the Total Product rises due to better utilization of resources. This is because the factor proportions become more suitable for production, leading to more efficient use of both the fixed and variable factors. Over time, however, as more of the variable input is added, the effect diminishes.

Thus, initially, Total Product increases because factor proportions become more suitable.

Key Concept: Real-world Application

c) The isoquant remains unchanged.

[Solution Description] Increasing one input while reducing another yet maintaining the same output level will result in moving along the same isoquant. Isoquants show different combinations of inputs that yield the same output, indicating the flexibility in substituting inputs.

Key Concept: Technology Impact

c) Maximum output doubles

[Solution Description]

When technology improves and each input’s efficiency doubles, it effectively means that for the same amount of inputs, the production capacity is doubled. This implies:

If original output was $$q = f(L, K)$$, then new output becomes $$q’ = 2f(L, K)$$, indicating the maximum output will double as well.

Key Concept: Scenario-Based Problem Solving, Complex Calculation

c) 20

[Solution Description] To solve for the average product at 5 units of labor, we need to analyze the information given:

From the problem statement:

$$TP_{5} = 100, \quad MP_{6} = 12$$

Total product at 6 units ($$TP_{6}$$) can be expressed as:

$$TP_{6} = TP_{5} + MP_{6} = 100 + 12 = 112$$

We are told that the average product decreases as the 6th unit is added, indicating that at 6 units:

$$AP_{6} = \frac{TP_{6}}{6} = \frac{112}{6} = \frac{56}{3} = 18.67$$

For AP to be decreasing, it must have been greater at 5 units. Calculate $$AP_{5}$$:

$$AP_{5} = \frac{TP_{5}}{5} = \frac{100}{5} = 20$$

Hence, the average product at 5 units of labor was 20.

Key Concept: Graph Interpretation

c) Marginal product

[Solution Description] The steepness or slope of the TP curve indicates the rate of change of total product with respect to labor, which is essentially the Marginal Product (MP). A steeper slope denotes a higher MP.

Key Concept: Curve Intersection

c) At the minimum point of the LRAC curve

[Solution Description] The LRMC curve intersects the LRAC curve at the minimum point of the LRAC. This is because, at this point, the marginal cost equals the average cost when the average cost is neither increasing nor decreasing.

Key Concept: Real-World Application

c) Output increases by approximately 93.3\%

[Solution Description] The production function suggests that output depends on the elasticities of labor and capital. Here, the output changes by a factor of $$3^{\alpha}$$, since capital stays constant. Calculating this as $$3^{0.6}$$:

$$3^{0.6} \approx 1.933$$

Therefore, the output is expected to increase by approximately 93.3\%.

Key Concept: Isoquant Combinations

b) (5L, 25K)

[Solution Description] We need to determine which combination satisfies $$L^{0.5}K^{0.5} = 25$$. Consider each option:

For option A: $$(25L, 1K)$$ gives $$q = 25^{0.5} \times 1^{0.5} = 5 \not= 25$$.

For option B: $$(5L, 25K)$$ gives $$q = 5^{0.5} \times 25^{0.5} = 5 \times 5 = 25$$.

For option C: $$(10L, 6.25K)$$ gives $$q = 10^{0.5} \times 6.25^{0.5} = \sqrt{10} \times \sqrt{6.25} \approx 7.905 \not= 25$$.

For option D: None satisfy except B, so it’s not “All of the above”.

Only option B satisfies the condition.

Key Concept: Curve Intersection

b) At the minimum point of LRAC

[Solution Description] According to the relationship between LRAC and LRMC, the LRMC intersects the LRAC at the minimum point of the LRAC curve. This is because at this point, the average cost is neither increasing nor decreasing, thus the marginal cost equals the average cost.

Key Concept: SAFTA Implementation, India’s Role in Regional Stability

b) It positions India as a more attractive trade partner due to reduced tariffs.

[Solution Description] The SAFTA agreement aims to increase trade between member countries by reducing tariffs and facilitating easier access to markets. As trade volumes increase, countries become economically interdependent, which can reduce tensions and enhance cooperation. For India, this economic interdependence is crucial because it allows India to act as an intermediary or a balancing power due to its large market and economy compared to its neighbors. By enhancing regional trade through SAFTA, India strengthens its relationships with neighboring countries, thus reinforcing its role as a regional stabilizer.

Key Concept: Relationship Understanding

c) SAC is at its minimum

[Solution Description] When SMC (Short Run Marginal Cost) equals SAC (Short Run Average Cost), it indicates that SAC has reached its minimum point. This is because the marginal cost curve intersects the average cost curve at its lowest point according to economic theory.

Key Concept: Long Run Cost Curves

c) It is U-shaped.

[Solution Description]

The LRAC curve in the long run is typically U-shaped due to what happens with returns to scale as a firm increases its production. Initially, increasing returns to scale cause the average cost to fall, whereas diminishing returns to scale at higher levels of output cause the average cost to rise. The LRMC intersects the LRAC curve at its minimum point.

Key Concept: Production Function Analysis

c) Constant returns to scale

[Solution Description] The Cobb-Douglas production function $$q = L^{0.7}K^{0.3}$$ has exponents $$\alpha = 0.7$$ and $$\beta = 0.3$$. To determine the returns to scale, we sum these exponents: $$0.7 + 0.3 = 1.0$$. When $$\alpha + \beta = 1$$, it indicates constant returns to scale, meaning if all inputs are doubled, the output will also double.

Key Concept: TP Curve Interpretation

d) TP increases at a decreasing rate

[Solution Description] Under the law of variable proportions, as more units of a variable input are added to fixed inputs, the Total Product initially increases. However, once diminishing returns set in, the rate of increase in TP slows down. Thus, while TP continues to rise, it does so at a decreasing rate.

Key Concept: Curve Shape

b) U-shaped

[Solution Description] The Long Run Marginal Cost (LRMC) curve is typically U-shaped because it decreases initially due to increasing returns to scale and then increases due to decreasing returns to scale.

Key Concept: Application of Formula

c) \$20

[Solution Description]

To find the Average Variable Cost (AVC), we first need to determine the Total Variable Cost (TVC). Using the formula $$TC = TFC + TVC$$, we solve for TVC:

$$TVC = TC – TFC = 150 – 50 = 100$$

Then, calculate AVC using the formula $$AVC = \frac{TVC}{q}$$:

$$AVC = \frac{100}{5} = 20$$

Thus, the Average Variable Cost (AVC) is \$20.

Key Concept: Calculation Application

c) Rs 5

[Solution Description] To find the AFC, we use the formula $$AFC = \frac{TFC}{q}$$. Here, TFC = Rs 300, and q = 60 units. Therefore:

$$AFC = \frac{300}{60} = 5$$

The AFC is Rs 5.

Key Concept: Output Level Analysis

b) LRMC is greater

[Solution Description] To the right of the minimum point of the LRAC, both curves begin to rise. In this region, the LRMC becomes greater than LRAC because the cost of producing one additional unit (marginal cost) exceeds the average cost per unit, which indicates diseconomies of scale.

Key Concept: Maximum Point

b) At the maximum of AP

[Solution Description] The intersection of the MP curve with the AP curve occurs at the maximum point of the AP curve. This is a fundamental property of these curves in economics, demonstrating the peak efficiency of resource usage.

Key Concept: Graph Interpretation

d) At the AP’s maximum

[Solution Description] The Marginal Product (MP) curve intersects the Average Product (AP) curve at the AP’s maximum point. This is because when MP is greater than AP, AP is rising, and when MP is less than AP, AP is falling. Hence, intersection occurs at the peak of AP.

Key Concept: Isoquant Concept

c) A level of output

[Solution Description] An isoquant is a curve that represents combinations of different inputs that yield the same level of output in production. Thus, an isoquant shows a constant level of output.

Key Concept: Curve Shapes

c) U-shaped

[Solution Description]

The Long Run Average Cost (LRAC) curve is typically U-shaped due to economies and diseconomies of scale. As production increases, the firm experiences Increasing Returns to Scale (IRS) where costs decrease, followed by Constant Returns to Scale (CRS), and eventually Decreasing Returns to Scale (DRS) where costs increase.

Key Concept: Relationship Analysis

c) SMC initially decreases and then increases

[Solution Description] In the short run, the SMC curve typically follows a U-shape due to initially increasing returns followed by diminishing returns as more units are produced. Hence, SMC initially decreases and then increases after reaching the minimum point.

Key Concept: Definition Understanding

c) Total cost per unit of output

[Solution Description] Short Run Average Cost (SAC) represents the total cost per unit of output produced. It combines both Average Variable Cost (AVC) and Average Fixed Cost (AFC), or can be computed directly from total cost divided by output.

Key Concept: Basic Formula Application

b) \$150

[Solution Description] To find the Total Cost (TC), we use the formula $$TC = TVC + TFC$$. Substitute the given values: $$TC = 100 + 50$$. Therefore, $$TC = 150$$.

Key Concept: Fixed and Variable Inputs

b) Capital

[Solution Description] In the short-run analysis of production, one of the inputs is typically fixed while others may vary. Here, if capital ($$K$$) is fixed at 5 units, then labor ($$L$$) is the variable input that can change.

Key Concept: Understanding Curve Shapes

b) Due to increasing returns initially and then decreasing

[Solution Description] The U-shape of the MP and AP curves is due to the law of variable proportions. Initially, as more units of labor are employed, the increasing returns cause MP and AP to rise. Eventually, diminishing returns set in, causing both curves to fall, leading to their U-shape.

Key Concept: Comparative Analysis

b) AVC is decreasing

[Solution Description]

To understand the change in cost behavior, we compare the Average Variable Cost (AVC) at two different levels of output. At 8 units, the AVC is \$12, and at 16 units, it drops to \$10. This indicates that as output increases, the AVC decreases. Such a pattern suggests economies of scale, where increasing production leads to lower variable costs per unit.

Key Concept: Short Run Cost Calculation

b) \$33.33

[Solution Description] The Short Run Average Cost (SAC) is calculated by dividing the total cost (TC) by the quantity of output produced.

\begin{align*}

TC &= TFC + TVC = \$40 + \$60 = \$100,

SAC &= \frac{TC}{Q} = \frac{\$100}{3} \approx \$33.33.

\end{align*}

Thus, the SAC is approximately \$33.33 per unit.

Key Concept: Relationship Analysis

d) TP increases at a decreasing rate

[Solution Description]

When MP is declining but still positive, it means that each additional unit of input adds less output than the previous one, but still contributes positively to the Total Product.

The Total Product will continue to increase because MP is positive, although at a decreasing rate.

Therefore, TP continues to rise as long as MP is positive.

Key Concept: Second Order Thinking, Conceptual Integration

a) At the initial stage, both AP and TP increase; eventually, AP decreases while TP increases but at a decreasing rate.

[Solution Description] Initially, when MP increases, it means AP is also increasing because MP > AP. As long as MP continues to rise, TP will rise at an increasing rate. Once MP starts decreasing but remains positive, AP reaches its maximum and begins to fall, indicating diminishing returns due to the law of diminishing marginal product. TP will continue to increase, but at a decreasing rate.

Key Concept: Trend Analysis

c) It increases at a decreasing rate.

[Solution Description] Total Product typically increases with more input; however, it may do so at a decreasing rate due to diminishing returns. Thus, as inputs rise from 1 to 5 units, Total Product will likely increase but not necessarily at a constant or accelerating rate.

Key Concept: Formula Application

c) Decreasing Returns to Scale

[Solution Description] When $$\alpha + \beta < 1$$ in a Cobb-Douglas function, it exhibits Decreasing Returns to Scale (DRS).

Key Concept: Regional Bloc Potential, Influence of Diasporas

b) It fosters economic stability, supporting closer regional ties.

[Solution Description] Remittances from the South Asian diaspora contribute significantly to the GDPs of their respective countries, which can stabilize economies and reduce poverty. This financial input encourages governments to pursue policies that enhance economic stability, potentially leading to stronger regional economic cohesion and support for a regional bloc. The answer reflects these potential outcomes.

Key Concept: Factor Proportions

b) They become more suitable initially

[Solution Description] Initially, as more units of a variable input are combined with a fixed input, the efficiency in using those inputs often increases, leading to better adjustment and higher productivity. This is described by the concept that they become more suitable at first.

Key Concept: Marginal and Average Cost

c) SAC is constant

[Solution Description]

When the SMC equals the SAC, the SAC is at its minimum point. This is because the SAC curve is typically U-shaped, and the SMC intersects the SAC at the minimum point of SAC.