The Theory of the Firm under under Perfect CompetitionClass 12 Introductory Microeconomics NCERT Solutions
27 Solutions
Generated by KedovoAI
Solution 1 of 27
Q1Questions
What are the characteristics of a perfectly competitive market?
Solution
Based on the chapter, a perfectly competitive market has the following four defining features:
- Large number of buyers and sellers: The market consists of so many buyers and sellers that no single individual can influence the market price. Each participant is very small relative to the market size.
- Homogenous product: All firms in the market produce and sell an identical product. From a buyer's perspective, the product of one firm is a perfect substitute for the product of any other firm.
- Free entry and exit: There are no barriers preventing new firms from entering the market or existing firms from leaving it. This ensures that a large number of firms can exist in the market.
- Perfect information: All buyers and sellers are fully informed about the price, quality, and other relevant details of the product and the market. This ensures that a single market price prevails.
Q2Questions
How are the total revenue of a firm, market price, and the quantity sold by the firm related to each other?
Solution
The total revenue (TR) of a firm is directly related to the market price (p) and the quantity of the good sold (q). The relationship is defined by the following formula:
TR = p × q
This means that the total revenue is calculated by multiplying the market price per unit of the good by the total number of units produced and sold by the firm.
Q3Questions
What is the 'price line'?
Solution
The 'price line' is a horizontal straight line that graphically represents the relationship between the market price and a firm's output level in a perfectly competitive market. Since a firm in perfect competition is a price-taker, the market price (p) is fixed for it, regardless of the quantity it sells. The price line's vertical height is equal to this fixed market price, p. It is also the firm's Average Revenue (AR) curve and the demand curve that the firm faces.
Q4Questions
Why is the total revenue curve of a price-taking firm an upward-sloping straight line? Why does the curve pass through the origin?
Solution
The total revenue (TR) curve of a price-taking firm has these characteristics for two main reasons:
-
Upward-sloping straight line: In a perfectly competitive market, the firm is a price-taker, meaning the market price (p) is constant regardless of the quantity (q) the firm sells. The total revenue is calculated as TR = p × q. Since p is a constant, TR increases at a constant rate as q increases. This constant proportional relationship between TR and q is represented graphically as an upward-sloping straight line.
-
Passes through the origin: The curve passes through the origin (point O) because if the firm sells zero units of output (q = 0), its total revenue is also zero (TR = p × 0 = 0). This point, where both quantity and revenue are zero, is the starting point of the TR curve.
Q5Questions
What is the relation between market price and average revenue of a price-taking firm?
Solution
For a price-taking firm in a perfectly competitive market, the average revenue (AR) is always equal to the market price (p).
This is because Average Revenue is defined as Total Revenue (TR) per unit of output (q). The calculation is as follows:
AR = TR / q
Since TR = p × q, we have:
AR = (p × q) / q = p
Therefore, for a price-taking firm, AR = p.
Q6Questions
What is the relation between market price and marginal revenue of a price-taking firm?
Solution
For a price-taking firm in a perfectly competitive market, the marginal revenue (MR) is always equal to the market price (p).
Marginal Revenue is the increase in total revenue from selling one additional unit of output. Since the firm can sell any quantity at the constant market price (p), each extra unit sold adds exactly 'p' to the total revenue.
Therefore, for a price-taking firm, MR = p. This also means that for a perfectly competitive firm, p = AR = MR.
Q7Questions
What conditions must hold if a profit-maximising firm produces positive output in a competitive market?
Solution
For a profit-maximising firm to produce a positive level of output in a competitive market, three conditions must be met:
-
Price must equal Marginal Cost (p = MC): The firm's profit is maximised at the output level where the revenue from the last unit sold (which is the price, p) is exactly equal to the cost of producing that last unit (Marginal Cost, MC).
-
Marginal Cost must be non-decreasing: At the profit-maximising output level, the MC curve must not be downward sloping. If it were, the firm could increase its profit by producing more, as the cost of additional units would be less than the price.
-
Price must be greater than or equal to Average Variable Cost (in the short run) or Average Cost (in the long run):
- In the short run, the price must be at least equal to the Average Variable Cost (p ≥ AVC). If p < AVC, the firm would lose more by producing than by shutting down and only paying its fixed costs.
- In the long run, the price must be at least equal to the Average Cost (p ≥ AC). If p < AC, the firm would be making a loss and would exit the market.
Q8Questions
Can there be a positive level of output that a profit-maximising firm produces in a competitive market at which market price is not equal to marginal cost? Give an explanation.
Solution
No, a profit-maximising firm will not produce a positive level of output where the market price is not equal to the marginal cost.
Here is the explanation:
- If Market Price > Marginal Cost (p > MC): This means the revenue from producing one more unit (p) is greater than the cost of producing it (MC). In this situation, the firm can increase its total profit by producing more. Therefore, it will not stop at this level of output.
- If Market Price < Marginal Cost (p < MC): This means the revenue from the last unit produced (p) is less than the cost of producing it (MC). The firm is making a loss on that last unit. It can increase its total profit by reducing its output. Therefore, it will not choose this level of output.
Thus, the only point where the firm has no incentive to change its output level is where profit is maximised, which occurs when p = MC.
Q9Questions
Will a profit-maximising firm in a competitive market ever produce a positive level of output in the range where the marginal cost is falling? Give an explanation.
Solution
No, a profit-maximising firm in a competitive market will not produce a positive level of output in the range where its marginal cost (MC) is falling. This is the second condition for profit maximisation.
Explanation:
Even if the first condition (p = MC) is met at a point where the MC curve is downward-sloping, this cannot be a point of maximum profit. If the firm were to produce one more unit beyond this point, the marginal cost for that unit would be even lower, and therefore less than the price (p). This means producing that additional unit would add more to revenue than to cost, thereby increasing the firm's profit. The firm would continue to increase its output as long as MC is falling and remains below the price. Therefore, a profit-maximising equilibrium can only be reached on the upward-sloping portion of the MC curve.
Q10Questions
Will a profit-maximising firm in a competitive market produce a positive level of output in the short run if the market price is less than the minimum of AVC? Give an explanation.
Solution
No, a profit-maximising firm will not produce a positive level of output in the short run if the market price is less than the minimum of its Average Variable Cost (AVC).
Explanation:
In the short run, a firm has both fixed and variable costs. If the firm shuts down and produces zero output, its loss will be equal to its Total Fixed Costs (TFC). If it produces a positive output when the price (p) is below the AVC, its Total Revenue (TR = p × q) will be less than its Total Variable Cost (TVC = AVC × q). This means the revenue earned does not even cover the variable costs of production. The firm's total loss in this case would be its Total Fixed Costs plus the part of the variable costs not covered by revenue. Since this loss is greater than the loss from shutting down (which is just TFC), the firm will choose to produce zero output.
Q11Questions
Will a profit-maximising firm in a competitive market produce a positive level of output in the long run if the market price is less than the minimum of AC? Give an explanation.
Solution
No, a profit-maximising firm will not produce a positive level of output in the long run if the market price is less than the minimum of its long-run Average Cost (AC).
Explanation:
In the long run, a firm has no fixed costs; all costs are variable. A firm must cover all its costs to stay in business. If the price (p) is less than the Average Cost (AC), then the Total Revenue (TR = p × q) will be less than the Total Cost (TC = AC × q). This means the firm is incurring a loss on its operations. In the long run, a firm facing a loss has the option to exit the market entirely. By exiting, its profit becomes zero. Since a profit of zero is better than a loss, the firm will choose to exit the market rather than produce at a price below its average cost.
Q12Questions
What is the supply curve of a firm in the short run?
Solution
The short-run supply curve of a firm is the rising part of its Short-run Marginal Cost (SMC) curve from and above the minimum point of the Average Variable Cost (AVC) curve. For any price below the minimum AVC, the firm will produce zero output. Therefore, the supply curve consists of two parts:
- The upward-sloping segment of the SMC curve that lies above the minimum AVC point.
- A vertical line segment on the price axis from the origin up to the minimum AVC price, representing zero output for all prices below the shutdown point.
Q13Questions
What is the supply curve of a firm in the long run?
Solution
The long-run supply curve of a firm is the rising part of its Long-run Marginal Cost (LRMC) curve from and above the minimum point of the Long-run Average Cost (LRAC) curve. For any price below the minimum LRAC, the firm will exit the market and produce zero output. Therefore, the long-run supply curve consists of two parts:
- The upward-sloping segment of the LRMC curve that lies above the minimum LRAC point.
- A vertical line segment on the price axis from the origin up to the minimum LRAC price, representing zero output for all prices below the exit point.
Q14Questions
How does technological progress affect the supply curve of a firm?
Solution
Technological progress allows a firm to produce a given level of output using fewer inputs, or produce more output with the same level of inputs. This improvement in efficiency lowers the firm's cost of production at every level of output. Specifically, it lowers the firm's marginal cost (MC). Since a firm's supply curve is a segment of its MC curve, a downward or rightward shift in the MC curve results in a rightward shift of the supply curve. This means that after the technological progress, the firm is willing to supply more units of output at any given market price.
Q15Questions
How does the imposition of a unit tax affect the supply curve of a firm?
Solution
A unit tax is a tax imposed by the government on each unit of output sold. This tax effectively increases the cost of production for the firm. For every unit produced, the firm's marginal cost (MC) increases by the amount of the tax. This causes the firm's MC curve to shift upward and to the left. Since the firm's supply curve is derived from its MC curve, the imposition of a unit tax shifts the supply curve of the firm to the left. This means that at any given market price, the firm will now supply fewer units of output than it did before the tax.
Q16Questions
How does an increase in the price of an input affect the supply curve of a firm?
Solution
An increase in the price of an input, such as labour wages or raw material costs, raises the firm's overall cost of production. This increase in costs leads to an increase in the firm's marginal cost (MC) at any level of output. Graphically, this is represented by an upward or leftward shift of the MC curve. As the firm's supply curve is a segment of its MC curve, an increase in input prices will cause the firm's supply curve to shift to the left. This signifies that at any given market price, the firm is now willing to produce and sell a smaller quantity of the good.
Q17Questions
How does an increase in the number of firms in a market affect the market supply curve?
Solution
The market supply curve is the horizontal summation of the supply curves of all individual firms in the market. When the number of firms in the market increases, there are more producers supplying the good at any given price. The total quantity supplied in the market at each price level will therefore be higher. This results in the market supply curve shifting to the right. Conversely, a decrease in the number of firms would shift the market supply curve to the left.
Q18Questions
What does the price elasticity of supply mean? How do we measure it?
Solution
The price elasticity of supply measures the degree of responsiveness of the quantity supplied of a good to a change in its market price. It indicates the percentage change in quantity supplied that occurs in response to a one percent change in price.
We measure it using the following formula:
Price elasticity of supply (eS) = (Percentage change in quantity supplied) / (Percentage change in price)
Mathematically, this can be expressed as:
eS = (ΔQ / Q) / (ΔP / P) = (ΔQ / ΔP) × (P / Q)
Where:
- ΔQ is the change in quantity supplied
- Q is the initial quantity supplied
- ΔP is the change in price
- P is the initial price
Q19Questions
Compute the total revenue, marginal revenue and average revenue schedules in the following table. Market price of each unit of the good is Rs 10.
Quantity Sold TR MR AR 0 1 2 3 4 5 6
Solution
Given the market price (P) = Rs 10.
- Total Revenue (TR) is calculated as Price × Quantity Sold.
- Average Revenue (AR) is calculated as TR / Quantity Sold. For a price-taking firm, AR is always equal to the price.
- Marginal Revenue (MR) is the change in TR from selling one more unit. For a price-taking firm, MR is always equal to the price.
Here is the completed schedule:
| Quantity Sold | TR (Rs) | MR (Rs) | AR (Rs) |
|---|---|---|---|
| 0 | 0 | - | - |
| 1 | 10 | 10 | 10 |
| 2 | 20 | 10 | 10 |
| 3 | 30 | 10 | 10 |
| 4 | 40 | 10 | 10 |
| 5 | 50 | 10 | 10 |
| 6 | 60 | 10 | 10 |
Q20Questions
The following table shows the total revenue and total cost schedules of a competitive firm. Calculate the profit at each output level. Determine also the market price of the good.
Quantity Sold TR (Rs) TC (Rs) Profit 0 0 5 1 5 7 2 10 10 3 15 12 4 20 15 5 25 23 6 30 33 7 35 40
Solution
Market Price Determination:
The market price (P) can be determined by dividing Total Revenue (TR) by Quantity Sold (Q) at any positive output level.
For Q = 1, P = TR / Q = 5 / 1 = Rs 5.
For Q = 2, P = TR / Q = 10 / 2 = Rs 5.
Thus, the market price of the good is Rs 5.
Profit Calculation:
Profit is calculated as Total Revenue (TR) minus Total Cost (TC).
Here is the completed table:
| Quantity Sold | TR (Rs) | TC (Rs) | Profit (TR-TC) |
|---|---|---|---|
| 0 | 0 | 5 | -5 |
| 1 | 5 | 7 | -2 |
| 2 | 10 | 10 | 0 |
| 3 | 15 | 12 | 3 |
| 4 | 20 | 15 | 5 |
| 5 | 25 | 23 | 2 |
| 6 | 30 | 33 | -3 |
| 7 | 35 | 40 | -5 |
Q21Questions
The following table shows the total cost schedule of a competitive firm. It is given that the price of the good is Rs 10. Calculate the profit at each output level. Find the profit maximising level of output.
Output TC (Rs) 0 5 1 15 2 22 3 27 4 31 5 38 6 49 7 63 8 81 9 101 10 123
Solution
Given the price (P) = Rs 10.
First, we calculate Total Revenue (TR = P × Output) and then Profit (Profit = TR - TC).
| Output (Q) | TC (Rs) | TR (Rs) (10 × Q) | Profit (Rs) (TR - TC) |
|---|---|---|---|
| 0 | 5 | 0 | -5 |
| 1 | 15 | 10 | -5 |
| 2 | 22 | 20 | -2 |
| 3 | 27 | 30 | 3 |
| 4 | 31 | 40 | 9 |
| 5 | 38 | 50 | 12 |
| 6 | 49 | 60 | 11 |
| 7 | 63 | 70 | 7 |
| 8 | 81 | 80 | -1 |
| 9 | 101 | 90 | -11 |
| 10 | 123 | 100 | -23 |
By observing the profit column, we can see that the maximum profit is Rs 12, which occurs at an output level of 5 units.
Therefore, the profit-maximising level of output is 5 units.
Q22Questions
Consider a market with two firms. The following table shows the supply schedules of the two firms: the SS₁ column gives the supply schedule of firm 1 and the SS₂ column gives the supply schedule of firm 2. Compute the market supply schedule.
Price (Rs) SS₁ (units) SS₂ (units) 0 0 0 1 0 0 2 0 0 3 1 1 4 2 2 5 3 3 6 4 4
Solution
The market supply schedule is computed by taking the horizontal summation of the individual firms' supply schedules. At each price, we add the quantity supplied by firm 1 (SS₁) to the quantity supplied by firm 2 (SS₂).
Market Supply (Sm) = SS₁ + SS₂
Here is the computed market supply schedule:
| Price (Rs) | SS₁ (units) | SS₂ (units) | Market Supply (Sm) (units) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 2 | 0 | 0 | 0 |
| 3 | 1 | 1 | 2 |
| 4 | 2 | 2 | 4 |
| 5 | 3 | 3 | 6 |
| 6 | 4 | 4 | 8 |
Q23Questions
Consider a market with two firms. In the following table, columns labelled as SS₁ and SS₂ give the supply schedules of firm 1 and firm 2 respectively. Compute the market supply schedule.
Price (Rs) SS₁ (kg) SS₂ (kg) 0 0 0 1 0 0 2 0 0 3 1 0 4 2 0.5 5 3 1 6 4 1.5 7 5 2 8 6 2.5
Solution
The market supply schedule is the horizontal summation of the individual supply schedules of firm 1 (SS₁) and firm 2 (SS₂). We find the total market supply at each price by adding the quantities supplied by both firms.
Market Supply (Sm) = SS₁ + SS₂
Here is the computed market supply schedule:
| Price (Rs) | SS₁ (kg) | SS₂ (kg) | Market Supply (Sm) (kg) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 |
| 2 | 0 | 0 | 0 |
| 3 | 1 | 0 | 1 |
| 4 | 2 | 0.5 | 2.5 |
| 5 | 3 | 1 | 4 |
| 6 | 4 | 1.5 | 5.5 |
| 7 | 5 | 2 | 7 |
| 8 | 6 | 2.5 | 8.5 |
Q24Questions
There are three identical firms in a market. The following table shows the supply schedule of firm 1. Compute the market supply schedule.
Price (Rs) SS₁ (units) 0 0 1 0 2 2 3 4 4 6 5 8 6 10 7 12 8 14
Solution
Since there are three identical firms in the market, the supply schedule for each firm is the same as that of firm 1 (SS₁). The market supply schedule is the sum of the quantities supplied by all three firms at each price. Therefore, we can find the market supply by multiplying the supply of firm 1 by 3.
Market Supply (Sm) = SS₁ × 3
Here is the computed market supply schedule:
| Price (Rs) | SS₁ (units) | Market Supply (Sm) (units) |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 0 | 0 |
| 2 | 2 | 6 |
| 3 | 4 | 12 |
| 4 | 6 | 18 |
| 5 | 8 | 24 |
| 6 | 10 | 30 |
| 7 | 12 | 36 |
| 8 | 14 | 42 |
Q25Questions
A firm earns a revenue of Rs 50 when the market price of a good is Rs 10. The market price increases to Rs 15 and the firm now earns a revenue of Rs 150. What is the price elasticity of the firm's supply curve?
Solution
To calculate the price elasticity of supply, we first need to find the initial and final quantities supplied.
Step 1: Find the initial and final quantities.
- Initial Price (P₁) = Rs 10, Initial Total Revenue (TR₁) = Rs 50 Initial Quantity (Q₁) = TR₁ / P₁ = 50 / 10 = 5 units
- Final Price (P₂) = Rs 15, Final Total Revenue (TR₂) = Rs 150 Final Quantity (Q₂) = TR₂ / P₂ = 150 / 15 = 10 units
Step 2: Calculate the price elasticity of supply (eS).
The formula is: eS = (Percentage change in quantity supplied) / (Percentage change in price)
eS = [(Q₂ - Q₁) / Q₁] / [(P₂ - P₁) / P₁]
- Change in Quantity (ΔQ) = 10 - 5 = 5
- Change in Price (ΔP) = 15 - 10 = 5
eS = (5 / 5) / (5 / 10) = 1 / 0.5 = 2
The price elasticity of the firm's supply curve is 2.
Q26Questions
The market price of a good changes from Rs 5 to Rs 20. As a result, the quantity supplied by a firm increases by 15 units. The price elasticity of the firm's supply curve is 0.5 . Find the initial and final output levels of the firm.
Solution
We are given the following information:
- Initial Price (P₁) = Rs 5
- Final Price (P₂) = Rs 20
- Change in Quantity (ΔQ) = 15 units
- Price Elasticity of Supply (eS) = 0.5
Let the initial output be Q₁ and the final output be Q₂. We know that Q₂ = Q₁ + 15.
Step 1: Use the price elasticity formula.
The formula for price elasticity of supply is: eS = (ΔQ / ΔP) × (P₁ / Q₁)
Step 2: Calculate the change in price (ΔP).
ΔP = P₂ - P₁ = 20 - 5 = Rs 15
Step 3: Substitute the known values into the formula to find Q₁.
0.5 = (15 / 15) × (5 / Q₁)
0.5 = 1 × (5 / Q₁)
0.5 = 5 / Q₁
Q₁ = 5 / 0.5
Q₁ = 10 units
Step 4: Calculate the final output level (Q₂).
Q₂ = Q₁ + 15
Q₂ = 10 + 15 = 25 units
Therefore, the initial output level is 10 units and the final output level is 25 units.
Q27Questions
At the market price of Rs 10, a firm supplies 4 units of output. The market price increases to Rs 30. The price elasticity of the firm's supply is 1.25 . What quantity will the firm supply at the new price?
Solution
We are given the following information:
- Initial Price (P₁) = Rs 10
- Initial Quantity (Q₁) = 4 units
- Final Price (P₂) = Rs 30
- Price Elasticity of Supply (eS) = 1.25
We need to find the new quantity supplied (Q₂).
Step 1: Use the price elasticity formula.
eS = [(Q₂ - Q₁) / Q₁] / [(P₂ - P₁) / P₁]
Step 2: Calculate the percentage change in price.
Percentage change in price = [(P₂ - P₁) / P₁] × 100
= [(30 - 10) / 10] × 100
= (20 / 10) × 100 = 2 × 100 = 200%
Step 3: Use the elasticity to find the percentage change in quantity.
1.25 = (Percentage change in quantity) / 200%
Percentage change in quantity = 1.25 × 200% = 250%
Step 4: Calculate the new quantity (Q₂).
A 250% increase in quantity means:
Change in Quantity (ΔQ) = 250% of Q₁ = 2.50 × 4 = 10 units
New Quantity (Q₂) = Initial Quantity (Q₁) + Change in Quantity (ΔQ)
Q₂ = 4 + 10 = 14 units
Therefore, the firm will supply 14 units at the new price.