Chapter 4: The Theory of the Firm under Perfect Competition

The Theory of the Firm under Perfect Competition

Introductory Microeconomics • Chapter 4

Q1 What are the characteristics of a perfectly competitive market?
  • Large Number of Buyers and Sellers: No single buyer or seller can influence the market price. They are price takers.
  • Homogeneous Product: Products sold by different firms are identical in all respects (perfect substitutes).
  • Free Entry and Exit: Firms can freely enter or exit the market in the long run.
  • Perfect Knowledge: Buyers and sellers have complete information about prices and products.
Q2-6 Revenue Relationships (TR, AR, MR)
  • Total Revenue (TR): $TR = P \times Q$. It is directly proportional to quantity sold.
  • Price Line: It is the graphical representation of the relationship between Price and Quantity. In perfect competition, it is a horizontal straight line.
  • TR Curve: It is an upward-sloping straight line passing through the origin because price is constant. $TR = P \cdot q$, so as $q$ increases, TR increases at a constant rate $P$. It starts at origin because at $q=0, TR=0$.
  • Relation (AR & MR): For a price-taking firm, Price is fixed.
    $$AR = \frac{TR}{Q} = \frac{P \cdot Q}{Q} = P$$
    $$MR = \frac{\Delta TR}{\Delta Q} = P$$
    Therefore, Price = AR = MR.
Q7-11 Profit Maximization Conditions

For a firm to produce a positive output and maximize profit:

  1. MR = MC: (Or Price = Marginal Cost).
  2. MC must be non-decreasing: The MC curve must cut the MR curve from below.
  3. Short Run Condition: Price $\geq$ Minimum AVC. (Otherwise, the firm shuts down).
  4. Long Run Condition: Price $\geq$ Minimum AC. (Otherwise, the firm exits).

Reason for Q8-Q11: If $P \neq MC$, profits can be increased by changing output. If MC is falling, increasing output adds more to revenue than cost. If $P < AVC$, the firm cannot even cover variable costs.

Q12-13 Supply Curve of a Firm
[Image of short run supply curve firm]
  • Short Run: The rising part of the SMC curve above the minimum AVC.
  • Long Run: The rising part of the LMC curve above the minimum LAC.
Q14-16 Factors Affecting Supply Curve
  • Technological Progress: Reduces marginal cost. MC curve shifts right/down. Supply curve shifts right (Supply increases).
  • Unit Tax: Increases marginal cost. MC curve shifts left/up. Supply curve shifts left (Supply decreases).
  • Input Price Increase: Increases marginal cost. Supply curve shifts left (Supply decreases).
Q17 Effect of Increase in Number of Firms

Market supply is the horizontal summation of individual firm supplies. An increase in the number of firms leads to an increase in market supply (Rightward shift of the market supply curve).

Q19 Compute TR, MR, AR Schedules. Price = Rs 10.
QPrice (P)TR ($P \times Q$)MR ($\Delta TR$)AR ($TR/Q$)
0100––
110101010
210201010
310301010
410401010
510501010
610601010
Q20 Calculate Profit and Market Price.

Market Price: $TR = P \times Q \Rightarrow P = TR/Q$. At Q=1, TR=5, so P = Rs 5.

QTRTCProfit ($\pi = TR – TC$)
005-5
157-2
210100
315123
420155 (Max)
525232
63033-3
73540-5

Profit maximizing output is Q = 4 units.

Q21 Calculate Profit and Maximising Level (Price = Rs 10).
OutputPriceTR ($P \times Q$)TCProfit ($TR-TC$)
01005-5
1101015-5
2102022-2
31030273
41040319
510503812 (Max)
610604911
71070637
8108081-1

Profit maximizing level of output is 5 units.

Q22-24 Compute Market Supply Schedules.

Q22 (Two firms): Market Supply ($S_m$) = $SS_1 + SS_2$

Price3456
$S_m$2468

Q23 (Two firms): Market Supply ($S_m$) = $SS_1 + SS_2$

Price345678
$S_m$12.545.578.5

Q24 (Three identical firms): Market Supply ($S_m$) = $3 \times SS_1$

Price2345678
$S_m$6121824303642
Q25 Calculate Price Elasticity ($E_s$).

Given:
Initial: $P_1 = 10, TR_1 = 50 \Rightarrow Q_1 = 50/10 = 5$.
Final: $P_2 = 15, TR_2 = 150 \Rightarrow Q_2 = 150/15 = 10$.

$$\Delta P = 5, \Delta Q = 5$$ $$E_s = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q}$$ $$E_s = \frac{5}{5} \times \frac{10}{5} = 2$$

Price Elasticity = 2 (Elastic)

Q26 Find Initial and Final Output ($E_s = 0.5$).

Given: $P_1 = 5, P_2 = 20 \Rightarrow \Delta P = 15$.
$\Delta Q = 15$. Elasticity $E_s = 0.5$.

$$E_s = \frac{\Delta Q}{\Delta P} \times \frac{P_1}{Q_1}$$ $$0.5 = \frac{15}{15} \times \frac{5}{Q_1}$$ $$0.5 = \frac{5}{Q_1} \Rightarrow Q_1 = \frac{5}{0.5} = 10$$

Initial Output ($Q_1$) = 10 units.
Final Output ($Q_2$) = $Q_1 + \Delta Q = 10 + 15 = 25$ units.

Q27 Find Quantity at New Price ($E_s = 1.25$).

Given: $P_1 = 10, Q_1 = 4$. $P_2 = 30 \Rightarrow \Delta P = 20$.
Elasticity $E_s = 1.25$. Find $Q_2$.

$$E_s = \frac{\Delta Q}{\Delta P} \times \frac{P_1}{Q_1}$$ $$1.25 = \frac{\Delta Q}{20} \times \frac{10}{4}$$ $$1.25 = \frac{10 \Delta Q}{80} = \frac{\Delta Q}{8}$$ $$\Delta Q = 1.25 \times 8 = 10$$

New Quantity ($Q_2$) = $Q_1 + \Delta Q = 4 + 10 = 14$ units.

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