This chapter discusses how firms operate under perfect competition, focusing on profit maximization and supply curves.
The Theory Of The Firm Under Perfect Competition – Formula & Equation Sheet
Essential formulas and equations from Introductory Microeconomics, tailored for Class 12 in Economics.
This one-pager compiles key formulas and equations from the The Theory Of The Firm Under Perfect Competition chapter of Introductory Microeconomics. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
TR = p × q
TR is Total Revenue, p is the market price per unit (in Rs) and q is the quantity sold. This formula calculates total revenue generated from sales.
AR = TR/q = p
AR is Average Revenue, defined as Total Revenue (TR) divided by the quantity sold (q). For a price-taking firm, AR equals the market price (p).
MR = ΔTR/Δq
MR is Marginal Revenue, calculated as the change in Total Revenue (ΔTR) divided by the change in quantity produced (Δq). This measures the revenue gained from selling one more unit.
π = TR – TC
π represents Profit, defined as Total Revenue (TR) minus Total Costs (TC). This shows the net profit or loss realized by the firm.
P = MC
In profit maximization, for a perfectly competitive firm, Price (P) equals Marginal Cost (MC) at optimum output level, indicating where a firm maximizes profit.
P ≥ AVC (short-run)
In the short run, to continue producing, the price must be greater than or equal to Average Variable Cost (AVC). If not, the firm will shut down.
P ≥ AC (long-run)
In the long run, the price must be greater than or equal to Average Cost (AC) for the firm to sustain operations. If not, it exits the market.
S_Q = SMR curve
The Short Run Supply Curve (S_Q) of a firm is derived from its Short Run Marginal Cost (SMC) curve above the minimum AVC, including zero output for prices below that.
LR_S = LRMC curve
The Long Run Supply Curve (LR_S) of a firm is derived from its Long Run Marginal Cost (LRMC) curve above the minimum LRAC, including zero output for prices below that.
e_S = %ΔQ/%ΔP
The price elasticity of supply (e_S) is defined as the percentage change in quantity supplied (%ΔQ) divided by the percentage change in price (%ΔP). This measures responsiveness of quantity supplied to price changes.
Equations
TR = p × q
Total revenue is calculated by multiplying the market price (p) by the quantity sold (q). Essential for revenue assessments.
ΔTR = p(Δq)
The change in total revenue (ΔTR) when quantity sold (q) changes is equivalent to price (p) multiplied by the change in quantity (Δq).
P = MC at q*
To maximize profit, a firm produces where Price (P) equals Marginal Cost (MC) at optimal output level (q*).
Q_S = f(p)
The short-run supply function (Q_S) of a firm is a function of market price (p), illustrating output levels supplied at various prices.
Normal Profit condition: P = AC
A firm earns normal profit when price (P) equals Average Cost (AC). This ensures the firm covers all costs and stays in business.
Supply of Firm: S(p)
The supply function of a firm depends on the market price (p). It shows how much output the firm is willing to produce at different price points.
Q_m = ∑S_i
The market supply (Q_m) is the sum of the supplies (S_i) of all individual firms in the market at a given price.
Tax Impact: TC = TC_initial + (t × Q)
Total Cost (TC) after tax imposition changes based on the unit tax (t) multiplied by the quantity produced (Q). Affects the firm's cost structure.
MC = ΔTC/ΔQ
Marginal Cost (MC) is defined as the change in Total Cost (ΔTC) over the change in quantity (ΔQ). Determines additional costs for producing one more unit.
e_S = (ΔQ/Q)/(ΔP/P)
The formula for price elasticity of supply (e_S) compares the relative change in quantity supplied (ΔQ/Q) to the relative change in price (ΔP/P), capturing sensitivity to price changes.
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