1.

Fixed Vs Variable Inputs

• Fixed Inputs: Resources that cannot be easily changed in the short run. Their quantity remains
constant regardless of the level of production (e.g., factory size, major equipment).

• Variable Inputs: Resources that can be readily adjusted in the short run. Their quantity varies with the
level of production (e.g., labor, raw materials).

Short Run Vs. Long Run

• Short Run: A time period where at least one input is fixed. Firms can only adjust variable inputs to
change output.

• Long Run: A time period long enough for all inputs to be variable. Firms can adjust the scale of their
operations, including plant size and technology.

Production in the Short Run: Production with One Variable Input

• Focuses on how output changes when only one input (typically labor) is varied, while others are held
constant.

Total Product, Marginal Product and Average Product

• Total Product (TP): The total quantity of output produced by a firm with a given level of inputs.

• Marginal Product (MP): The change in total product resulting from using one additional unit of a
variable input (e.g., one more worker), *ceteris paribus*. MP = ΔTP / ΔInput

• Average Product (AP): The total product divided by the quantity of the variable input used. AP = TP /
Input

Graphing the Short Run Production Curves0

• TP Curve: Typically increases at an increasing rate, then at a decreasing rate, and eventually declines.
It plots total product against the quantity of the variable input.

• MP Curve: Initially rises, reaches a maximum, and then declines, eventually becoming negative. It
represents the slope of the TP curve.

• AP Curve: Rises, reaches a maximum, and then declines.

The Relationship Between AP and MP of the Variable Input

• When MP > AP, AP is rising.

• When MP < AP, AP is falling.

• MP intersects AP at the maximum point of the AP curve.

2. The Law of Diminishing Marginal Returns (LDMR): short –run law of
production.
• LDMR: As more and more units of a variable input are added to a fixed input, beyond a certain point,
the marginal product of the variable input will eventually decline. This occurs because the fixed input
becomes increasingly strained.

Efficient Region of Production in the short-run

• The region where MP is positive but declining and AP is positive but declining.

• Rational producers will only operate in the region where LDMR is in effect.

• The efficient region is generally between the point where the AP is maximized and the point where
MP becomes zero.

3. Long run Production: Production with two variable inputs

• Firms can adjust both capital and labor. Focuses on choosing the optimal combination of inputs to
produce a given level of output at the lowest cost.

The short-run production function in which the firm uses one variable input (labor) and one fixed input
(capital).
Now we turn to the long run analysis of production. Remember that long run is a period of time
(planning horizon) which is sufficient for the firm to change the quantity of all inputs.

Isoquants
An isoquant is a curve that shows all possible efficient combinations of inputs that can yield equal level
of output.
If both labor and capital are variable inputs, the production function will have the following form.
Q = f (L, K)
Given this production function, the equation of an isoquant, where output is held constant at q is
q = f (L, K)
Thus, isoquants show the flexibility that firms have when making production decision: they can usually
obtain a particular output (q) by substituting one input for the other.

• A curve that shows all the different combinations of two inputs (e.g., capital and labor) that can
produce the same level of output.

Properties of Isoquants
• Downward sloping: To maintain the same output level, if you increase one input, you must decrease
the other.

• Convex to the origin: Reflects the diminishing marginal rate of technical substitution (MRTS).
• Do not intersect: Each isoquant represents a specific level of output.

• Higher isoquants represent higher levels of output.

Shape of Isoquants
• The shape reflects the substitutability of the inputs.

• Linear Isoquants: Perfect substitutes.

• L-shaped Isoquants: Perfect complements (fixed proportions).

• Convex Isoquants: Imperfect substitutes (the typical case).

4. Cost
Cost encompasses the value of resources sacrificed, both in terms of direct expenses (explicit costs) and
forgone opportunities (implicit costs). Understanding the different types of costs is crucial for making
sound business and economic decisions.

Economic Vs Accounting Costs

Accounting Costs
• Definition: These are the explicit costs, meaning the actual monetary outlays (payments) a firm makes
for its resources. They're the costs you'd typically see recorded in a company's financial statements.

• Focus: Track actual expenses and cash flows.

• Purpose: Used for financial reporting, tax compliance, and basic profitability analysis.

Examples of Accounting Costs:

1. Wages and Salaries: The money paid to employees for their labor. Example: A company pays its
employees 500,000 in wages this year.

2. Rent: The payment for using a building or land. Example: A business rents office space for 2,000 per
month, totaling 24,000 per year.

3. Raw Materials: The cost of materials used to produce goods. Example: A bakery spends 10,000 on
flour, sugar, and other ingredients.

4. Utilities: Payments for electricity, water, and gas. Example: A manufacturing plant spends 5,000 per
month on electricity.

5. Advertising Expenses: Money spent on marketing and promotion. Example: A store spends 2,000 on
newspaper ads.
6. Interest Paid on Loans: The cost of borrowing money. Example: A company pays 3,000 in interest on a
business loan.

7. Depreciation: The allocation of the cost of an asset over its useful life (often using a method like
straight-line depreciation). Example: A company's equipment depreciates by 5,000 this year, according
to an accounting method.

Economic Costs
• Definition: This includes both explicit (accounting) costs and implicit (opportunity) costs. It's a broader
measure of cost that considers the full value of resources used, regardless of whether a direct payment
is made.

• Focus: Considers the forgone benefits of alternative uses of resources.

• Purpose: Used for decision-making, resource allocation, and evaluating the true profitability of a
business.

Examples of Economic Costs:

Let's say a small business owner, Sarah, runs a bakery.

1. Sarah's Forgone Salary (Implicit Cost): Sarah could be working as a baker for another company and
earning 60,000 per year. This forgone salary is an implicit cost of running her own bakery.

2. Forgone Rent on Building (Implicit Cost): Sarah owns the building where her bakery is located. She
could rent the building to someone else for 30,000 per year. This forgone rental income is another
implicit cost.

3. Explicit Costs (Accounting Costs):

• Flour and Ingredients: 10,000

• Employee Wages: 40,000

• Utilities: 5,000

• Advertising: 2,000

Calculating Costs

• Accounting Cost: The sum of Sarah's explicit costs: 10,000 + 40,000 + 5,000 + 2,000 = 57,000

• Economic Cost: Explicit costs + Implicit Costs: 57,000 + 60,000 (forgone salary) + 30,000 (forgone rent)
= 147,000

Profit Calculation

• Assume Sarah's Bakery has Total Revenue = 150,000

• Accounting Profit: Total Revenue - Accounting Costs = 150,000 - 57,000 = 93,000

• Economic Profit: Total Revenue - Economic Costs = 150,000 - 147,000 = 3,000

• Accounting Profit: Sarah's bakery appears to be quite profitable, earning 93,000.

• Economic Profit: However, after considering the opportunity costs of her time and resources, Sarah's
bakery is only marginally profitable, earning just 3,000 in economic profit. This means she is only slightly
better off running the bakery than pursuing her next best alternative (working for another baker and
renting out her building). If economic profit were negative, it would indicate that she should close shop
and pursue her alternative

Costs in the Short-run

• Firms must consider both fixed and variable costs when making short-run production decisions.

Normal Profit Vs Economic Profit (Pure Profit)

• Normal Profit: The minimum level of profit needed to keep a firm in its current activity. It is included
as a cost of production (an implicit cost).

• Economic Profit (Pure Profit): Total revenue minus total economic cost (including normal profit). A
firm is earning economic profit if its revenue exceeds all its costs, including the opportunity cost of all
resources used.

• Economic Profit = Total Revenue - (Explicit Costs + Implicit Costs)

Total Fixed, Total Variable and Total Cost Curves

• Total Fixed Cost (TFC): Costs that do not vary with output. It's a horizontal line.

• Total Variable Cost (TVC): Costs that vary with output. Typically increases at a decreasing rate
initially, then at an increasing rate.

• Total Cost (TC): The sum of total fixed cost and total variable cost. TC = TFC + TVC. The TC curve has
the same shape as the TVC curve but is shifted upward by the amount of TFC.

Relationship between cost and production

• Costs are derived from production. The shape of the cost curves is directly related to the shape of
the production function (especially the law of diminishing marginal returns).

• Increasing returns to the variable input (in production) lead to decreasing costs. Diminishing returns
lead to increasing costs.
5. Perfect Competitive market
Assumptions of Perfect Competitive market

• Large number of buyers and sellers: No single buyer or seller can influence the market price.

• Homogeneous product: All firms sell an identical product.

• Free entry and exit: Firms can easily enter or leave the market.

• Perfect information: All buyers and sellers have complete information about prices and product
quality.

• No barriers to entry:

• Price takers: Individual firms have to accept the market price.

Costs under perfect competition

• Firms aim to minimize their production costs to maximize profit.

• Cost structure influences a firm's supply decision.

Demand and revenue functions under perfect competition

• Demand: The demand curve facing an individual firm is perfectly elastic (horizontal) at the market
price.

• Revenue: Price = Marginal Revenue = Average Revenue (P = MR = AR).

Marginal Approach

• Firms maximize profit by producing at the level where Marginal Cost (MC) equals Marginal Revenue
(MR). MC = MR.

Mathematical derivation of the equilibrium condition

Okay, let's break down the mathematical derivation of the equilibrium condition in a perfectly
competitive market with some worked examples.

Mathematical Derivation: Profit Maximization

In a perfectly competitive market, a firm's goal is to maximize its profit.

1. Profit Function: Profit (π) is defined as total revenue (TR) minus total cost (TC):
 π = TR - TC

2. Total Revenue: Since a firm in perfect competition is a price taker, it sells all its output at the market
price (P). So, total revenue is:

TR = P * Q (where Q is the quantity produced and sold)

3. Total Cost: Total cost (TC) is a function of quantity produced, TC(Q).

4. Profit Function (Revised): Substitute TR and TC into the profit function:

π(Q) = P * Q - TC(Q)

5. Maximization Condition: To maximize profit, we take the first derivative of the profit function with
respect to quantity (Q) and set it equal to zero:

dπ/dQ = d(PQ)/dQ - d(TC)/dQ = 0

Since P is constant in perfect competition:

P - d(TC)/dQ = 0

6. Marginal Cost: The derivative of total cost with respect to quantity is marginal cost (MC):

MC = d(TC)/dQ

7. Equilibrium Condition: Substitute MC back into the equation:

P - MC = 0 or P = MC

This is the key equilibrium condition: A firm in perfect competition maximizes profit by producing at
the quantity where the market price equals its marginal cost.

8. Second-Order Condition: To ensure that we've found a *maximum* (rather than a minimum) profit,
we need to check the second-order condition. This requires taking the second derivative of the profit
function with respect to Q: d²π/dQ² = -d(MC)/dQ < 0

This implies that d(MC)/dQ > 0, which means that the marginal cost curve must be upward-sloping at
the profit-maximizing point.

Worked Examples

Let's consider two examples to illustrate this:

Example 1: Simple Cost Function

• the market price is P = $10.

• a firm's total cost function is TC(Q) = 2Q² + 4Q + 10.

1. Find Marginal Cost:

MC = d(TC)/dQ = 4Q + 4

2. Set Price Equal to Marginal Cost: $10 = 4Q + 4

3. Solve for Q:

6 = 4Q

Q = 1.5

The firm will produce 1.5 units to maximize profit.

4. Verify Second-Order Condition: The derivative of MC is 4, which is positive, satisfying the second-
order condition.

5. Calculate Profit:

* TR = P * Q = $10 * 1.5 = $15

* TC = 2(1.5)² + 4(1.5) + 10 = 4.5 + 6 + 10 = $20.5

* π = TR - TC = $15 - $20.5 = -$5.5

Here the firm is taking a loss but will continue producing in the short run if P>AVC.

6. The short run supply curve of the firm and the industry in perfectly
competitive market structure
The short run supply curve of the firm

• The firm's short-run supply curve is the portion of its marginal cost (MC) curve that lies *above* its
average variable cost (AVC) curve. This is because the firm will only produce if it can cover its variable
costs.

• If the market price falls below the minimum AVC, the firm will shut down production.

Short run supply curve of the industry

• The industry supply curve is the horizontal summation of the individual firms' supply curves. At each
price, you add up the quantity supplied by all firms in the industry.

Short run equilibrium of the industry

• Occurs where the industry supply curve intersects the industry demand curve.
• Determines the market price and the total quantity produced.

• Individual firms then take this price as given and produce the quantity where MC = P.

7. The long-run Equilibrium in perfectly competitive market structure

Equilibrium of an individual firm in the long run

• In the long run, firms can enter or exit the market.

• Long-run equilibrium occurs when firms are earning zero economic profit.

• At this point, Price (P) = Marginal Cost (MC) = Average Total Cost (ATC) at the minimum point of the
ATC curve.

Long run shut down decision

• A firm should shut down if it cannot cover its total costs (both fixed and variable) in the long run.

• If P < min ATC, the firm will exit the industry.

The long-run supply curves the firm

• Is perfectly elastic, meaning firms can supply any quantity at that price in the long run.

The Long run supply curve of the industry

• Can be horizontal, upward-sloping, or downward-sloping, depending on whether the industry is a

constant-cost, increasing-cost, or decreasing-cost industry.

* Constant-cost industry: Input prices remain constant as the industry expands. The LRAS is
horizontal.

* Increasing-cost industry: Input prices increase as the industry expands. The LRAS is upward-sloping.

* Decreasing-cost industry: Input prices decrease as the industry expands. The LRAS is downward-
sloping.

Long-run equilibrium of the industry

• Occurs when:

* Firms are earning zero economic profit (P = min ATC).

* There is no incentive for new firms to enter or existing firms to exit.

* The market is in equilibrium (quantity supplied equals quantity demanded).

Perfect competition and optimal resource allocation

• Perfect competition leads to allocative efficiency: resources are allocated to their most valued uses.

• P = MC, meaning that the price consumers pay reflects the marginal cost of producing the good.

• Productive efficiency: Firms produce at the lowest possible cost (at the minimum point of the ATC
curve).

• Perfect competition serves as a benchmark for economic efficiency, although it is rarely fully achieved
in the real world.