Costs and Revenues

Question 1

The Cost Function

For given input prices, what will different isoquants entail and what will it allow for?

What does each isoquant correspond to…and?

Since the cost of production increases as…? It is useful to let C(Q) denote? The function C is called?

Answer 1

• For given input prices, different isoquants will entail different production costs, even allowing for optimal substitution between capital and labor.
• Each isoquant corresponds to a different level of output, and the isocost line tangent to an isoquant will identify the cost-minimizing input mix.
• Since the cost of production increases as higher isoquant are reached, it is useful to let 𝐶(𝑄) denote the cost to the firm of producing isoquant 𝑄 in the cost-minimizing fashion. The function, 𝐶 is called the cost function.

Question 2

The Cost Function

Short run total costs formula?
2 facts about long-run costs

Answer 2

Short-run costs

• Fixed costs: 𝐹𝐶 (unrelated to output)
• Short-run variable costs: 𝑉𝐶(𝑄)
• Short-run total costs: 𝑇𝐶(𝑄)=𝐹𝐶+𝑉𝐶(𝑄)

Long-run costs

• All costs are variable
• No fixed costs since all inputs are variable in LR

Question 3

Variable Costs definition?
Total cost definition?
Short-run cost function definition?

Answer 3

Variable costs

• Costs that change with output.

Total cost

Sum of fixed and variable costs.

Short-run cost function

A function that defines the minimum possible cost of producing each output level when variable factors are employed in the cost-minimizing fashion.

Question 4

Average and Marginal Costs

Formulas for:
Average fixed
Average variable costs
Average total cost
Marginal cost

Answer 4

see picture

Question 5

Classic Short-Run Costs graph (picture)

Total costs
Variable costs
Fixed costs

Answer 5

This shape makes certain assumptions about the usage of L and K such that marginal costs fall (i.e. flatter TC curve) as output increases but eventually a point Is reached where, due to fixed K, it becomes increasingly costly to make
additional outputs and MC rises steeply, pulling up the TC curve too.

Question 6

Classic Short-Run Costs graph (picture)

Variable costs

Answer 6

AVC at any point of the VC curve = slope of the relevant ray from the origin

Question 7

Classic Short-Run Costs graph
Total Costs (picture)

Answer 7

MC = slope of the TC curve; slope always positive but flattest part = min MC point

Question 8

The Relationship between Average and Marginal Costs in Action (picture)

Answer 8

Question 9

The Relationship between Average and Marginal Costs

Answer 9

When 𝑀𝐶(𝑄)<𝐴𝐶(𝑄), average cost declines as output increases;
When 𝑀𝐶(𝑄)>𝐴𝐶(𝑄), average cost rises as output increases;
When 𝑀𝐶(𝑄)=𝐴𝐶(𝑄), average cost is at its minimum;

Question 10

Algebraic Forms of Cost Functions

Answer 10

In practice, cost functions may take many forms, but the cubic cost function is frequently encountered :

Question 11

Algebraic Forms of Cost Functions

Quadratic cost function and linear cost function

Answer 11

Question 12

Long-Run Costs

In the long run, all costs are variable since a manager is free to adjust levels of all inputs.

Long-run average cost curve

Definition?
It is the envelope..?

Answer 12

In the long run, all costs are variable since a manager is free to adjust levels of all inputs.

Long-run average cost curve

• A curve that defines the minimum average cost of producing alternative levels of output, allowing for optimal selection of both fixed and variable factors of production.
• It is the envelope of all the SRATC curves for different plant sizes (i.e. capital input) – see below

Question 13

Short Run ATC – for a particular plant size

Answer 13

Question 14

Economies and Diseconomies of Scale in Action

Answer 14

Question 15

Long-Run Average Total Costs in Action

Answer 15

Question 16

MES - example (picture)

Answer 16

Question 17

Economies of Scale

Answer 17

Economies of scale

• Portion of the long-run average cost curve where long-run average costs decline as output increases.

Diseconomies of scale

• Portion of the long-run average cost curve where long-run average costs increase as output increases.

Constant returns to scale

• Portion of the long-run average cost curve that remains constant as output increases.

Question 18

Constant Returns to Scale in Action

Answer 18

Question 19

Short Run Profit Maximization (or Loss Minimization)

Key points (3)

Answer 19

SRTC Curve: Short Run Total Cost curve

Revenue Function for a Price-Taker: In perfect competition, firms are price-takers and cannot influence the market price.

Key Points:

Perfect Competition: Many small producers with no power to alter prices.

Revenue Function: If the market price is £10 per unit, the revenue function is
𝑅(𝑄)=10𝑄

Revenue Graph: A straight line with a slope of 10, indicating constant revenue per unit sold.

Question 20

Loss Minimization using Total Revenue and Total costs under Perfect Competition (picture)

Answer 20

Total Cost (TC): This curve starts at a higher point on the vertical axis and increases at an increasing rate, showing the total cost of production at various output levels.

Total Revenue (TR): A straight line with a positive slope starting from the origin, showing revenue generated by selling output at a fixed price per unit (price-taker scenario).

Notable Points:

Point M: Where the TC curve intersects a horizontal line labeled 𝑇𝐶𝑀 indicating the total cost at a specific output level.

Point N: Where the TR curve intersects a horizontal line labeled 𝑇𝑅𝑁, showing the total revenue at a particular output level.

Labels:

𝑄0: The initial output quantity.

𝑄min: The output quantity directly below point N, indicating the minimum efficient scale.

𝑇𝐶𝑀 and 𝑇𝑅𝑁: Horizontal lines indicating the specific values of total cost and total revenue at the points M and N.