lec 4 Flashcards
What is the cost function in production analysis?
It is the total cost associated with producing a given amount of goods or services over a specified period.
How is Total Production Cost (TC) defined?
TC is the sum of Total Fixed Cost (FC) and Total Variable Cost (VC): TC = FC + VC.
What is the distinction between fixed and variable costs in the short term?
Fixed costs do not vary with production levels in the short term, whereas variable costs change directly with the amount produced.
How do you calculate Average Cost (AC) of production?
Average Cost is calculated by dividing total cost by the quantity produced: AC = TC / Q.
How is Average Fixed Cost determined?
AFC is obtained by dividing fixed costs by the quantity produced: fc = FC / Q.
How is Average Variable Cost determined?
AVC is calculated by dividing variable costs by the quantity produced: vc = VC / Q.
What is the Revenue Function and its formula?
The revenue function expresses total revenue as the product of unit price and quantity: TR = p × Q.
What is the total profit formula?
TP = TR -TC
What is the break-even point in cost analysis?
The break-even point is the production level where total revenue equals total cost, resulting in zero profit. TP = 0
MR = AC
How is the break-even condition mathematically expressed?
The break-even condition is given by TR = TC or p × Q = FC + VC.
What does the contribution margin represent?
The contribution margin is the amount each unit contributes toward covering fixed costs, calculated as p - vc (unit price minus variable cost per unit).
Higher contribution margin = lower BE Q, => efficient operation, flexible
How can a lower break-even rate benefit a company?
A lower break-even rate means fewer units need to be produced to cover costs, often reflecting greater flexibility, lower variable costs, and reduced risk.
How to get a lower Q*?
Decrease vc (can also decrease FC or increase price)
What is a generalized cost function as described in the content?
A generalized cost function can capture non-linear cost behaviors and is often represented as: TC = FC + aQ – bQ² + cQ³.
How do you obtain the Marginal Cost (MC) function from the Total Cost function?
Marginal Cost is the derivative of the total cost function with respect to quantity: MC = dTC/dQ, which for the generalized form becomes MC = a – 2bQ + 3cQ².
What is the significance of the minimum average cost point?
The minimum average cost point indicates the most efficient combination of fixed and variable resources
Maximum average profit
Where the AC curve intersects the MC curve.
Point of tangency
What is marginal revenue
MR = AR = p
Under what condition is maximum profit achieved in production?
Maximum profit is generally achieved where Marginal Revenue (MR) equals Marginal Cost (MC), i.e., MR = MC. since MP =0 at that point
dTP/dQ = 0
What is meant by ‘profit limit’ in the context of this summary?
The profit limit is the production level beyond which total cost exceeds total revenue, meaning that additional production results in lower profits. AC = AR second time
What does the ‘minimum marginal cost’ point indicate?
It marks the production level at which the cost of producing an extra unit is the lowest—the point of inflection where marginal costs begin to rise after being at their minimum.
Pt inflection
How does the typical cost function relate to economies of scale?
The typical cost function (TC = FC + aQ – bQ² + cQ³) may initially show downward sloping costs (economies of scale) when b < 1, until diseconomies set in as production increases. -> increasing production leads to higher average costs per unit
Break even rate formula
Q* = FC/ (p-vc)
Theory of the Business Firm assumptions
- unlimited resources, i.e. process can continue indefinitely
- perfect market competition, i.e. price determined by supply and demand conditions, which are unaffected by individual producers’ production decisions (producers are small relative to total market).
- conditions of certainty prevail, i.e. all variables are exactly known for present and future time periods.
using only marginal and average cost, revenue or variable cost, when do you know when a firm makes profit
MR = P > AC
If a perfectly competitive firm is earning zero economic profit, then its price must be
Equal to average total cost (AC).
