7.3 Costs in the Short Run

Production and costs in the short run are crucial concepts in microeconomics. They explain how firms make decisions about output levels and resource allocation when faced with fixed and variable factors of production.

Understanding these concepts helps us analyze a firm's cost structure, profitability, and decision-making process. We'll explore how different types of costs interact and how firms determine optimal production levels to maximize profits or minimize losses.

Production and Costs in the Short Run

Production and costs in short run

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• In the short run, at least one factor of production is fixed, usually capital
  • Fixed factors lead to fixed costs, which must be paid regardless of the level of output (rent, insurance)
• Variable factors, such as labor, can be changed in the short run
  • Variable factors lead to variable costs, which change with the level of output (wages, raw materials)
• As output increases, variable costs increase, while fixed costs remain constant
  • Total costs = Fixed costs + Variable costs
• Increasing output requires using more of the variable input, which increases variable costs
  • Law of Diminishing Marginal Returns: As more units of a variable input (labor) are added to a fixed input (capital), the marginal product of the variable input eventually decreases, leading to rising marginal costs

Factor prices of production

• Labor: Wages paid to workers
• Capital: Interest paid on borrowed funds or the opportunity cost of using owned capital
• Land: Rent paid for the use of land or natural resources (farmland, mining sites)
• Entrepreneurship: Profits earned by the business owner for organizing and managing production

Types of short-run costs

• Total Cost (TC): The sum of all costs associated with producing a given level of output
  • TC = Fixed Costs (FC) + Variable Costs (VC)
• Fixed Costs (FC): Costs that do not change with the level of output in the short run
  • Examples: Rent, insurance, and depreciation of capital equipment (machinery)
• Variable Costs (VC): Costs that change with the level of output
  • Examples: Wages, raw materials (lumber, steel), and utilities (electricity)
• Marginal Cost (MC): The change in total cost resulting from producing one additional unit of output
  • $MC = \frac{\Delta TC}{\Delta Q}$
• Average Total Cost (ATC): Total cost divided by the quantity of output produced
  • $ATC = \frac{TC}{Q}$
• Average Fixed Cost (AFC): Fixed cost divided by the quantity of output produced
  • $AFC = \frac{FC}{Q}$
  • As output increases, AFC decreases because fixed costs are spread over more units
• Average Variable Cost (AVC): Variable cost divided by the quantity of output produced
  • $AVC = \frac{VC}{Q}$
  • AVC initially decreases as output increases due to increasing efficiency, but eventually increases due to the law of diminishing marginal returns

Average profit calculation

• Profit: The difference between total revenue (TR) and total cost (TC)
  • $Profit = TR - TC$
• Average Profit: Profit divided by the quantity of output produced
  • $Average Profit = \frac{Profit}{Q}$
• A positive average profit indicates that the firm is earning more revenue per unit than its costs per unit
• A negative average profit (loss) indicates that the firm's costs per unit exceed its revenue per unit

Cost patterns for profitability

• Compare the firm's marginal revenue (MR) to its marginal cost (MC)
  1. If MR > MC, increasing output will increase profits
  2. If MR < MC, reducing output will increase profits
  3. If MR = MC, the firm is maximizing profits or minimizing losses
• Shutdown Point: The level of output where the firm's revenue equals its variable costs
  • If the firm cannot cover its variable costs, it should shut down in the short run (temporary closure)
• Break-even Point: The level of output where the firm's revenue equals its total costs
  • If the firm can cover its variable costs but not its fixed costs, it should continue producing in the short run but consider exiting the market in the long run
• Profit-maximizing Point: The level of output where marginal revenue equals marginal cost
  • This is the point where the firm is making the most profit possible given its cost structure and market conditions (demand, competition)

Graphical Analysis of Costs and Profitability

Types of short-run costs

• Graphical representation of costs:
  • Total Cost (TC) curve: Shows the relationship between total costs and output level
  • Fixed Cost (FC) curve: A horizontal line, as fixed costs do not change with output
  • Variable Cost (VC) curve: Increases with output, initially at a decreasing rate, then at an increasing rate
  • Marginal Cost (MC) curve: U-shaped, reflecting the law of diminishing marginal returns
  • Average Total Cost (ATC) curve: U-shaped, showing the average cost per unit at each output level
  • Average Fixed Cost (AFC) curve: Decreases continuously as output increases, approaching the horizontal axis asymptotically
  • Average Variable Cost (AVC) curve: U-shaped, initially decreasing due to increasing efficiency, then increasing due to the law of diminishing marginal returns

Cost patterns for profitability

• Graphical analysis of profitability:
  • Marginal Revenue (MR) curve: Shows the additional revenue generated by selling one more unit of output
    • In a perfectly competitive market, MR is equal to the market price (P)
  • Profit-maximizing point: Where MR intersects MC from above
    • At this point, the slope of the TC curve equals the slope of the TR curve
  • Shutdown point: Where AVC intersects MR
    • If the firm cannot cover its variable costs, it should shut down in the short run
  • Break-even point: Where ATC intersects MR
    • If the firm can cover its variable costs but not its fixed costs, it should continue producing in the short run but consider exiting the market in the long run
• Profit per unit: The vertical distance between the MR curve and the ATC curve at the profit-maximizing quantity
• Loss per unit: The vertical distance between the ATC curve and the MR curve at the loss-minimizing quantity

Time Horizons and Scale Economies

• Short run: A period in which at least one factor of production is fixed
• Long run: A period in which all factors of production can be varied
• Economies of scale: Occur when a firm's long-run average total cost decreases as the scale of production increases
• Diseconomies of scale: Occur when a firm's long-run average total cost increases as the scale of production increases
• Opportunity cost: The value of the next best alternative foregone when making a decision