appendix 8

• In the short run, the level of capital (K0) is fixed, while labour (L) is variable.
• the average product of labour is the output per unit of labour.
• The marginal product of labour measures how much additional output is produced by adding one more unit of labour, holding capital constant.
• Isoquants represent different combinations of inputs (capital KKK and labour LLL) that yield the same level of output.
• Points on higher isoquants represent higher levels of output.
• • Isoquants slope downwards: to maintain the same output, less capital requires more labour and vice versa.
• The slope of an isoquant gives the marginal rate of technical substitution (MRTS).
• Takeaway: In the short run, total cost is the sum of what you spend on workers and the fixed cost of capital.
• In the long run, both labour and capital are variable. This means the firm can adjust both to find the cheapest combination for producing a given amount of output.
• Isocost Line: This is a line that shows all the combinations of labour and capital a firm can afford for a given total cost.
• Isoquant: This is a curve showing different combinations of labour and capital that produce the same output.
• Cost Minimization:

  • The goal of the firm is to produce a given output at the lowest cost. This happens where the isocost line is tangent to the isoquant.
• Marginal Rate of Technical Substitution (MRTS): This is the rate at which the firm can substitute labour for capital while keeping output constant.
• The firm minimizes cost by balancing the substitution of capital and labour based on their relative prices
• How wage increases affect costs:

  • A higher wage means the firm has to pay more to hire workers, so the cost-minimization strategy will change.
  • The firm will shift to using more capital (because labour is now more expensive), moving along the isoquant to a point where it uses fewer workers but more capital.
• A firm should not produce if the price of its output is lower than the average variable cost (AVC). In simple terms, if making and selling the product costs more than the money earned from selling it, the firm is better off not producing at all.
• • A firm should stop production if: P(Q)<AVC(Q)P(Q)
  • What this means: If the price is less than what it costs just to cover variable costs (wages, raw materials, etc.), then the firm will lose more money by producing than if it simply shuts down temporarily.
• Isoquant Diagrams:

  • Isoquants represent different combinations of capital and labour that give the same level of output.
• Key points:

  • The higher the isoquant, the higher the level of output.
  • The slope of the isoquant tells you the MRTS, showing how much you need to adjust one input (labour or capital) to keep output constant.
• Isocost Line:

  • An isocost line shows all the combinations of capital and labour that have the same total cost.
• • The slope of the isocost line is determined by the relative prices of labour and capital (wages vs rental rate).
  • The firm minimizes cost where an isocost line is tangent to an isoquant.
• TC(Q)=wL∗(Q,w,r)+rK∗(Q,w,r)

  Where:

  • TC(Q) is the total cost of producing quantity Q
  • L∗(Q,w,r)) is the optimal amount of labour used for producing QQQ at given wage www and rental rate of capital rrr,
  • K∗(Q,w,r) is the optimal amount of capital used for producing QQQ,
  • w is the wage rate (cost of labour),
  • r is the rental rate (cost of capital).
• Unlike the short run, where capital might be fixed, in the long run, both capital and labour can be changed to find the least costly combination.
• Cost Minimization: The firm’s goal is to minimize the cost of production. This happens where the isocost line (showing combinations of inputs with the same cost) is tangent to the isoquant (showing combinations of inputs that produce the same output).
• Factor Prices Influence: The total cost depends on the prices of the inputs:

  • www = cost per unit of labour,
  • rrr = cost per unit of capital.

  1. The firm will adjust its use of labour and capital based on these prices to minimize costs.
• the long-run total cost function helps a firm figure out the cheapest way to produce a certain amount of goods by choosing the best mix of inputs (labour and capital) while taking into account their prices.
• • Cost Minimization Curve shows different cost-minimizing combinations of inputs for different levels of output.
• Long-Run Total Cost Curve shows the relationship between output and total cost. As output increases, costs rise, but the rate of increase depends on economies of scale.