EC109 Microeconomics Term 2, Part 1 Cost Curves Laura Sochat 26/01/2016 Plan Long run total cost curves Long run average and marginal cost curves Economies and diseconomies of scale Short run cost curves Relationship with long run total cost curves Short run average and marginal cost curves Relationship with long run average and marginal cost curves Economies of scope K, Capital services Long run total cost curve 2 1
2 1 B A 2 million TVs per year 1 million TVs per year 1 2 2 L, Labor services B 2= 2+ 2 1 = 1 + 1 1
() A 1 million 2 million TVs per year As the level of output varies, holding input prices constant, the cost minimizing combination of input changes The long run total cost curve shows how minimized total cost varies with output, assuming constant input prices and that the firm chooses the input combination to minimize its costs. The long run total cost curve must be increasing in Q, and must be equal to 0, when Finding the total cost curve from a production function Assume a production function of the form:
a) How does minimized total cost depend on the output level, and the input prices, for this production function? b) What is the graph of the long run total cost curve when and ? K, Capital services How does the long run cost curve shift when input prices change? isocost line before the price of capital goes up million isocost line after the price of capital goes up million isocost line after the price of capital goes up 1 3 2 A B 1 million TV per year Labor services per year
Starting from point A, where the firm produces 1 million televisions, on isocost line . After the price increase, the cost minimising input combination occurs at point B, where total cost is greater than it was at point A. Long run total cost curve: Change in the price of inputs The effect a proportional increase in the price of both inputs TC, dollars per year TC, dollars per year The effect of an increase in the price of capital on the TC(Q) curve after the increase in the price of capital after the increase in the price of both
inputs by 10% B 3 1 A 1 million before the increase in the price of capital TVs per year 2=1.10 1 1 B A 1 million
before the increase in the price of both inputs by 10% TVs per year TC, dollars Long run average and marginal cost curves Long run average cost: () C 1,500 A The relationship between the two is such that: B ,, per unit 0 50
Q, units per year = slope of 30 A slope of ray from O to 10 A 50 Long run marginal cost: Q, units per year When AC is decreasing in Q,
When AC is increasing in Q, When AC is at a minimum, Economies and diseconomies of scale We saw before that when a firm exhibits increasing returns to scale, output increases more than proportionally to an proportional increase in both inputs: The firms average cost falls as output increases. If a firms average cost decreases as output increases, the firm is said to enjoy Economies of Scale. when a firm exhibits decreasing returns to scale, output increases less than proportionally to an proportional increase in both inputs: The firms average cost increase as output increases. If a firms average cost increases as output increases, the firm is said to enjoy Diseconomies of Scale. when a firm exhibits constant returns to scale, output increases proportionally to an proportional increase in both inputs: The firms average cost stays unchanged as output increases. If a firms average cost neither increases or decreases as output increases, the firm does not enjoy economies, or diseconomies of scale.
AC, per unit Economies and diseconomies of scale ( ) Economies of scale: Average cost falls as output increases Diseconomies of scale: Average cost increases as output increases The smallest quantity at which the long run average cost curve attains its minimum efficient scale (MES). The size of the MES relative to the size of the market indicates the significance of economies of scale in particular industries. The largest MES-market size ratio represent significant economies of scale. The lowest MES-market size ratio
represent weaker economies of scale. 1 2 Q units per year Some examples of production functions Production functions L(Q) TC(Q) AC(Q)= AC(Q) How does long run average cost vary with output Decreasing Increasing Constant
Economies/ diseconomies of scale? Economies of scale Diseconomies of scale Neither Returns to scale? Increasing Decreasing Constant The output elasticity of total cost as a measure to the extent of Economies of scale Output elasticity of total cost is the percentage change in total cost per 1 percent change in output. Recall that ; We can therefore rewrite the output elasticity of total cost such as: The output elasticity of total cost as a measure to the extent
of Economies of scale Taking account of the relationship between long run average and marginal cost corresponds with the way average cost varies with output. We can tell the extent of economies of scale, using the output elasticity of total cost. Value of MC versus AC How AC varies as Q increases Economies/ diseconomies of scale Decreases Economies of scale Increases Diseconomies of scale Constant Neither
Short run total cost curve We have seen when looking at the firms cost minimization problem, that in the short run the firm faces both fixed and variable costs. The firms short run total cost will be the sum of those two components. Assuming the firm is constrained by the amount of capital it can use, , and that the price of capital is , we can rewrite the expression for the short run total cost of the firm as: Short run total cost curve TC, per year Lets go back to the production function we have been using: Assume again that and that . If capital is fixed at a level What is the short run total cost curve? What are the total variable and total fixed cost curves? Q, units per year TC, per year
K, Capital Relationship between the long run and short run total cost curves Long run expansion path 2 1 B Short run expansion path C A A C B million TVs isoquant
million TVs Isoquant 1 L, Labor 1 million 2 million Q, units per year Cost per unit Short run average and marginal cost curves () Short run average cost: () () Short run marginal cost: Average fixed and variable cost: Where we can write that:
() Q, units per year Cost, per year The long run average cost curve as an envelope curve ( ) , , , 60 A 50 C 35 B 1 million 2 million 3 million Q, TVs per year
The long run average cost curve forms a boundary around the set of shot run average cost curves corresponding to different levels of output and fixed input. Each short run average curve corresponds to a different level of fixed capital. Point A is optimal for the firm to produce 1 million TVs per year, with fixed level of capital . Economies of scope We have so far been looking at firms producing a single product. Consider now a firm which produces two different products. The firms total cost will depend on the quantity of product 1 it manufactures (), and on the quantity of product 2 (). When it is less costly for a single firm to produce both products, relative to two separate firms manufacturing the product separately, that is, when we have that: Efficiencies have arisen, which are called economies of scope The additional cost of producing units of the second product, when the firm is already producing units of the first product is lower that the additional cost of producing when the firms does not manufacture product 1.
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