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MBA201a: Economic Costs & Costs of Production

MBA201a: Economic Costs & Costs of Production. Economic categorizations of costs: cost functions. We have seen how economic costs include opportunity costs and exclude sunk costs. Once we’ve got the right costs, what do we do with them? Cost functions

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MBA201a: Economic Costs & Costs of Production

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  1. MBA201a: Economic Costs & Costs of Production

  2. Economic categorizations of costs: cost functions • We have seen how economic costs include opportunity costs and exclude sunk costs. • Once we’ve got the right costs, what do we do with them? • Cost functions • Cost functions relate some cost to the quantity a firm produces. • Cost functions represent ideal rather than actual costs. • A firm’s cost function may change over time. MBA201a - Fall 2009

  3. T-shirt factory example • You run a t-shirt factory for Fruit-of-the-Loom. • You’re currently producing 45 t-shirts a week, and selling them to headquarters for $1.80 each, for total revenues of $80/week. • Your division manager tells you that if you’re making 45 t-shirts a week, your total costs are $71/week, so your average cost per t-shirt is $1.58. • Are you happy? MBA201a - Fall 2009

  4. Categorizing the costs • Upon further investigation, you learn that your cost structure looks like this: • To produce t-shirts: • You must lease one machine at $20 / week. • The machine requires one worker. • The machine, operated by the worker, produces one t-shirt per hour. • Worker is paid $1/hour on weekdays (up to 40 hours), $2/hour on Saturdays (up to 8 hours), $3 on Sundays (up to 8 hours). • Are you still happy? MBA201a - Fall 2009

  5. The Average Cost Fallacy • The first 40 t-shirts cost: • C(n) = F + V(n) = $20 + $1*40 = $60 • At a price of $1.80, profits on these is $12. • The next 5 t-shirts cost: • $2*5 = $10 • At a price of $1.80, they generate revenue of $9. • You’re losing $1 by producing up to 45! You should have stopped at 40. fixed variable MBA201a - Fall 2009

  6. We will talk about 6 types of cost functions • Total cost (C): total cost of inputs the firm needs to produce output q. Denoted C(q). • Fixed cost (FC): the cost that does not depend on the output level, C(0) [or really C(0.00001)] • Variable cost (VC): that cost which would be zero if the output level were zero, C(q) – C(0) [or really C(q) – C(0.00001)]. • Average total cost (ATC) (aka simply “average cost” (AC)): total cost divided by output level, C(q)/q. • Average variable cost (AVC): variable cost divided by output level, VC(q)/q. • Marginal cost (MC): the unit cost of a small increase in output. • Derivative of cost with respect to output, dC/dq • Approximated by C(q)-C(q-1), e.g. C(40)-C(39) MBA201a - Fall 2009

  7. A total cost function graphically An example: C(Q) = 10 + .5Q MBA201a - Fall 2009

  8. The average total cost function ATC(Q) = C(Q)/Q = 10/Q + .5 MBA201a - Fall 2009

  9. Marginal costs MC(Q) = dC(Q)/dQ = .5 MBA201a - Fall 2009

  10. T-shirts: costs • Suppose output level is 40 t-shirts per week. Then, • Fixed cost: FC = $20. • Variable cost: VC = 40 x $1 = $40. • Average total cost: ATC = (20+40)/40 = $1.5 • Average variable cost: AVC = (40)/40 = $1 • Marginal cost: MC = $1. (Note that producing an extra T-shirt would imply working on Saturday, which costs more: MC(41) = $2.) • Similar calculations can be made for other output levels, leading to the cost functions … MBA201a - Fall 2009

  11. T-shirt factory cost functions Cost ($) MC 3 2 ATC 1.5 1 48 T-shirts 10 20 30 40 50 MBA201a - Fall 2009

  12. Marginal and average cost curves: generic shape Cost ($) MC p2 ATC p1 q1 q2 Marginal cost always crosses average cost at its minimum. MBA201a - Fall 2009

  13. More average cost and marginal cost in Excel C(Q) = 10 + .2Q2; ATC = 10/Q +.2Q; AVC= .2Q; MC = .4Q MBA201a - Fall 2009

  14. Economies of scale • Economies of scale describe how the firm’s average costs change as output increases. • ATC  with quantity = “diseconomies of scale” • ATC  with quantity = “economies of scale” Note: a cost function can exhibit economies of scale at some output levels and diseconomies of scale at other output levels. MBA201a - Fall 2009

  15. T-shirt factory profits Cost ($) MC 3 Profits 2 ATC 1.8 1.5 1 48 T-shirts 10 20 30 40 50 MBA201a - Fall 2009

  16. What if Fruit-of-the-LoomTM offers a lower price? • Scenario B: Fruit-of-the-Loom™ offers p = $1.3 per t-shirt. • No matter how much factory produces, price is below per-unit cost; i.e., no matter how much factory produces, it will lose money:  • p < AC implies q x p < q x AC • implies Revenue < Cost • Optimal decision is not to produce at all. MBA201a - Fall 2009

  17. General lessons on output decisions • There is a general lesson from the factory example. • What to produce: Firms should produce every unit for which the income on that unit (in this case the price) is greater than the cost. • What not to produce: Firms should not produce any unit for which the income on that unit is less than the cost. • Note that AC(q) is not playing a role in determining how much to produce, only whether to produce at all. Marginal cost: how much to produce Average Cost: whether to produce MBA201a - Fall 2009

  18. Output decisions in the generic case Cost ($) MC p2 ATC p1 q1 MBA201a - Fall 2009

  19. Output decisions in the generic case Cost ($) MC p2 = lost profits q1 q2 MBA201a - Fall 2009

  20. Supply curve • Supply curve: how much a firm produces at each price. • Generalizing from previous example: Firm can sell all it wants at given price (we say market is “perfectly competitive”). If price is below minimum average cost, p0, then firm is better off by shutting down. If price is greater than P0, say P’, then firm should sell output q’ such that MC=P’. Supply curve is given by MC curve for values of P greater than the minimum of AC, zero for values of p below minimum of AC. MBA201a - Fall 2009

  21. Supply curve for a competitive (price-taking) firm Price S p’ AC p0 MC Quantity q0 q’ MBA201a - Fall 2009

  22. Next week • Next week, we’ll talk about how to take a supply curve for a single firm producing a perfectly competitive industry (what we just saw for the t-shirt example)… • and derive the aggregate industry supply curves that we’ve been drawing since the first lecture. • We’ll also begin talking about monopoly pricing, which you’ll see is an extension of the ideas we’ve introduced today. MBA201a - Fall 2009

  23. Takeaways • We defined a number of economic cost functions. • We discussed how fixed costs do not include sunk costs. • Similarly, fixed and variable costs do include opportunity costs. • We saw how cost functions help firms make decisions about how much to produce and whether to produce at all. • If a firm is facing a fixed price, it will: • Use ATC to decide whether to produce or shut down (produce if p > ATC, otherwise shut down). • Use MC to decide how much to produce (produce as long as p > MC). In fact, MC defines the firm’s supply function if it is producing. MBA201a - Fall 2009

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