MBA 201 a Economic Costs Costs of Production

MBA 201 a: 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? Ø 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. Professor Wolfram MBA 201 a - Fall 2009 Page 1

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 tshirt is $1. 58. Are you happy? Professor Wolfram MBA 201 a - Fall 2009 Page 2

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? Professor Wolfram MBA 201 a - Fall 2009 Page 3

The Average Cost Fallacy • The first 40 t-shirts cost: C(n) = F + V(n) = $20 + $1*40 = $60 fixed variable 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. Professor Wolfram MBA 201 a - Fall 2009 Page 4

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, d. C/dq – Approximated by C(q)-C(q-1), e. g. C(40)-C(39) Professor Wolfram MBA 201 a - Fall 2009 Page 5

A total cost function graphically An example: C(Q) = 10 +. 5 Q Professor Wolfram MBA 201 a - Fall 2009 Page 6

The average total cost function ATC(Q) = C(Q)/Q = 10/Q +. 5 Professor Wolfram MBA 201 a - Fall 2009 Page 7

Marginal costs MC(Q) = d. C(Q)/d. Q =. 5 Professor Wolfram MBA 201 a - Fall 2009 Page 8

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 … Professor Wolfram MBA 201 a - Fall 2009 Page 9

T-shirt factory cost functions Cost ($) MC 3 2 ATC 1. 5 1 48 10 Professor Wolfram 20 30 40 MBA 201 a - Fall 2009 50 T-shirts Page 10

Marginal and average cost curves: generic shape Cost ($) MC p 2 ATC p 1 q 2 Marginal cost always crosses average cost at its minimum. Professor Wolfram MBA 201 a - Fall 2009 Page 11

More average cost and marginal cost in Excel C(Q) = 10 +. 2 Q 2; ATC = 10/Q +. 2 Q; AVC=. 2 Q; MC =. 4 Q Professor Wolfram MBA 201 a - Fall 2009 Page 12

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. Professor Wolfram MBA 201 a - Fall 2009 Page 13

T-shirt factory profits Cost ($) MC 3 Profits 2 ATC 1. 8 1. 5 1 48 10 Professor Wolfram 20 30 40 MBA 201 a - Fall 2009 50 T-shirts Page 14

What if Fruit-of-the-Loom. TM 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. Professor Wolfram MBA 201 a - Fall 2009 Page 15

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 Professor Wolfram MBA 201 a - Fall 2009 Page 16

Output decisions in the generic case Cost ($) MC p 2 ATC p 1 q 1 Professor Wolfram MBA 201 a - Fall 2009 Page 17

Output decisions in the generic case Cost ($) MC p 2 = lost profits q 1 Professor Wolfram MBA 201 a - Fall 2009 q 2 Page 18

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, p 0, then firm is better off by shutting down. If price is greater than P 0, 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. Professor Wolfram MBA 201 a - Fall 2009 Page 19

Supply curve for a competitive (price-taking) firm Price S p’ AC p 0 MC q 0 Professor Wolfram MBA 201 a - Fall 2009 q’ Quantity Page 20

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. Professor Wolfram MBA 201 a - Fall 2009 Page 21

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. Professor Wolfram MBA 201 a - Fall 2009 Page 22