Cost functions Cost function is total cost of inputs the firm needs to produce output q. Denoted C(q). Fixed cost (FC): the cost that does not depend.

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Presentation transcript:

Cost functions Cost function is total cost of inputs the firm needs to produce output q. Denoted C(q). Fixed cost (FC): the cost that does not depend on output level. Variable cost (VC): that cost which would be zero if the output level were zero, C(q) – FC. Average cost (AC) (aka “unit cost”): total cost divided by output level, C(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)

Marginal cost is the increase in costs when output is increased by one unit. the change (increase or decrease) in costs as a result of one more or one less unit of output. the rate of change of total cost as output is changed by an infinitesimal amount the first derivative of the total cost function with respect to output q.

T-shirt factory example To produce T-shirts: Lease one machine at $20 / week. 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).

Suppose the factory produces 40 T-shirts per week. Please compute the Fixed Cost, the Variable Cost, the Average Cost, and the Marginal Cost.

Answers When the factory produces 40 T-shirts per week the numbers are … Fixed cost: $20 Variable cost: $40 Average cost: (40 + 20)/40 = $1.5 Marginal cost: $2

T-shirts : how many to make Benetton™, the sole buyer of T-shirts from this small factory, is offering a price of $1.8 per T-shirt. They will buy as many as the factory can supply. Given this offer, should the factory operate on Saturday?

T-shirts : how many to make Benetton™ offers price p = $1.8 per T -shirt. p = 1.8, AC = 1.5, MC = 2 Although factory is making money at q = 40 (because p > AC), profits will be lower if it produces more (because p < MC); it will lose money at the margin. [Verify: compute profit at q = 40,41]

One last example QUANTITY AC 199 200 201

Currently you are producing 200 units of output Currently you are producing 200 units of output. Should you produce one more unit if you can sell it at P = 300?