Where Do Supply Curves Come From?

P = b-aQ What IS a Supply Curve? What is the MATHEMATICAL FORMULA for LINEAR Supply? P = b-aQ

Where Do Supply Curves Come From? Supply Curves are MC curves ABOVE the minimum AVC! Short-run Individual firm supply curve Why not here?? Here’s a graph that relates price and quantity… What if price is here? Economic loss! Shutdown! P<AVC Test yourself: Does the supply curve have anything to do with fixed costs?

What is the optimal input combination GIVEN cost or quantity? “No matter what the structure of industry may be… (for profit or not for profit) … the objective of most producers is to produce any given level and quality of output at the lowest possible cost. Equivalently, the producer wants to produce as much output as possible from a given expenditure on inputs.” (Frank p. 233) Duality w = cost of labor Maximize Q given C Minimize C given Q Remember how we got here… r = cost of capital Marginal products per dollar

Short Run vs Long Run Costs Key: long run total costs are those associated with the optimal inputs for a given quantity Short run cost curves Long run cost curves No fixed or variable costs in the long run! Inflection point Total costs can be zero in the long run Tangency point Key – the total costs are the cost associated with the optimal inputs for a given quantity The change in total costs reflects a change in optimal inputs to reach a new quantity isoquant What happens when we combine the short and long run curves…

The long-run average cost curve is the envelope of the short run curves. Viner told his draftsman PK Wong, a mathematician, to draw the envelope curve so that it intersected at the minimum of the short run curves. Wong told him that was impossible. The debate/confusion raged for decades. Some tried to explain the discrepancy using a time dimension, but Silberberg gives a nice intuitive proof of why this must be the case. Why doesn’t the LAC curve intersect with the minimum points of the short run cost curves? “…it is the occasional errors of geniuses like Viner…which seminally advance the body of science.” Paul Samuelson (1972) JPE 72:5 – 11. Jacob Viner

And the marginal cost curves must have the same slope Why doesn’t the LAC curve intersect with the minimum points of the short run cost curves? When the short run cost curve is tangent to the long run curve the average cost has the same slope And the marginal cost curves must have the same slope The minimum point on the short run curve will be where the slope of the average equals the marginal This will be everywhere above the long run cost curve except where the long and short run curves are tangent at the long run minimum. Why isn’t that slope always the minimum slope of the short run curves? Emphasize the difference between long-run unconstrained and short run constrained – short run curves must lie above the long run ones. Silbergerg on the Envelop Theorem http://www.ems.bbk.ac.uk/faculty/phdStudents/kim/me_env.pdf Eugene Silberberg

This mix of labor & capital is optimal to make Q2 Short run cost curves Capital is fixed At high Q too much labor At low Q too much capital This mix of labor & capital is optimal to make Q2 Since everything is variable in the long run, we are going to compare the short-run average variable cost to the long run average cost The only think that is varying in the short-run graph is labor GIVEN the production process with fixed capital in the short run graph, it is optimal to produce Q3 where MC = ATC. HOWEVER, with the given costs of capital and labor, and the level of capital given in the short run curve, the optimal (least cost) output is 2. The short-run minimum cost to produce Q3 will have more capital and less labor. Long run cost curves: everything is variable

Organizations produce where marginal cost = marginal benefit on the rising part of the marginal cost curve!