Transcription of 0.1 Strictconvexityandconcavity - Exeter
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0.1 Strictconvexityandconcavity - Exeter
BEE1020 Basic Mathematical EconomicsWeek 7, Lecture Tuesday , concavity. Sign Strict convexity and concavityIf we look again at the cost increases in Example 2 we notice that the cost increases arethemselves increasing:Q01234567TC110135170215270335 410495 TC25354555657585 2TC101010101010In other words, the increase of the increase (written as 2TC= ( TC)) is alwayspositive. Costs are accelerating, the more is already produced, the more costly it is tofurther increase production. Economists speak ofincreasing marginal costs, the costs ofproducing one unit more is higher when more is produced. Mathematicians speak here ofastrictly convex the graphs we see this as follows: The graph is upward-bowed. The tangents get steeper from left to right, , their slopes are , the marginal costsMC(Q) = 10Q+ 20 are increasing, not only positive, ifwe draw the graph of the marginal cost curve:100200300400500TC0 1 2 3 4 5 6 7 QThe total costs in Example 2020406080100MC1 2 3 4 5 6 7 QIncreasing marginal call a function with a graph which is upward-bowed (like a cup )strictlyconvex.
BEE1020—BasicMathematicalEconomics Week7,LectureTuesday17.11.05 Convexity,concavity. Signdiagrams 0.1 Strictconvexityandconcavity ...
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