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Some Economic applications of one variable functions. Martin Fajkus Faculty of applied informatics Tomas Bata University in Zlin A: Small motivation How to fence a garden ! S = πππ₯ c = 100 S = 5 · 90 = 450 S = 30 · 40 = 1200 S = 40 · 20 = 800 A: Small motivation How to fence a garden ! S = πππ₯ c = 100 S = π. π c = 2π + π = 100 π = 100 β 2π S = π. (100 β 2π) S = 100π β 2π2 ! S ´ = 100 β 4π = 0 π = 25 π = 100 β 2.25 π = 50 Smax = 25·50 = 1250 B: Economic applications I. Basic functions of economic analysis I. A. β utility function I. Basic functions of economic analysis I. A. β utility function; surplus Consumer surplus I. Basic functions of economic analysis Co-ordinate axes x-axis β· x (or q) β QUANTITY y-axis β· p β PRICE I. B. β demand and supply Demand p = d(x) β· Supply x = D(p) Usually decreasing: With higher price people want to buy less. p = s(x) β· x = S(p) Usually increasing: With higher price producers want to produce more. Demand function (copies marginal utility of the buyer) Market equlibrium; surplus and shortage supply demand I. Basic functions of economic analysis I. C. β costs, revenue; profit FIXED VARIABLE TOTAL COSTS FC VC(x) TC(x) = FC + VC(x) REVENUE FR VR(x) = p.x TR(x) = FR + VR(x) PROFIT FP VP TP(x) = TR(x) β TC(x) AVERAGE π΄πΆ = ππΆ π₯ π΄π = ππ π₯ π΄π = ππ π₯