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Lecture 6

# Lecture notes week 6

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University of Toronto Scarborough

Economics for Management Studies

MGEA02H3

Gordon Cleveland

Fall

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ECMA04H Week 6 Costs: how do they behave as output increases? What does the typical graph of cost curves look like (in the short run)? What is the algebra of cost curves? 2 Example: TC = 400 + 5q + q FC = 300 VC = 100 + 5q + q 2 MC = dTC dq = dVC dq = 5 + 2q Rate of change of firms costs as output increases; incremental cost Without calculus., MC = TCq (an approximation) 2 AC = TC q = (400 + 5q + q ) q = 400 q + 5 + q AC = (FC + VC)q = AFC + AVC AFC = 300 q AVC = (100 + 5q + q 2) q = 100 q + 5 + q AC = 300 q + 100 q + 5 + q Find minimum of AC, AVC AC = 400 q + 5 + q dAC dq = -400 q 2 + 1 = 0, which implies that q = 20 AC = 400 20 + 5 + q = 20 + 5 + 20 = 45 At an output level of 20, AC will reach its minimum at a cost of $45. AVC = 100 q + 5 + q 2 dAVC dq = -100 q + 1 = 0, which implies that q = 10 AVC = 100 10 + 5 + 10 = 10 + 5 + 10 = 25 At an output level of 10, AVC will reach its minimum at a cost of $25. Check value of MC at min AC and min AVC MC = 5 + 2q At q = 20, for AC, MC = 5 + 2 * 20 = $45 At q = 10 for AVC, MC = 5 + 2 * 10 = $25 Graph MC, AC, AVC Cost Graph 450 400 350 300 250 MC $ ACC 200 AFC 150 100 50 0 0 20 40 60 80 100 120 140 160 q www.notesolution.com

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