Unformatted text preview: Cost Curves 127 Cost Curves A. Family of cost curves 1. total cost: c(y ) = cv (y ) + F 2. c(y) = cv (y) + F y y y AC = AV C + AFC 3. see Figure 20.1. 4. marginal cost is the change in cost due to change in output c0 (y ) = dc(y )=dy = dcv (y )=dy a) marginal cost equals AV C at zero units of output Cost Curves 128 AC AVC MC AC MC AVC y Figure 20.2 b) goes through minimum point of AC and AV C . Figure 20.2. 1) 2) this is negative (for example) when c0 (y ) < d c(y) = yc0 (y) c(y) dy y y2 c(y)=y Cost Curves 129 MC MC Variable costs y Figure 20.3 c) fundamental theorem of calculus implies that cv (y) = Z y 0 c0 (t) dt d) geometrically: the area under the marginal cost curve gives the total variable costs. Figure 20.3. e) intuitively: the maginal cost curve measures the cost of each additional unit, so adding up the MC s gives the variable cost Cost Curves 130 B. Example: c(y ) = y 2 + 1 1. AC = y + 1=y 2. AV C = y 3. MC = 2y 4. Figure 20.4. AC MC AVC MC AC AVC 2 1 y Figure 20.4 Cost Curves 131 C. Long-run cost from short-run cost 1. average costs: Figure 20.8. 2. marginal costs: Figure 20.9. ...
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- Spring '08