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Question at position 10 A manufacturer’s total-cost function is given by c(q)=q24+3q+400c(q)=\frac{q^2}{4}+3q+400 where c(q) is the total cost of producing q units. At what level of output will average cost per unit be a minimum?23340-40
Options
A.23
B.3
C.40
D.-40
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Step-by-Step Analysis
To evaluate where average cost is minimized, I start by expressing average cost as a function of output q. AC(q) = c(q)/q = (q^2/4 + 3q + 400)/q = q/4 + 3 + 400/q.
Next, I differentiate AC with respect to q to find critical points: d(AC)/dq = 1/4 - 400/q^2.
I set the derivative equal to ......Login to view full explanationLog in for full answers
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Consider a producer that produces a high-quality commodity, which costs 20$ per unit, and a low-quality commodity, which costs 10$ per unit. Given that the consumers do not distinguish between the high-quality and the low-quality commodities, the market price for this commodity is 16$. In order to stay competitive with the other producers, what must be the ratio of the high-quality commodities to all the produced commodities?
Part 1A firm has two plants that produce identical output. The cost functions areUpper C 1 equals 399 q minus 12 q squared plus 0.5 q cubedC1=399q−12q2+0.5q3 and Upper C 2 equals 399 q minus 16 q squared plus 1.0 q cubedC2=399q−16q2+1.0q3.Part 2First, note that if AC 1AC1equals=399399minus−1212qplus+0.50.5q squaredq2, then StartFraction dAC 1 Over dq EndFraction equals negative 12 plus 2 left parenthesis 0.5 right parenthesis qdAC1dq=−12+2(0.5)q. Similarly, if AC 2AC2equals=399399minus−1616qplus+1.01.0q squaredq2, then StartFraction dAC 2 Over dq EndFraction equals negative 16 plus 2 left parenthesis 1.0 right parenthesis qdAC2dq=−16+2(1.0)q.Part 3At what output level does the average cost curve of each plant reach its minimum?Part 4The first plant reaches minimum average cost at [input]1212 units of output. (Enter a numeric response using an integer.)Part 5The second plant reaches minimum average cost at [input]enter your response here units of output. (Enter a numeric response using an integer.)
Refer to Table 1 below: Table 1: Production Costs of the Firm A [table] Quantity of output per hour | Total Fixed Costs per hour($) | Total Variable Costs per hour ($) | Marginal Cost per hour of the…. ($) | Average Cost per hour ($) 0 | 250 | 0 | N/A | N/A 1 | 250 | 25 | 1st item = 25 | 275 2 | 250 | 43 | 2nd item = 18 | 146.50 3 | 250 | 58 | 3rd item = 15 | 102.67 4 | 250 | 75 | 4th item = 17 | 81.25 5 | 250 | 95 | 5th item = 20 | 6 | 250 | 126 | 6th item = | 62.67 [/table] What is the average cost of 5 items?
Production efficiency is attained where a firm is maximizing output and minimizing input. This takes place visually at the ATC minimum. According to the Average Cost model, production efficiency is attained at an approximate quantity of:
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