Assignment
1. Coretta leases a workshop, in which she weaves rugs from marsh grass she gathers (for free) from a nearby riverside. She finds that if she works alone for a day, she can weave two rugs. If she hires one additional worker, together they can weave 5 rugs in a day, each specializing in some of the tasks. Adding a third worker also allows for more specialization, bringing production up to 8 rugs. Adding a fourth worker adds only 2 rugs to production, because there are no more gains from specialization to be had. Hiring a fifth worker adds only one additional rug to daily production, because now the workshop space is getting crowded.
a. What is the output in this example? What is the fixed input? What is the variable input?
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(1)
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(2)
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(3)
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(4)
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(5)
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(6)
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(7)
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Quantity of Labor (Number of Worker-Days)
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Quantity of Output (Number of Rugs)
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Marginal Return (product) to an Additional Worker-Day (Number of Rugs)
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Average Fixed Cost ($)
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Average Variable Cost ($)
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Average Total Cost ($)
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Marginal Cost of Production ($ per Rug)
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0
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--
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--
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1
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2
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3
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4
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5
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b. Find marginal product and complete column (2) and (3):
from 0 to 1 worker: _____
from 1 to 2 workers: _____
from 2 to 3 workers: _____
from 3 to 4 workers: _____
from 4 to 5 workers: _____
c. Suppose that rent for the workshop space costs Coretta $70 per day (whether she produces anything or not). Her cost for labor (including the opportunity cost of "hiring" herself!) is $60 per worker per day. Complete columns (4) through (6) in the table above, showing her average fixed, variable, and total costs of producing various numbers of rugs.
d. Find marginal cost and complete column (7).
2. Suppose Heritage Corporation believes that its total variable costs follow a cubic speci-fi¬ca¬tion and so it estimates its average variable costs using the following specification:
AVC = a + bQ + cQ2
The regression analysis produces the following computer output:
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DEPENDENT VARIABLE:
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AVC
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R-SQUARE
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F-RATIO
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P-VALUE ON F
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OBSERVATIONS:
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45
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0.6145
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33.47
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0.0001
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VARIABLE
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PARAMETER ESTIMATE
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STANDARD ERROR
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T-RATIO
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P-VALUE
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INTERCEPT
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175.0
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25.00
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6.00
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0.0001
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Q
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-4.15
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0.80
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-4.00
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0.0003
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Q2
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0.065
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0.01
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8.00
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0.0001
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a. Do the estimated coefficients have the required signs to yield a -shaped AVC curve? Discuss the significance using the p-values.
b. Heritage Corporation's marginal cost function is
c. At what level of output does AVC reach a minimum? What is the value of AVC at its minimum?
d. Compute AVC and SMCwhen Heritage produces 8 units.