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I have been working on this assignment for a few days now. I am unable to solve this assignment. Some of the questions have been answered but I particularly need help with Question 1, 4 and 6. Help is

ECON 2011 Assignment 1 Feel free to work as a group, but every student should hand in his/her own "hand-written" copy! Olivia wants to…

I have been working on this assignment for a few days now. I am unable to solve this assignment. Some of the questions have been answered but I particularly need help with Question 1, 4 and 6. Help is much appreciated. 

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ECON 2011
Assignment 1
Feel free to work as a group, but every student should hand in his/her own “hand

written” copy!
1.
Olivia wants to plant apple trees in two orchards. Orchard A is larger than Orchard B but is less level,
rocky, and more difficult to irrigate, so that apple trees in Orchard A tend to produce fewer apples.
Orchard B is small but the soil is rich, the land is level and apple production is initially higher per tree
than in Orchard A. Olivia has 150 trees to plant; if she estimates the apple production in each orchard
to reflect the following data, how many trees should she plant in each orchard?
Orchard A
Orchard B
Number of Trees
Number of Apples
Number of Trees
Number of Apples
10
750
10
1200
20
1500
20
2400
30
2250
30
3200
40
3000
40
4000
50
3750
50
4750
60
4500
60
5400
70
5250
70
5800
80
6000
80
6000
90
6750
90
5900
100
7500
100
5600
2.
State whether the following production functions exhibit decreasing returns to scale, increasing
returns to scale, or constant returns to scale, briefly explain:
a.
Q = K/ (L)
2
.
b.
Q = 4K + 2L.
c.
Q = A K
a
L
b
(
a + b
= 1).
d.
Q = A K
a
L
b
(
a + b
< 1). 3. Federal tax authorities have hired you to audit a dead economist's consulting firm. He left his records incomplete so that only a student trained in economics could fill in the blanks. The figures for Marginal Cost refer to the change from the preceding row to the row in which a given number appears. Clients Total Cost Fixed Cost Variable Cost Average Total Cost Average Variable Cost Average Fixed Cost Marg. Cost 0 100 1 75 2 65 3 250 4 112.5 5 100 6 200 7 1100 Does the consulting firm exhibit diminishing marginal productivity for any number of clients between 0 and 7? View the Answer 4. Doug wants to go into the donut business. For $500 per month he can rent a bakery complete with all the equipment he needs to make a dozen different kinds of donuts (K = l). He must pay unionized donut bakers a monthly salary of $400 each. He projects his production function to be Q = 5KL (where Q is tonnes of donuts). a. What is Doug's monthly total cost function, variable cost function, and marginal cost? b. How many bakers will Doug hire to make 25 tonnes of donuts? c. Give Doug's total cost function if his production function turns out to be Q = 2KL. 5. If the long-run total costs for each firm in a competitive industry are given by LTC(Q) = 2Q 3 – 12Q 2 + 25Q, with long-run marginal costs given as LMC = 6Q 2 – 24Q + 25, where LTC is in $ and Q is in kgs, what is the long-run equilibrium price for the industry? 6. In a competitive industry consisting of 10,000 firms, the short-run marginal cost curve for each firm is given by MC = 200 + 30Q. The demand curve faced by the industry is given as P = 400 – 0.002Q. P and MC are in $/tonne and Q is in tones. a. Find the equilibrium price and quantity sold, for the industry and for each firm. b. Find the producer and consumer surpluses at the equilibrium price. 7. True or False a. The marginal product curve intersects the average product curve at the latter curve's minimum point. b. The short run MC curve slopes upward due to increasing returns to scale. c. The fixed cost curve is always downward sloping. d. The average total cost curve can be created by adding the average variable cost curve to the average fixed cost curve. e. Suppose a perfectly competitive industry is in long-run equilibrium. An increase in demand will raise the price for the product, but in the long run the price will necessarily return to its former level. f. A perfectly competitive firm has a perfectly elastic supply curve.

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