## 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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