Question
In: Economics
Kent sells lemonade in a competitive market on a busy street corner. His production function is...
- Kent sells lemonade in a competitive market on a busy street
corner. His production function is F(L, K) = L1/3
K1/3 where output q is gallons of lemonade, K is the
pounds of lemons he uses and L is the number of labour-hours spent
squeezing them. The corresponding marginal products are
MPL=
13L-23K13
and MPK=
13L13K-23.
Every pound of lemons cost r and the wage rate of lemon squeezers
is w.
- Prove that this production process has decreasing returns to scale.
- On a graph with hours of lemon-squeezing (L) on the horizontal axis and pounds of lemons (K) on the vertical axis, illustrate an isoquant that represents a particular production level q. What is the equation of the isoquant?
- What is the equation for a slope of an isoquant? Is it constant? What does the slope indicate? Explain.
- What are the conditions that identify the cost minimizing bundle for any output? Illustrate on a clearly labelled diagram.
- Set up the cost minimization problem and solve for the conditional input demands as functions of the exogenous variables.
- Derive the cost function (as a function of only the exogenous variables).
- Continue with total cost function derived in previous part and derive the average cost. Is it upward or downward sloping? Explain.
Solutions
Rahul Sunny answered 8 months agoRelated Solutions
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Kelly sells orange juice in a competitive market on a busy
street corner in New York. Her production function is ?(?1, ?2) =
?1 1/3 ?2 1/3, where output is measured in gallons, ?1 is number of
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At the cost minimizing input bundle, how...
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corner in your neighborhood. Each cup of lemonade costs Beth $0.20
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10 people who walk by Beth's lemonade stand each day are listed in
the following table.
Person
1
2
3
4
5
6
7
8
9
10
Reservation
price
$0.50
$0.45
$0.40
$0.35
$0.30
$0.25
$0.20
$0.15
$0.10
$0.05
Beth knows the distribution of reservation prices (that...
Beth is a second-grader who sells lemonade on a street corner in your neighborhood. Each cup...
Beth is a second-grader who sells lemonade on a street corner in
your neighborhood. Each cup of lemonade costs Beth $0.90 to
produce; she has no fixed costs. The reservation prices for the 10
people who walk by Beth's lemonade stand each day are listed in the
following table.
Person
1
2
3
4
5
6
7
8
9
10
Reservation
price
$1.50
$1.40
$1.30
$1.20
$1.10
$1.00
$0.90
$0.80
$0.70
$0.60
Beth knows the distribution of reservation prices (that...
Cost of Competitive Firm In Stockholm, there is a competitive market for the production of canopy...
Cost of Competitive Firm
In Stockholm, there is a competitive market for the production
of canopy beds. Max’s canopy bed production firm can make at most
six canopy bed’s per week.
Quantity
Fixed Cost ($)
Variable Cost ($)
Total Cost ($)
Marginal Cost ($)
0
0
5000
---
1
5000
2000
2
6000
3
6000
4
8000
5
35000
6
42000
Complete the four cost columns in the table above.
If the market price of pianos is $6000 this week,...
Cost of Competitive Firm In Vienna, there is a competitive market for the production of upright...
Cost of Competitive Firm
In Vienna, there is a competitive market for the production of
upright pianos. David’s piano production firm can make at most six
pianos per week.
Quantity
Fixed Cost ($)
Variable Cost ($)
Total Cost ($)
Marginal Cost ($)
0
2000
---
1
5000
2
2000
11000
3
18000
4
8000
5
37000
6
45000
Complete the four cost columns in the table above.
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Suppose Andy sells basketballs in the perfectly competitive basketball market. His output per day and costs...
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0 $10.00
1 $20.50
2 $24.50
3 $28.50
4 $34.00
5 $43.00
6 $55.50
7 $72.00
8 $93.00
9 $119.00
1) Make a table with Quantity (Q), Total Cost (TC), Fixed Cost
(FC), Variable Cost (VC), Average Total Cost (ATC), Average
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Quincy’s operates in a perfectly competitive environment (in both
input and output markets), so it is both a price-taker and a
wage-taker.a) Fill in the missing values in the table, assuming the selling
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Product
0
0
1
10
10
$30
2
18
_____
$24
3
24
6
_____ ...
Problem. Suppose that, in a large city, 200 identical street vendors compete in a competitive market...
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1. The vendors total costs to produce q hot dogs is,
C(q) = 1/4q + 1/8q².
What is
the marginal cost function of each firm?
2. Given your answer from above, how many hot dogs will each
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A competitive firm has a production function ?(?, ?) = (? +
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?. Which of the following is true?
Regardless of ? and ?, cost minimisation requires that ? =
?.
If ? > ?, contingent demand for labour is 0.
The technology has increasing returns to scale.
If ? < ?, profit maximisation requires that...
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