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Cobb-Douglas Production Function

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Hi,

I am fairly new to economics with only a basic understand of the topic and because of this I am struggling to answer (and understand the explanation for the answer) a question about the Cobb Douglas production function.

Q. Under what conditions does a Cobb-Douglas production function (q=AL^(alpha)K^(beta)) exhibit decreasing, constant or increasing returns to scale?

Alongside this, can someone please breakdown for me how and why '(alpha) + (beta) > 1' would indicate increasing returns. All answers online and in the textbook have been out of my depth in terms of understanding.

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If the sum of the inputs' exponents = 1 then constant returns to scale.
If the sum of the inputs' exponents < 1 then decreasing returns to scale.
If the sum of the inputs' exponents > 1 then increasing returns to scale.

In the normal capital and labor equation as you stated, (alpha) and (beta) are the exponents. So in this case you would add alpha and beta and see which of the three cases above you ...

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The expert examines Cobb-Douglas production functions.

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A firm used a combination of inputs that was to the left of its isocost line, it would indicate that
a. it is exceeding its budget.
b. it is not spending all of its budget.
c. it is operating at its optimal point because it is saving money.
d. None of the above.

When the exponents of a Cobb-Douglas production function sum to more than 1, the function exhibits
a. constant returns.
b. increasing returns
c. decreasing returns.
d. either increasing or decreasing returns.

What does the following Cobb-Douglas production function, Q = 1.8L0.74K0.36, exhibit
a. increasing returns.
b. constant returns.
c. decreasing returns.
d. Both A and B.

Marginal rates of technical substitution (MRTS) represent
a. the optimum combinations of inputs.
b. cost minimizing combinations of inputs.
c. the degree to which one input can replace another without output changing.
d. All of the above.

If a firm is using two inputs, X and Y, is using them in the most efficient manner when
a. MPX = MPY.
b. PX = PY and MPX = MPY.
c. MPX/PY = MPY/PX.
d. MPX/MPY = PX/PY.
e. none of the above

Which of the following would indicate when Stage II ends and Stage III begins in the short-run production function?
a. when AP = 0
b. when MP = 0
c. when MP = AP
d. when MP starts to diminish
e. none of the above

In economic theory, if an additional worker adds less to the total output than previous workers hired, it is because
a. there may be less that this person can do, given the fixed capacity of the firm.
b. he/she is less skilled than the previously hired workers.
c. everyone is getting in each other's way.
d. the firm is experiencing diminishing returns to scale.
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A major advantage of the ________ production function is that it can be easily transformed into a linear function, and can be analyzed with the linear regression method.
a. cubic
b. power
c. quadratic
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________ functions are very useful in an analyzing production functions, which exhibit both increasing and decreasing marginal products.
a. Cobb-Douglas
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In the short run, finding the optimal amount of variable input involves which relationship?
a. MP = MC
b. AP = MP
c. MP = 0
d. MRP = MFC
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