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Optimal mix of input factors of production for long run cost

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Explain why a firm's long-run costs are minimized when it employs a mix of resources such that the ratio of all of the resources' marginal products to their wage rates are equalized. Use a graph to illustrate.

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See the attached file. The text here may not print correctly for tables and symbols. Thanks

Long Run Costs
________________________________________
Explain why a firm's long-run costs are minimized when it employs a mix of resources such that the ratio of all of the resources' marginal products to their wage rates is equalized. Use a graph to illustrate.
Let us assume that there are two types of resources used for production.
X= Quantity of input X
Y= Quantity of input Y
Px=Wage rate for resource X
Py=Wage rate for resource Y
I= Budget available with the firm to spent on resource X and Y.
The amount of money spent on resource X= X*Px
The amount of money spent on resource Y= Y*Py
Total amount spent on both resources = X*Px + Y*Py
Total Cost (TC) = X*Px + Y*Py
Since the total ...

Solution Summary

This post proves mathematically with the help of equations for budget line, isocost curves and isoquant curves that the long run costs are minimized when the firm employs a mix of resources such that the ratio of all of the resources' marginal products to their wage rates are equalized. All assumptions and symbols used in the equations are explained and the post also includes the graphical representation for easier understanding.

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Production and Cost Analysis in the Short-Run

1.
Given the output and Total Cost Data in the Table below, Complete the following columns: Variable cost , Fixed Costs, marginal Cost, Average Total Cost columns. Then on a graph, plot the marginal and average costs data. (Plot them on the same graph, not on two separate graphs). Then from the graph identify the level of output at which Marginal Cost equals Average Cost.
Total
Output Cost
0 50
1 60
2 75
3 100
4 150
5 225
6 400

2. Which of the following statements best represents a difference between short-run and long-run cost?
a. Less than one year is considered the short run; more than one year the long run.
b. There are no fixed costs in the long run.
c. In the short-run labor must always be considered the variable input and capital the fixed input.
d. In the short run, all inputs could be variable.
e. All of the above are true.

3. In economic theory, if an additional worker adds less to the total output than the 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.

4. Which of the following relationships is correct?
a. When marginal product starts to decrease, marginal cost starts to decrease.
b. When marginal cost starts to increase, average cost starts to increase.
c. When marginal cost starts to increase, average variable cost starts to increase.
d. When marginal product starts to decrease, marginal cost starts to increase

5. The total cost (TC) of producing computer software diskettes (Q) is given by TC + 200 + 5Q. What is the fixed cost?
a. 200
b. 5Q
c. 5
d. 5 + (200/Q)
e. none of the above

6. Which of the following relationships implies that a firm's short-run cost function is linear?
a. MC = AC
b. MC = AVC
c. AC = AFC + AVC
d. MC > AC

7. A Production Function represents
a. the method used to convert inputs into outputs.
b. the amounts of output that can be created by various amounts of inputs.
c. the optimum mix of inputs to maximize output.
d. All of the above.

8. If total cost equals $2000 and quantity produced is 100 units,
a. then fixed cost is $200 and average variable cost is $18.
b. then fixed cost is $600 and average variable cost is $14.
c. then fixed cost is $500 and marginal cost is $15.
d. then either A or B can be correct.

9. Diseconomies of scale can be caused by
a. the law of diminishing returns.
b. bureaucratic inefficiencies.
c. increasing advertising and promotional costs.
d. All of the above.

10. In a call center, which of the following would be considered to be a variable input in the short run?
a. the level of computer-telephony software being utilized
b. the number of call center representatives on duty at the center
c. the number of call center managers or supervisors
d. the size (e.g. square footage) of the call center

11. When a firm's MC curve shifts to the right, it implies that
a. new firms are entering the market.
b. labor productivity is decreasing.
c. labor productivity is increasing.
d. the firm's overhead costs are decreasing.
e. labor productivity is constant.

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