QUESTION 1 A financial analyst has reported the following information about Shan
ID: 1187645 • Letter: Q
Question
QUESTION 1
A financial analyst has reported the following information about Shangui Corporation’s cost and production structure:
Year
Total Cost (TC) ($10,000)
Quantity Produced (Q) (Unit)
2009
20
50
2010
22
100
2011
24
120
2012
26
130
Use Ordinary Least Squares Method (OLS) to estimate the ABC Corporation’s total cost function; that is, TC = β + β Q ;
What is ABC Co’s marginal cost?
What is ABC Co’s fixed cost?
Calculate scale elasticity at the mean of the data;
In order to reduce unit cost would you recommend an increase or a decrease in total production? Why?
01
Year
Total Cost (TC) ($10,000)
Quantity Produced (Q) (Unit)
2009
20
50
2010
22
100
2011
24
120
2012
26
130
Explanation / Answer
PRODUCTION ISOQUANTS An important tool of analysis when two inputs are variable is the production isoquant or simply isoquant. An isoquant is a curve showing all possible combinations of the inputs physically capable of producing a given (fixed) level of output. Each point on an isoquant is technically efficient; that is, for each combination on the isoquant, the maximum possible output is that associated with the given isoquant. The concept of an isoquant implies that it is possible to substitute some amount of one input for some of the other, say, labor for capital, while keeping output constant. Therefore, if the two inputs are continuously divisible, as we will assume, there are an infinite number of input combinations capable of producing each level of output. To understand the concept of an isoquant, return for a moment to Table 8.1 in the preceding chapter. This table shows the maximum output that can be produced by combining different levels of labor and capital. Now note that several levels of output in this table can be produced in two ways. For example, 108 units of output can be produced using either 6 units of capital and 1 worker or 1 unit of capital and 4 workers. Thus these two combinations of labor and capital are two points on the isoquant associated with 108 units of output. And if we assumed that labor and capital were continuously divisible, there would be many more combinations on this isoquant. Other input combinations in Table 8.1 that can produce the same level of output are: Q = 258: using K = 2, L = 5 or K = 8, L = 2 Q = 400: using K = 9, L = 3 or K = 4, L = 4 Q = 453: using K = 5, L = 4 or K = 3, L = 7 Q = 708: using K = 6, L = 7 or K = 5, L = 9 Q = 753: using K = 10, L = 6 or K = 6, L = 8 Each pair of combinations of K and L is two of the many combinations associated with each specific level of output. Each demonstrates that it is possible to increase capital and decrease labor (or increase labor and decrease capital) while keeping the level of output constant. For example, if the firm is producing 400 units of output with 9 units of capital and 3 units of labor, it can increase labor by 1, decrease capital by 5, and keep output at 400. Or if it is producing 453 units of output with K = 3 and L = 7, it can increase K by 2, decrease L by 3, and keep output at 453. Thus an isoquant shows how one input can be substituted for another while keeping the level of output constant. Characteristics of Isoquants We now set forth the typically assumed characteristics of isoquants when labor, capital, and output are continuously divisible. Figure 9.1 illustrates three such isoquants. Isoquant Q1 shows all the combinations of capital and labor that yield 100 units of output. As shown, the firm can produce 100 units of output by using 10 units of capital and 75 of labor, or 50 units of capital and 15 of labor, or any other combination of capital and labor on isoquant Q1. Similarly, isoquant Q2shows the various combinations of capital and labor that can be used to produce 200 units of output. And isoquant Q3 shows all combinations that can produce 300 units of output. Each capital
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