Q12. A computer company鈥檚 cost func... [FREE SOLUTION]

Chapter 7: Q12. (page 281)

A computer company鈥檚 cost function, which relates its average cost of production AC to its cumulative output in thousands of computers Q and its plant size in terms of thousands of computers produced per year q (within the production range of 10,000 to 50,000 computers), is given by AC = 10 - 0.1Q + 0.3q
Is there a learning-curve effect?
Are there economies or diseconomies of scale?
During its existence, the firm has produced a total of 40,000 computers and is producing 10,000 computers this year. Next year it plans to increase production to 12,000 computers. Will its average cost of production increase or decrease? Explain.

Short Answer

Expert verified

There exists a learning curve effect.
There are diseconomies of scale.
The average cost of production will decrease in the next year.

Step by step solution

Meaning of the learning curve and its relation with the average cost

The learning curve shows a relationship between the cumulative output produced and the amount of input required for each output unit.Since the output produced increases, the requirement for input per unit of output decreases. Thus, both the variables are inversely related. It happens because firms increase their efficiency with experience.

The average cost is the value of inputs per unit of total output produced. The average cost decreases with increasing cumulative output, shown by the negative coefficient of cumulative production in the average cost equation.

Thus, there is a learning curve effect in the company鈥檚 cost function.

Diseconomies of scale

Diseconomies of scale arise with decreasing returns to scale. Under the diseconomies of scale, the cost of inputs per unit increases with an increase in output.

The cost function of the company shows that as the output produced per year increases, the average cost of the company increases. Therefore, there are diseconomies of scale.

Change in average cost of production during the years

Case 1: In the present year:

The cumulative output (Q) is 40, plant size (q) is 10, the average cost is:

AC = 10 鈥� 0.1Q + 0.3q

AC = 10 鈥� 0.1脳40 + 0.3脳10

AC = 9

Case 2: In the next year:

The plant size (q) is 12, and the cumulative output is 50 (40 + 10). The average cost is:

AC = 10 鈥� 0.1Q + 0.3q

AC = 10 鈥� 0.1脳50 + 0.3脳12

AC = 8.6

The average cost in the next year will be $8.6 (in thousands), which is $0.4 (in thousands) lesser than this year. Thus, the average cost will decrease next year.