Question

Part I: Using a well labeled graph and words that explain your graph, show the short run average variable cost curve and the marginal cost curve.

Explain the shapes of the two cost curves.
Where do the two cost curves intersect? Why?

Answer 1

The marginal cost is the change in total cost for the change in an additional unit of output. The average variable cost is the total variable cost per unit of output. In the short-run, some inputs, like land, heavy machines, etc. remain fixed or constant. The cost on this type of inputs is one-time cost and is called fixed cost in short-run. So in the short-run, a firm's total cost is the sum of fixed cost and variable cost.

In the short-run, at the initial stage of production, with the employment of variable input, the total product first rises at an increasing rate, then increases at a decreasing rate and reaches its maximum. After reaching its maximum, the total product decreases with further employment of variable input.This happens because in the short-run as at least one of the inputs remains fixed, the productivity of this fixed input gradually decreases as the pressure on this input rises with more and more employment of variable input. As a result, the marginal productivity of variable input first rises, then reaches its maximum, and then decreases. When the marginal productivity of variable input rises, the marginal cost of production decreases. When the marginal productivity of variable input reaches the maximum, the marginal cost of production reaches the minimum. When the marginal productivity of variable input decreases, the marginal cost of production increases. So we get that the marginal cost first decreases, then reaches its minimum, and then increases. Thus, the marginal cost(MC) curve is 'U' shaped.

We have discussed that at the initial stage of production in the dhort-run, with the employment of variable input, the total product first rises at an increasing rate, then increases at a decreasing rate,reaches its maximum, and the with further employment of variable input, the total product decreases. When total product increases at an increasing rate, then the average product rises. When total product stops to increase at incressing rate and starts to increase at decreasing rate, the average product is maximum. Then the average product starts to fall with the further employment of variable input. Now, when the average product rises, the average variable cost falls; when the average product is maximum, the averrage variable cost is minimum; when the average product decreases, the average variable cost rises. So we get that the average variable cost first decreases, then reaches its minimum, and then increases. Thus, the average variable cost(AVC) curve is 'U' shaped.

So, we get that both the MC curve and AVC curve are 'U' shaped. These two curves are shown in the above figure, where output is measured on the horizontal axis, and cost is measured on the vertical axis. The curve 'MC' shows the marginal cost curve, and the curve 'AVC' shows the average variable cost curve in the figure. From the figure we see that the MC curve reaches its minimum point at point 'N', and the AVC curve reaches its minimum point at point 'L', i.e., MC reaches its minimum before the AVC reaches its minimum. When AVC reaches its minimum, the AVC and MC are equal. Thus, the MC curve crosses the AVC curve at the minimum point of AVC. So, AVC and MC intersect each other at the minimum point of AVC curve.

In the short-run, the MC is the additional cost incurred on an additional variable input. When the MC is lower than the average variable cost, it pulls the AVC down. The cost curves and the product curves are mirror images of each other.The marginal product starts to fall before the fall of the average product of the variable input. Thus the MC starts to increase before the increase of the AVC. When the average product reaches its maximum, then marginal product and average product are equal. Thus, when AVC is minimum, then MC and AVC are equal. All these things explain why MC reaches its minimum before the AVC reaches its minimum.

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