In the previous posts we discussed total, marginal, and average cost curves for both short run and long run. The relationships between these cost curves have a very wide range of applications for managerial use. Here we will discuss a few applications of these concepts.
Determining Optimum Output Level
Earlier we have seen that the optimum output level is the point where average cost is minimum. In other words, the optimum output level is the point where average cost equals marginal cost. Consider the following example.
Breakeven Output Level
An analytical tool frequently employed by managerial economists is the breakeven chart, an important application of cost functions. The breakeven chart illustrates at what level of output in the short run, the total revenue just covers total costs. Generally, a breakeven chart assumes that the firm’s average variable costs are constant in the relevant output range; hence, the firm’s total cost function is assumed to be a straight line. Since variable cost is constant, the marginal cost is also constant and equals to average variable cost.
Figure -7 shows the breakeven chart of a firm. Here, it is assumed that the price of the product will not be affected by the quantity of sales. Therefore, the total revenue is proportional to output. Consequently, the total revenue curve is a straight line through the origin. The firm’s fixed cost is Rs. 500, variable cost per unit is Rs. 4 and the unit sales price of output is Rs. 5. The breakeven chart, which combines the total cost function and the total revenue curve, shows profit or loss resulting from each sales level. For example, Figure-7 shows that if the firm sells 200 units of output it will make a loss of Rs. 300. The chart also shows the breakeven point, the output level that must be reached if the firm is to avoid losses. It can be seen from the figure, the breakeven point is 500 units of output. Beyond 500 units of output the firm makes profit.
Breakeven charts are used extensively for managerial decision process. Under right conditions, breakeven charts can produce useful projections of the effect of the output rate on costs, revenue and profits. For example, a firm may use breakeven chart to determine the effect of projected decline in sales or profits. On the other hand, the firm may use it to determine how many units of a particular product it must sell in order to breakeven or to make a particular level of profit. However, breakeven charts must be used with caution, since the assumptions underlying them, sometimes, may not be appropriate. If the product price is highly variable or if costs are difficult to predict, the estimated total cost function and revenue curves may be subject to these errors.
We can analyse the breakeven output with familiar algebraic equations.
Therefore, the breakeven output (Q) will be 500 units. Similarly, the breakeven output value will be Rs.2500 (P * Q = Rs. 5 * 500).
Profit Contribution Analysis
In making short run decisions, firms often find it useful to carry out profit contribution analysis. The profit contribution is the difference between price and average variable cost (P – AVC). That is, revenue on the sale of a unit of output after variable costs are covered represents a contribution towards profit. In our example since price is Rs.5 and average variable cost is Rs.4, the profit contribution per unit of output will be Rs.1 (Rs.5 – Rs.4). At low rates of output the firm may be losing money because fixed costs have not yet been covered by the profit contribution. Thus, at these low rates of output, profit contribution is used to cover fixed costs. After fixed costs are covered, the firm will be earning a profit.
A manager wants to know the output rate necessary to cover all fixed costs and to earn a ‘required’ profit (pR). Assume that both price and AVC are constant. Profit is equal to revenue less the sum of total variable costs and fixed costs. Thus
pR = P * Q – [(Q * AVC) + FC]
Solving this equation for Q gives a relation that can be used to determine the rate of output necessary to generate a specified rate of profit. Thus
Managers must make comparisons among alternative systems of production. Should one type of plant be replaced by another? Breakeven analysis can be extended to help make such comparisons more effective. Consider the degree of operating leverage (Ep), which is defined as the percentage change in profit resulting from a 1% change in the number of units of product sold. Thus
Example: Consider three firms I, II and III having the following fixed costs, average variable costs and price of the product.
Firm-I has more fixed cost than firm-II, and firm-III. However, Firm-I has less average costs than firm-II, and firm-III. Essentially, firm-I has substituted capital (fixed costs) for labour and materials (variable costs) with the introduction more mechanized machines. On the other hand, firm-III has less fixed costs and more average variable costs when compared to other two plants because firm-III has less mechanized machines. The firm-II occupies middle position in terms of fixed costs and average variable costs.
In comparing these plants, we use the degree of operating leverage. Suppose for all the three plants Q = 40,000
Thus, a 1% increase in sales volume results in a 6% increase in profit at firm- I, a 4% profit at firm-II, and 3% profit at firm-III. This means firm-I’s profits are more sensitive to changes in sales volume than firm-II and firm-III and firm-II’s profits are more sensitive to changes in sales volume than firm- III.