accounting homework

The profit maximizing level of output is achieved when the marginal revenue is equal to its marginal cost.  In other words: MC = MR 

Let’s start by familiarizing ourselves with marginal revenue and marginal cost: 

Marginal revenue is defined as the addition revenue that is generated by increasing product sales by one additional unit of output. Marginal revenue is calculated by dividing the change in total revenue by the change in total output quantity.

Marginal cost is defined as the change in the total cost that results from producing one additional unit.  Total costs will include all costs associated with the additional production including labor, materials, and overhead.  As fixed costs do not vary based on production level, the variable costs will be where the changes in marginal cost are seen.

A company is considered to be perfectly competitive when the equality of marginal costs and marginal revenue is reached.  In other words, this means that the production level has been reached where profits have been maximized. 

This concept may be a little confusing as this equation may make it appear that the company is earning nothing if the marginal revenue equals the marginal cost.  However, this is not the case.  The company is looking at increasing production by one more unit.  Let’s assume that the increased unit proves to be profitable (the increase in revenue is greater than the increase in cost).  Now, the company will evaluate increasing production by an additional unit, and so on.  This increase in production continues until the company reaches a level where the latest unit added does not add profit.  This is the point where marginal costs equal marginal revenue and it no longer makes sense to increase production by that single unit.        

Example 1: You are given the following for Marginal Cost and Marginal Revenue.  Based on the information provided, at what level of output Q would profit be maximized?

MC = 20 Q – 120,000

MR = 250 Q – 240,000

At what level of output Q is the profit maximized?

Using MC = MR we setup the problem as follows:

20 Q – 120,000 = 250 Q – 240,000

120,000 = 230 Q

Q = 120,000 / 230

Q = 522

Alternatively, this concept can be applied in a situation where you are given a varying number of units along with corresponding variable costs per unit and sales price per unit.  Based on that information, you can then evaluate the number of units that would maximize profits. Profits are evaluated based on the following equation: P x Q – VC x Q where P is sales price per unit, Q is the number of units, and VC is the variable cost per unit.  As previously noted, fixed costs would not change based on quantity, so it is not included in this calculation.  Let’s work through an example that evaluates profit maximizing output from this perspective.   

Example 2:  Your company estimates variable costs and price per unit based on the following levels of production.  Based on this information, what level of production would you recommend?

Using P x Q – VC x Q we calculate the following for each level of units produced:

Analyzing the profit at each level of units, we find that 11,000 units produces the maximum profit for the company.  As a result, it is recommended that 11,000 units be produced by the company.