Optimal amount of Research and Development (R&D)

How do firms decide what amount of research and development to use? This depends on the amount of marginal benefit and marginal cost firm gets after R&D activity. This decision comes from one basic rule of economics: In order to get the greatest profit a firm should expand a specific activity until marginal benefit (MB) will be equal to its marginal costs (MC). If a firm sees that a R&D activity brings more marginal benefit than the marginal cost then this firm should expand its activity. However, if marginal benefit is less than marginal cost then this R&D activity should stop or shouldn’t be started. R&D spending decisions is a complex one, because it involves a possible future gain for present sacrifice. While R&D spending is immediate the expected benefits are uncertain and may occur at some possible future point in time. The MB=MC idea is still relevant for R&D decisions.

Spending in R&D
In order to obtain funds for R&D activities firms have several options:
  Bank loans– Some firms are able to finance their R&D activities by obtaining loans from banks or other type of financial institutions. The cost of using this kind of funds is the interest rate paid to the lender. The marginal cost is the Future Value (FV) of money borrowed.
Bonds– Profitable firms may borrow funds for R&D by issuing bonds and selling them. In this case, interest is the cost paid by bondholders to lenders. In this case, again, marginal cost is the interest rate paid for money borrowed.
Retained earnings– some big firms may finance their R&D activity by retaining some earnings. In this case firm retains a part of its profit rather than paying dividends to its owners. Some undistributed corporate profit, called retained earnings, can be used to finance R&D activity. The marginal cost in this case is the rate that could be earned from interest as deposits in financial institutions.
Venture capital– A small start-up firm may be able to attract venture capital to attract R&D projects. Venture capital is simply money, not real capital. Venture capital is part of household savings that is used to finance high-risk business venture in exchange of possible future share if thus ventures succeed. Marginal cost of this type of financing is the share of expected profit that business will have to pay to these people that offered this money.
Personal savings– Sometimes entrepreneurs may finance R&D activities from their own savings. In this case marginal cost is the forgone interest rate.
To sum up, we may state that whatever are the funds for R&D, the marginal cost in all the cases is forgone interest rate, i. Let’s assume that interest rate is the same for all amount of money needed. Also, let’s say that a firm call EcoMoney must pay an interest rate of 10% for the least expensive funding available to it. Let’s draw a graph called interest-rate cost-of-funds curve that denotes marginal cost of each amount of money borrowed for 10% interest rate and is shown simply by a horizontal line. Let’s make a graph and a table that depicts this situation.

With this information EcoMoney want to determine how much R&D to finance in the next year.
Expected Rate of Return
Firm’s marginal benefit from each dollar spent on R&D is it is profit (or return) gained from it. Thus R&D is expected to result in a new product or production method that will increase firm’s revenue. This return isn’t guaranteed but it is possible, so there is a risk to invest money in research and development process. Let’s suppose that after considering all risks EcoMoney constructs an expected-rate of return versus research and development cost graph and table. Expected-rate of return curve is marginal benefit of each dollar spent on R&D. This curve slope is negative because of diminishing returns from R&D expenditures. A firm will direct its initial R&D expenditures to the highest expected-rate of return activities and additional funding will be invested in activities that offer successively lower rates of returns. Thus firm increases R&D spending it uses to finance R&D activities of progressively lower rates of returns.


Optimal R&D spending
The figure bellow combines interest-rate-cost-of-funds curve and the expected rate of return curve. These two curves intersect at EcoMoney’s optimal amount of R&D, which is 35 million of dollars. This result can also be determined from the previous tables that showed amount of funding at various rates of return and interest cost of borrowing (in this case 10%). AT this point MR and MC from expenditures on R&D are equal. The firm should undertake all R&D expenditures up to 35 million of dollars, since these parameters yield higher marginal benefit and expected rate of return, r, than interest costs of borrowing money, i.
Optimal vs. affordable R&D
As we know there can be too much, or too little of a good thing. So it is with R&D and technological advance. The figures from above show that R&D expenditures make sense as long as the expected return equals or exceeds the expenditures needed to finance it. Many R&D expenditures may be affordable but also most of them aren’t worthwhile, because their marginal benefit is less than their marginal cost.
Not Guaranteed returns
    The outcome of R&D researches are expected, but not guaranteed. At the time of decision, it may look worthwhile, but they can’t predict with high accuracy future events, that’s why sometimes some R&D decisions are like an informed gamble and not as typical business decision. Invention and innovation carry with them high possibility of risk. So there may be a successful outcome or a costly disappointment.

Profit-Maximization in Short-Run (Pure competitive Market)

   Since the purely competitive firm is a price-taker, then to increase its revenue in short run it can change only quantity output.  Thus it can adjust its output by changes in amount of variable resources (materials, labor) it uses. So to maximize its revenues or to minimize its losses our firm has to adjust its quantity of resources used.
   There are two ways how to calculate the level of output for which our firm, in a pure competitive market, will get highest revenues. One of the methods is to compare total revenues and total costs, and another one is to compare marginal revenues and marginal costs. By the way, these methods can be applied not just in pure competitive market but also in pure monopoly, monopolistic competitive market and oligopoly.

Total Revenue- Total Cost Approach
       Total cost increases with output, because more production require more resources, but the rate of increase in the total cost varies with the efficiency of the firm. Specifically, the cost data reflect law of diminishing returns. Initially it increases with smaller amounts but after a point total cost rise by increasing amounts. Total revenue covers all costs (including normal profit) but there isn’t an economic profit. Economists call break-even point: an output value for which a firm makes a normal profit but not an economic profit. Any output between two break-even points produces an economic profit. The firm achieves maximum profit, where the vertical distance between Total Revenue and Total Cost is greatest.

Marginal Revenue- Marginal Cost Approach
   In this approach the firm compares marginal revenue (MR) and (MC) of each successive unit of output. The firm will produce any output for which marginal revenue is greater than marginal benefit because the firm will add more revenue from selling that item than the costs of producing it.
MR=MC Rule
   In the initial stages of production, when output is relatively low then the Marginal Revenue (MR) is usually greater than Marginal Cost (MC). So it’s profitable to produce in this range of output. But with additional units of output where quantity produced is relatively high, rising marginal cost will become greater than the marginal revenue. That’s why firms will try to avoid output quantity in this range. A point, where marginal revenue equals with marginal cost, separates these two regions.  In the short run, the firm will maximize profits or minimize its loss by producing that quantity of output where marginal cost equals with marginal benefit. This profit maximizing rule is known as MR=MC Rule.
Characteristics of MR=MC rule
    There are some important features of MR=MC rule and they can be stated as follows:

• The rule is applied only if producing is preferable to shutting down.
• The rule of profit maximization is applied to all firms whether they are purely competitive, monopolistic, monopolistically competitive, or oligopolistic.
• In pure competitive market our rule is transformed into P=MC, because demand faced by this seller is perfectly elastic. In this case marginal cost is equal to marginal revenue. So only in pure competitive market we may substitute P (price) instead of MR.

Profit Maximization Rule   
   How to determine the profit maximization output? It’s quite easy, all output values for which marginal revenue is greater than marginal cost add to total revenue, so the maximizing output is the last value for which marginal revenue is bigger than marginal cost. In Short Run the firm produces its goods until total revenue is greater than negative Average fixed Cost, however, if it is smaller, then it is better to shut down. Take care, “shut down” doesn’t mean to get off from market, because in short run a firm can’t leave the market.
   An example of Total Revenue and Total Cost -Quantity Demanded Graph(maximum economic profit is taken randomly, since no values are present) :

Short Run Production Costs

   Production information must contain resource prices in order to determine total and per unit price of diverse amount of output. It’s known that in short run prices are associated with plant’s variable resources. Its capital resources are limited so we shouldn’t consider them. Short run costs can be either variable or fixed. So let’s describe them:
Fixed Cost: these costs don’t vary with changes in output. These costs must be paid even if the firm doesn’t produce anything. Such costs may be: rental payments, interests of firm’s debts, money paid for insurance. These costs are paid even when the firm has zero output, so firm can’t avoid paying these costs.
Variable Cost:
 These costs vary with the change in output. They include payment for raw material, fuel, wages, transportation prices, fuel etc. These payments vary directly with output. As the production begins variable costs will increase by a decreasing amount, but after a point they will rise by an increasing amounts (as a result of law of diminishing marginal returns) also this reason lies in the shape of Marginal Product (MP) curve, which is increasing with smaller and smaller amounts and when diminishing returns are encountered marginal product begin to decline, so larger and larger amounts of variable resources are needed to produce a successive unit of output. Total variable cost then is increasing by an increasing amount.
Total Cost:
Economists call sum of fixed costs and variable costs as total costs. At zero unit of output total costs are equal with fixed costs. Graphically, amount of vertical Total Fixed Cost (TFC) summed with vertical value of Total Variable Cost (TVC) should result in Total Cost (TC).
For business manager these distinctions between fixed and variable costs are very important. Variable costs can be controlled or changed by changing production levels in short-run. However, fixed costs are beyond control of business manager, because they are included in short run and must be paid regardless the output level. In short run firms can’t get out of industry and leave the market.

 Per-unit and Average Costs:
 Average fixed cost (AFC) is found by dividing total fixed cost by output quantity (Q):

Because Total fixed Cost by definition is the same regardless of output, then AFC curve will decline as output increases,because as output quantity increases Total Fixed Cost (TFC) is spread over a larger output produced. Q≠0.

Average Variable Cost (AVC): for any output quantity (Q≠0) is calculated by dividing Total Variable Cost (TVC) by Quantity output (Q):

As added more variable resources increase output, average variable cost (AVC) declines initially, reach a minimum and then increases again, so AVC curve is U shaped. It can be explained by the fact that AVC (also TVC) curve reflects law of diminishing returns.

  To explain in simple terms, at very low levels of output, production is inefficient because of high-costs and low quantity produced. Initially, since firm is understaffed, average variable cost is relatively high. As output expands greater level of specialization, greater division of labor and better use of firm’s capital occurs. However, when we still add more variable resources, a point is reached when diminishing returns are incurred. Also the firm is being overstaffed so each additional unit of variable resource doesn’t increase marginal product (MP) as before.

ATC
    Average Total Cost (ATC) for any output level is found by dividing Total Cost (TC) by output (Q) or by adding average variable cost (AVC) and average fixed cost (AFC):

Graphically ATC can be found by adding vertically average variable cost (AVC) and average fixed cost (AFC). Q≠0. 

Marginal Cost
  Marginal Cost is the additional cost of producing one more unit of output. Marginal cost can be found by following formula:

Marginal Cost is important for firm’s managers because a firm can control it immediately. It is used to find the cost of production of an additional product, so it helps to save some money if the firm doesn’t produce this unit (because of the loss that may occur at production).