Business Economics The Behavior of Firms

Assumption: Profit Maximization Problem: You have 6 acres of land and you are deciding how many acres to spray with insecticide-Variable costs but no fixed cost Acres Sprayed Total Benefit Total Cost Net Gain Marginal Benefit Marginal Cost - 6 3 1 6 3 3 2 11 6 5 5 3 3 15 9 4 18 12 5 20 6 21 6 5 3 4 3 2 1 Note that benefit is defined as revenue and not as profits. Suppose that you have 6 acres of land planted with wheat and you are deciding how many of them to spray with insecticide. If you do not spray any of them the insects destroy all your plantation. The cost of spraying is $3 per acre. If you spray one acre you save $6 worth of crops and your cost is $3. If you spray an additional acre, your total benefit is $11 and your total cost is $6. Note that the second acre that you spray is less fertile than the first one because on that acre you get $5 worth of crops instead of $6. If you decide to spray exactly one acre you might (should) decide to spray the most fertile one instead of choosing one random acre. The marginal benefit on that second acre is $5 and the marginal cost is $3. What is the optimal number of acres you should spray if the goal is to maximize profits?

Profit Maximization Total Benefits 6 6 Total Cost The firm maximizes profits when the distance between total benefits and total costs is highest.

Profit Maximization Marginal Benefit Marginal Cost Marginal costs are constant at $3 per acre. The firm produces a quantity at which the amount it adds to it benefits and the amount it adds to it costs is the same. Below that quantity it is adding more to benefits than to costs. Above that quantity it adds more to costs than to benefits.

Profit Maximization Total Benefit=5+10ln(acre) Marginal Benefit=10/acre Total Cost=3(acre) Marginal cost=3 Marginal Benefit=Marginal Cost 10/acres=3 acres=10/3 Net Gain=Total Benefit-Total Cost Choose acre to: Max{Net Gain}=Max{5+10ln(acre)-3(acre)} First Order Condition (10/acre)-3=0 Second Order Condition -10/(acre^2)<0

Maximizing Profits Total Benefits Max Total Costs Net Gain

Maximizing Profits Marginal Benefits= 10/acres Marginal Costs=3

Profit Maximization Fix Cost of $4 Acres Sprayed Total Benefit Total Cost 4 Net Gain -4 Marginal Benefit Marginal Cost - 6 3 1 6 7 -1 2 11 10 3 15 13 4 18 16 5 20 19 6 21 22 1 2 -1 5 3 4 2 1 There is a fixed cost of $4. Marginal costs and marginal benefits do not change and therefore there is no change in the optimal amount of production (given that it is worth to produce at all). The change in fixed costs will not affect the optimal choice (if it does not make the activity not worth at all). Note, however, that the net gain is smaller.

Profit Maximization

Profit Maximization Marginal Benefit Marginal Cost Marginal cost is constant at $3 per acre.

Profit Maximization Fix cost of $10 Acres Sprayed Total Benefit Total Cost 10 Net Gain -10 Marginal Benefit Marginal Cost - 6 3 1 6 13 -7 2 11 16 3 15 19 4 18 22 5 20 25 6 21 28 -5 -4 -7 5 3 4 2 1 There is a fixed cost of $10. Marginal costs and marginal benefits do not change. However, it is not worth to produce at all. The net gain is negative for every quantity.

Profit Maximization

Marginal Rule If it is worth to produce at all, then it should be produced up to the point where marginal costs are equal to marginal benefits

Revenues Revenues= Price X Quantity Price Quantity Demanded Total Revenue $10 1 9 2 18 8 3 24 7 4 28 6 5 30 Revenues= Price X Quantity Before we assumed that the price of crops was fixed and that you could only save some crops from the insects and sell them at the market price which was out of your control. Some firms face a demand function and can actually set the price. However, notice that firms can either set prices or they can set quantities. Once one of these variables is chosen, the other variable is given by the demand curve.

Revenue Price Should firms maximize revenues? D2 P P’ Q Q’ Quantity

Profit Maximization Price Quantity Total Revenue Marginal Revenue $10 $10 1 10 9 2 18 8 3 24 6 7 4 28 5 30 -2 -4 Total Cost Marginal Cost Profit 2 3 1 7 5 13 8 16 12 4 17 23 6 30 -2 38 -14 Firms decide to choose prices or quantities in order to maximize profits. There is a fix cost of 2.

Change on Fixed Costs Total Cost 3 Total Cost 2 Total Costs $ Total Revenue Total Cost 1 A change on fixed costs does not change the optimal quantity of production (unless the new total cost curve is above the total revenue curve for every production quantity in which case the firm does not produce at all). Fixed Cost 2 Fixed Cost 1 Quantity Q*

Change on Variable Costs Total Cost 2 Total Costs $ Total Cost 1 Total Revenue A change on variable costs affects the optimal production quantity. Fixed Cost Quantity Q** Q*

Marginal Costs and Revenues $ per (last) unit Marginal Revenue Marginal Cost 1 A change in variable costs affects the optimal production quantity. A change in fixed costs does not affect the marginal cost (except for the cost at zero) and therefore does not affect the optimal production quantity (if it is worth for the firm to produce at all!). Q** Q* Quantity

Fixed Costs & Sunk Costs We will call fixed costs to costs that do not change with the level of production and are avoidable by closing the firm (exit the market). Sunk costs are costs that do not change with the level of production and are not avoidable by closing the firm. Sunk costs cannot be recouped by closing the firm. For example, if the firm has already paid the rent for the next year, that cost (that was fixed before paying it because it did not change with the level of production) is a sunk cost. The economic implication is that sunk costs should not be added to costs in the computation of profitability when the firm decides whether to exit the market. The firm may be unprofitable if sunk costs were added to costs but profitable if these costs are not added to costs. The firms should stay in the market, if this is the case, because these sunk costs cannot be recouped by exiting the market.