Chapter 10 The Price-Taking Firm
A price-taking firm chooses its actions under the assumption that it cannot influence the prices of the output that it sells or the inputs that it buys.
We examine the behavior of price-taking firms because:
1. Many firms are price-takers – no single cherry farmer can influence the price of cherries, nor the price of tractors.
2. We can summarize a price-taking firm's behavior entirely in terms of its supply curves in product markets and its input demand curve in factor markets.
3. It is particularly easy to analyze a price-taking firm's input and output choices.
Supply in Product Markets
Two Rules for Profit Maximization
1. Marginal Output Rule: If the firm does not shut down, then it should produce at an output level where marginal revenue is equal to marginal cost.
2. Shut-Down Rule: If for every choice of output level the firm's average revenue is less than its average economic cost, then the firm should shut down.
A price-taking firm's marginal revenue is always equal to the price that it takes as given – it is perfectly elastic at that price (horizontal line). The demand, marginal revenue (MR) and average revenue (AR) curves are all equal to the price.
Marginal Output Rule for a Price-Taker: If a firm takes the price of its output as given, then unless the firm shuts down entirely, it should produce output at a level where the price is equal to marginal cost.
Shut-Down Rule For a Price Taker: If the firm takes the price of its output as given and this price is less than average economic cost for every output level, then the firm should shut down.
The Long and the Short of the Matter
The short run is a period over which only one factor is variable. The long run is a period over which all factors are variable. These conditions result in different cost curves and different outcomes for the marginal output and shut-down rules.
The Firm's Short-Run Supply Curve
A price-taking firm's short-run supply curve coincides with the vertical axis at prices less than the minimum of its short run average variable cost. The short-run supply curve coincides with the firm's short run marginal cost curve where it is above the firm's short-run average variable cost curve.
Note that a firm may produce a product even when it is suffering short-run accounting losses – when revenues are less than its short-run total costs (including fixed and variable inputs).
Deriving a Firm’s Long-Run Supply Curve
A price-taking firm's long-run supply curve coincides with the vertical axis at prices less than the minimum of its long-run average cost. The long-run supply curve coincides with the firm's long-run marginal cost curve where it is above the firm's long-run average cost curve.
Comparison of the Firm’s Short- and Long-Run Supply Curves
1. In the short run, some factors are fixed and expenditures on these fixed factors are not short-run economic costs. In the long run, all factors are variable and expenditures on them are economic costs.
2. In the long run, the firm has opportunities to substitute one factor for another. In the short run, it does not.
Because the firm has more opportunities to make adjustments, the long-run supply curve is more price elastic than is the short-run supply curve.
Long-run marginal cost is equal to short-run marginal cost when the level of capital is fixed at its long-run equilibrium – i.e. the firm uses the same input combination in both the short and long-runs. (In this case, they have the same marginal physical product of labor, and the marginal cost – w/MPPL – is the same.)
If the output price changes after the long-term plans are made (after a factory is built, for example), then the firm will have to adjust its output level, using the short-run curve (which will not include the fixed cost of the already-built-factory).
10.2 Factor Demand
A firm's demand for an input is known as derived demand because it depends on, or is derived from, the demand for the firm's output.
Short-Run Factor Demand
The firm should hire an input just up to the amount at which the marginal benefit to the firm is equal to the marginal cost.
The Marginal Benefit of an Input
The marginal revenue product is the change in revenue due to the sale of the additional output contributed by the hiring of one additional factor.
To find the marginal revenue product of an input, simply multiply its marginal physical product by the marginal revenue associated with each unit of input. For labor, this would be: MRPL=MPPL*MR
For a price-taking firm, a factors' marginal revenue product is equal to its marginal physical product multiplied by the price of output. MRPL=MPPL*p
(Where p is the price of the output)
The Marginal Cost of an Input
The marginal revenue cost is the increase in the firm's total expenditures on inputs when it hires one more unit of a factor.
For a price taker in an input market, the marginal factor cost is equal to the price of a factor.
The Profit-Maximizing Input Level
Factor Hiring Rule: A profit-maximizing firm should hire a factor up to the point at which its marginal revenue product is equal to the marginal factor cost (MRP=MFC)
The marginal output rule provides one way of calculating the profit-maximizing output level. But the factor hiring rule provides another.
Factor Hiring Rule: Firm should hire input up to level where MRP=MFC;
MRP=MPP*MR, so MPP*MR=MFC
Marginal Output Rule: Firm should choose an output level at which MR=MC;
MC=MFC/MPP, so MR=MFC/MPP
Factor Hiring Rule for a Price-Taker: For a price-taking firm, marginal revenue product is equal to the marginal physical product times the output price (p), and marginal factor cost is equal to the input price (w). Therefore, a firm that is a price-taker in both the factor market and the output market maximizes its profit by hiring a factor up to the point at which marginal physical product times the output price is equal to the input price, or MPP*p=w
The short-run derived demand curve for a firm that is a price-taker in the market for the variable input coincides with the firm's marginal revenue product curve for that factor.
The output effect is the change in quantity demanded of an input due to a change in the firm's output level that results from an increase in the input's price. (For example, a higher input price leads to a lower output and therefore less of the input being demanded – so the input demand curve slopes downward.)
Long-Run Factor Demand
In the long-run, in addition to the output effect, we must consider the factor substitution effect. The factor substitution effect is the reduction in the quantity demanded of an input that results from the firm's substituting away from that factor when its price rises.
Factor Substitution Effect: When the price of one factor rises relative to the other, the firm substitutes away from the factor whose price has risen and replaces it with the factor whose relative price has fallen (as long as it is possible for the firm to substitute one input for the other in production).
Output Effect: In the long run, the output effect may be either positive or negative. (e.g. A manufacturer is planning to scrap its current factory and build a new factory in order to increase its production level. If the increase in output is substantial, then the firm may choose to build a highly automated factory requiring almost no workers. Thus, even though output has increased, the quantity of labor hired will go down.)
Factor Substitution and Output Effect Simultaneously
When the price of a factor rises, the quantity of that input demanded falls – the sum of the factor substitution effect and the output effect is always negative. A profit-maximizing firm would never increase its use of an input in response to an increase in that input's price.
Algebraic Approach – Analyzing Long-Run Factor Demand
Applying the factor hiring rule to each input, the firm's quantities of labor and capital must satisfy: p*MPPL=w and p*MPPK=r
Divide the first equation by the second to get: MPPL/MPPK=w/r
This tells us that the marginal physical product of each input should be proportional to its marginal factor cost at the margin.
Investment and the Demand of Capital
The firm should invest in a project if and only if it has a nonnegative net present value.
The higher the interest rate, the lower the present value of any given machine, and the fewer the number of machines that will have a positive net present value. Hence, as the interest rate rises, the number of machines demanded falls, all else equal.