I. Basic Concepts of Input Markets

University of Pacific-Economics 53 Lecture Notes #10 I. Basic Concepts of Input Markets In this lecture we ll look at the behavior of perfectly competitive firms in the input market. Recall that firms demand inputs (land, labor and capital) and we will look at how firms decide how much of each input they want. To start we will introduce several basic concepts that will be useful in our analysis. 1. Demand for inputs is a derived demand. What this means is that the demand for inputs depends on the demand for the output sold. If nobody wants to purchase the firm s product, there will be no need for the firm to demand any labor or capital. On the other hand, if the firm has a product that is in great demand, they will demand more inputs in order to meet the high demand. 2. Productivity of inputs may differ. We define productivity as the amount of output produced per unit of input. If Sam is able to produce 10 widgets while Dan can only produce 5 widgets we say that Sam has a higher productivity than Dan. Some inputs may have high productivity while others may have low productivity. 3. Inputs can be either complementary or substitutes. a. Complements-Two inputs are complements if both are needed to produce an output. For example in order to bus school children you need both a school bus (capital) and a driver (labor). If you only have the school bus you won t produce any service. b. Substitutes-Two inputs are substitutes if one input can be used to replace another. There are cases, which we will soon see, in which capital can be used to replace labor or where labor may be used to replace capital. 4. Inputs exhibit diminishing returns. In earlier chapters we have seen the law of diminishing returns. Increasing the amount of an input in the production process, while holding another input fixed, will increase output but at a decreasing rate. For example, suppose a firm has a fixed level of capital and it starts increasing its workforce. The marginal product of labor (MPL) is the extra output generated by each new worker hired. The law of diminishing returns says that the MPL decreases as labor increases. 5. Firms make input demand decisions based on the marginal revenue product (MRP). The marginal revenue product (MRP) is the extra revenue generated by a firm by employing one additional unit of input, holding all else constant. For example, consider labor. The marginal revenue product of labor is the extra revenue generated by a firm when they hire one more worker. That extra worker will produce some output, the marginal product of labor (MPL). If you multiply the MPL times the price of the output you ll get the marginal revenue product of labor. MRP L = MP L x P Where MRP L = marginal revenue product of labor MP L = marginal product of labor P = price of the output

Let s work through an example: Example: Fred's Pizza Palace sells pizzas in a competitive market. The price of the pizzas is $1.25 each. Complete the table Total Product Marginal Product Marginal Revenue # Workers (pizzas/hour) of Labor Product 0 0 ---- ---- 1 20 2 35 3 47 4 55 5 59 What is the marginal product of labor if the firm decides to hire the 1 st worker? The total output for the firm jumps from 0 to 20. Thus the MPL for the 1 st worker is 20. When the firm hires the 2 nd worker, total output goes from 20 to 35. The extra output generated by the 2 nd worker is 15 which is the MPL and so on. What is the MRP for the 1 st worker? We know that the first worker will contribute 20 units of output for the firm. Since the price of each pizza is $1.25 (very cheap pizzas!) the marginal revenue product will be MRP = 20 x $1.25= $25. The completed table is shown below. Total Product Marginal Product Marginal Revenue # Workers (pizzas/hour) of Labor Product 0 0 ---- ---- 1 20 20 $25.00 2 35 15 $18.75 3 47 12 $15.00 4 55 8 $10.00 5 59 4 $5.00 Figure 1 shows the marginal revenue product curve for the above example.

Figure 1 30 MRP Ouput 25 20 15 10 5 MRP 0 0 1 2 3 4 5 6 Number of Workers Now that you understand MRP we ll now see how firms are able to determine how many workers they wish to hire. First, we ll assume that perfectly competitive firms are price takers in the input markets. Wages are determined in the labor market. Individual firms can hire as many workers as they want at the market real wage. Figure 2 shows the labor market and how wages are determined. Figure 2: The Labor Market We see in Figure 2 that the wages are determined by the supply of labor and the demand for labor. Where the curves intersect is the market wage rate. In this example the market wage rate is $10 an hour. At that wage rate, 560,000 workers will be employed. G

Given that the market wage rate is $10 an hour, how many workers will Fred s Pizza Place want to hire? We can derive Fred s demand for workers using the following marginal revenue product analysis. Should Fred hire the first worker? The first worker will generate revenues of $25, but Fred only has to pay him $10. Thus Fred should definitely hire the 1 st worker. How about the 2 nd worker? The second worker will generate revenues of $18.75 to the pizza place. Again the revenue brought in by the worker is greater than the cost of hiring that worker. Thus Fred should definitely hire the 2 nd worker. The same will hold true for the third and fourth worker. The 4 th worker generates revenue of $10 which is offset by the cost of hiring that worker. We ll assume that when revenues equals the cost the firm will still hire that worker. Should Fred hire the 5 th worker? The fifth worker will generate revenues of $5 to the firm which is less than the cost of hiring the worker. The pizza parlor will lose money by hiring that worker. Thus Fred will not hire that worker and will stop at the 4 th worker. We can see that Fred will stop hiring when the market wage is equal to the MRP. This is true in general **Firms will hire workers until MRP = market wage rate*** Looking back at Figure 1 we can see that the MRP tells us how much labor a firm will hire at each potential market wage rate. We see that if the wage is $25 the firm will hire 1 worker, when the wage rate is $15 it will hire 3 workers, etc Notice that as the wage rate falls the demand for workers will be higher. When the wage rate rises the quantity of labor will fall. This fact leads to a downward sloping demand curve for labor. The above analysis applies for any factor of production, and not just labor. II. Choosing Two Variable Inputs So far we ve looked at a situation where a firm had to decide how much labor to hire holding everything else constant. In that case the decision for the firm was a simple choice of choosing the amount of one input. What if we were to add another input to the firms decision matrix. How would firms decide how much input to demand? Suppose that a firm had to choose the level of capital and labor. Suppose also that the price of capital is P K while the price of labor is P L Suppose that the firm has to choose between two technologies to produce its output. Technology Units of Capital (K) Units of Labor (L) Variable Costs if P L =$1; P K =1 A 300 1000 $1300 B 1000 500 $1500 Variable Costs if P L =$2; P K =1

Technology A is more labor intensive than Technology B. What if the price of inputs were $1 per unit for both capital and labor. The total variable costs using technology A will be (300 x $1) + (1000 x $1) = $1300 while The total variable costs using technology B will be (1000 x $1) + (500 x $1) = $1500 Recall that firms want to minimize costs, so the firm will choose the technology that results in the least-cost which is Technology A. However, what will happen if the price of labor doubles so P L =$2. The total variable costs using technology A will be (300 x $1) + (1000 x $2) = $2300 while The total variable costs using technology B will be (1000 x $1) + (500 x $2) = $2000. The firm now will choose Technology B. As labor costs increase, the firm will move away from the expensive input and substitute labor with capital. Relative input prices are a important determinant of input demand. This fact that we just observed is called the factor substitution effect. The factor substitution effect states that when the price of an input rises, firms have a tendency to substitute away from that factor. Conversely, when the price of an input has fallen, firms will substitute toward that factor. The factor substation effect helps explains why the demand curve for inputs is downward sloping. As the price of labor decreases, firms will substitute away from other factors of production (such as labor) and increase demand for labor. There is another factor behind the downward sloping demand curve. Notice in our example that the least-cost technology before the price of labor increase was Technology A at $1300. After the price increase in labor the least-cost technology was Technology B at $2000. To produce the same amount of output, the cost for the firm has increased and the firm may be losing money. We would expect that most firms will respond by producing less. But recall that demand for inputs is a derived demand. If the firm will be producing less, they ll need less inputs such as capital and labor and thus the demand for both capital and labor will decline due to the increase in the price of labor. This is called the output effect of a factor price increase. A decrease in the price of a factor production will have the opposite effect. The output effect is another explanation behind the downward sloping demand curve. III. Land Markets Much of our analysis of the labor markets can be easily extended to the land markets. The only real difference between land and labor markets is the supply curves. In the land market, we assume that the amount of land is fixed. At any given location, the supply of land is fixed. Thus the supply curve is vertical. See Figure 3 The price of land is demand determined. That is the price of land is determined solely by shifts in the demand curve. Suppose we start at Point A and the price of land is P 0. If demand for land is higher, this will drive up the price of land to Point B. If the demand for land is lower, this will drive down the price of land to Point C. The lesson here is that land will be sold to the user who is willing to pay the most for it.

Figure 3 The demand for land is derived exactly the same as it was for labor. The firm will continue to demand land as long as the marginal revenue product of land is greater than the price of a unit of land. If an extra acre of farmland would generate $50 for the farmer and the price of an acre of land is $40, the farmer should purchase that acre of land. If, on the other hand, the extra acre of farmland would generate only $30, the farmer would not purchase the acre of land. P A = MRP A Where P A = Price of land in acres MRP A = Marginal revenue product of land in acres. IV. Profit-Maximization Rule in Input Markets Although we will talk about the capital market in the next lecture, you can probably guess that the firm will demand capital based on the following rule: P K = MRP K Where P K = Price of capital MRP K = Marginal revenue product of capital. We can look at our three input demand rules for land, labor and capital and derive a general profit maximization rule. (1) P L = MRP L P L = MP L x P

(2) P A = MRP A P A = MP A x P (3) P K = MRP K P K = MP K x P Where P = price of output Doing some rearranging we get (1) P = P L /MP L (2) P = P A /MP A (3) P = P K /MP L Which lead to the following relationship: P = P L /MP L = P A /MP A = P K /MP K The final step is to take the reciprocal of each term to get 1/P = MP L /P L = MP A /P A = MP K /P K This is the profit maximizing rule for input demand. Firms will continue to demand inputs until they reach this equilibrium. Why must this condition hold? Think about what would happen if it did not hold. Suppose that MP L /P L > MP K /P K This inequality implies that if the firm spent an extra $1 on labor as opposed to capital the firm would get more output from labor. Thus the firm will demand more labor and less capital. As demand for labor increases, the marginal product of labor decreases (law of diminishing returns). As the demand for capital decreases, the marginal product of capital increases. This will continue until the ratios are equal. V. Shifts in Input Demand Curves There are several factors that would cause the demand curves for land, labor and capital to shift. These include (1) Demand for Outputs. If the demand for output increases, the firm will demand more units of inputs to meet the higher output demand. At any given input price, the firm will demand more of the input. Thus the demand curve would shift to the right. (2) Quantity of Complementary and Substitutable Inputs. Suppose that a school district has 5 new school buses to transport children. Those buses will be useless unless they hire 5 new drivers. Thus for complementary inputs, if there is an increase in the number of one of the inputs, this will increase the demand for its complement. As another example suppose that a textile firm can either use labor to cut cloth or a cutting machine. If the firm were to get a whole shipment of cutting machines, that will reduce its demand for labor. Thus for substitutable inputs, if there is an increase in the quantity of one of the inputs, this will decrease the demand for its substitute. (3) The Price of Other Inputs. An increase in the price of one input, may lead firms to substitute away from that input and towards another. The demand for that other input will increase as this occurs. (4) Technological Change. Technological change means that new methods of production are now available that allows firms to be able to produce more output using the same

amount of input as before. The marginal product of input will be greater. Each unit of input will be able to generate more revenue for the firm than before which should increase the demand for inputs.