The Labor and Land Markets Input Demand: The Labor and Land Markets 10

Demand for Inputs: A Derived Demand is demand for resources (inputs) that is dependent on the demand for the outputs those resources can be used to produce. Inputs are demanded by a firm if, and only if, households demand the good or service produced by that firm.

Complementary and Substitutable Inputs: Complementary and Substitutable The productivity of an input is the amount of output produced per unit of that input. Inputs can be complementary or substitutable. This means that a firm’s input demands are tightly linked together.

Marginal product of labor (MPL ) Diminishing Returns Faced with a capacity constraint in the short-run, a firm that decides to increase output will eventually encounter diminishing returns. Marginal product of labor (MPL ) is the additional output produced by one additional unit of labor.

Diminishing Returns Marginal Revenue Product per Hour of Labor in Sandwich Production (One Grill) (1) Total Labor Units (Employees) (2) Total Product (Sandwiches per Hour) (3) Marginal Product Of Labor (MPL) (Sandwiches per Hour) (4) Price (PX) (Value Added per Sandwich)a (5) Marginal Revenue Product (MPL X PX) (per Hour) - 1 10 $ 0.50 5.00 2 25 15 7.50 3 35 4 40 5 2.50 42 1.00 6 aThe “price” is essentially profit per sandwich.

Marginal Revenue Product The marginal revenue product (MRP) of a variable input is the additional revenue a firm earns by employing one additional unit of input, ceteris paribus. MRPL equals the price of output, PX, times the marginal product of labor, MPL.

Under diminishing returns, both MPL and MRPL eventually decline. Marginal Revenue Product Per Hour of Labor in Sandwich Production (One Grill) MRPL = PX  MPL When output price is constant, the behavior of MRPL depends only on the behavior of MPL. Under diminishing returns, both MPL and MRPL eventually decline.

A Firm Using One Variable Factor of Production: Labor A competitive firm using only one variable factor of production will use that factor as long as its marginal revenue product exceeds its unit cost. If the firm uses only labor, then it will hire labor as long as MRPL is greater than the going wage, W*.

The hypothetical firm will demand 210 units of labor. Marginal Revenue Product and Factor Demand for a Firm Using One Variable Input (Labor) The hypothetical firm will demand 210 units of labor. W* =MRPL = 10

Short-Run Demand Curve for a Factor of Production When a firm uses only one variable factor of production, that factor’s marginal revenue product curve is the firm’s demand curve for that factor in the short run.

Comparing Marginal Revenue and Marginal Cost to Maximize Profits Assuming that labor is the only variable input, if society values a good more than it costs firms to hire the workers to produce that good, the good will be produced. Firms weigh the value of outputs as reflected in output price against the value of inputs as reflected in marginal costs.

The Two Profit-Maximizing Conditions The two profit-maximizing conditions are simply two views of the same choice process.

The Trade-Off Facing Firms Firms weigh the cost of labor as reflected in wage rates against the value of labor’s marginal product. Assume that labor is the only variable factor of production. Then, if society values a good more than it costs firms to hire the workers to produce that good, the good will be produced.

A Firm Employing Two Variable Factors of Production Land, labor, and capital are used together to produce outputs. When an expanding firm adds to its stock of capital, it raises the productivity of its labor, and vice versa. Each factor complements the other.

Substitution and Output Effects of a Change in Factor Price Response of a Firm to an Increasing Wage Rate Technology Input Requirements Per Unit Of Output Unit Cost if PL = $1 PK = $1 (PL x L) + (PK x K) Unit Cost if PL = $2 PK = $1 (PL x L) + (PK x K) K L A (capital intensive) 10 5 $15 $20 B (labor intensive) 3 $13 $23 When PL = PK = $1, the labor-intensive method of producing output is less costly.

Substitution and Output Effects of a Change in Factor Price Two effects occur when the price of an input changes: Factor substitution effect: The tendency of firms to substitute away from a factor whose price has risen and toward a factor whose price has fallen. Output effect of a factor price increase (decrease): When a firm decreases (increases) its output in response to a factor price increase (decrease), this decreases (increases) its demand for all factors.

This is true in all competitive labor markets. Many Labor Markets If labor markets are competitive, the wages in those markets are determined by the interaction of supply and demand. Firms will hire workers only as long as the value of their product exceeds the relevant market wage. This is true in all competitive labor markets.

Unlike labor and capital, the total supply of land is strictly fixed Land Markets Unlike labor and capital, the total supply of land is strictly fixed (perfectly inelastic).

Demand Determined Price The price of a good that is in fixed supply is demand determined. Because land is fixed in supply, its price is determined exclusively by what households and firms are willing to pay for it. The return to any factor of production in fixed supply is called pure rent.

Land in a Given Use Versus Land of a Given Quality The supply of land in a given use may not be perfectly inelastic or fixed. The supply of land of a given quality at a given location is truly fixed in supply.

Rent and the Value of Output Produced on Land A firm will pay for and use land as long as the revenue earned from selling the output produced on that land is sufficient to cover the price of the land. The firm will use land (A) up to the point at which: MRPA = PA

The Firm’s Profit-Maximization Condition in Input Markets Profit-maximizing condition for the perfectly competitive firm is: PL = MRPL = (MPL X PX) PK = MRPK = (MPK X PX) PA = MRPA = (MPA X PX) where L is labor, K is capital, A is land (acres), X is output, and PX is the price of that output.

The Firm’s Profit-Maximization Condition in Input Markets Profit-maximizing condition for the perfectly competitive firm, written another way is: In words, the marginal product of the last dollar spent on labor must be equal to the marginal product of the last dollar spent on capital, which must be equal to the marginal product of the last dollar spent on land, and so forth.

Input Demand Curves If product demand increases, product price will rise and marginal revenue product will increase.

Input Demand Curves If the productivity of labor increases, both marginal product and marginal revenue product will increase.

Impact of Capital Accumulation on Factor Demand The production and use of capital enhances the productivity of labor, and normally increases the demand for labor and drives up wages.

Shifts in Factor Demand Curves The Demand for Outputs If product demand increases, product price will rise and marginal revenue product (factor demand) will increase—the MRP curve will shift to the right. If product demand declines, product price will fall and marginal revenue product (factor demand) will decrease—the MRP curve will shift to the left. The Quantity of Complementary and Substitutable Inputs The production and use of capital enhances the productivity of labor and normally increases the demand for labor and drives up wages.

Shifts in Factor Demand Curves The Prices of Other Inputs When a firm has a choice among alternative technologies, the choice it makes depends to some extent on relative input prices. Technological Change The introduction of new methods of production or new products intended to increase the productivity of existing inputs or to raise marginal products.

Resource Allocation and the Mix of Output in Competitive Markets marginal productivity theory of income distribution At equilibrium, all factors of production end up receiving rewards determined by their productivity as measured by marginal revenue product.

PROBLEM # 1 The table below shows the number of cakes that could be baked daily at a local bakery, depending on the number of bakers. a. Calculate the marginal product of labor. b. Do you observe the law of diminishing marginal returns? c. Suppose each cake sells for $10. Calculate the marginal revenue product of labor. d. If each baker is paid $80 per day, how many bakers will the bakery owner hire, given that the goal is to maximize profits? How many cakes will be baked and sold each day?

Solution: The marginal product of labor (MPL) is calculated in the third column, using the following formula: MPL = Δ(Number of cakes)/ΔL b. Yes, the marginal product of labor declines as more bakers are hired. c. The marginal revenue product of labor (MRPL) is calculated in the fourth column, using the following formula: MRPL = MPL × P d. If each baker is paid $80 per day, 2 bakers would be hired and 18 cakes would be baked and sold daily.

Fill in the gaps in the table below: PROBLEM # 2 Fill in the gaps in the table below:

Solution:

PROBLEM # 3 Suppose a firm with some market power faces a downward-sloping demand curve for the product it produces. Using the information on demand given in the table below, complete the table.

Solution: