Factor Markets: Derived Demand and Marginal Revenue Product

Labor demand is a derived demand, which means firms want workers not for their own sake but for the output those workers help produce and sell. The number of workers a firm hires is set by comparing the extra revenue one more worker brings in, called marginal revenue product (MRP), to the extra cost of that worker, called marginal resource cost (MRC), and hiring stops where MRP equals MRC. In a competitive labor market that stopping point is where MRP equals the wage.

This is AP Microeconomics Unit 5, and it reuses one idea you already know: keep doing something as long as the marginal benefit is at least as large as the marginal cost. In output markets you learned firms produce where marginal revenue equals marginal cost. In factor markets the same logic points at inputs instead of output, so the "marginal benefit" of a worker is the revenue that worker generates and the "marginal cost" is what the firm pays to employ them. If you can graph and explain that one comparison, most of this unit falls into place. You can build the labor-market diagram step by step in the factor markets sandbox.

Why labor demand is derived

Households own the four factors of production (land, labor, capital, and entrepreneurship) and sell them in factor markets. Firms buy those factors and pay rent, wages, interest, and profit. Notice the roles flip from the product market you studied earlier: in output markets firms are the sellers and households are the buyers, but in factor markets firms are the buyers and households are the sellers.

Because a firm only wants labor to make a product it can sell, the demand for labor is derived from the demand for that product. If demand for smartphones rises and their price goes up, firms that assemble phones will want more assembly workers even though nothing changed about the workers themselves. If phone demand collapses, so does demand for those workers. This is the single most important sentence in the unit, and graders reward you for saying it explicitly on the free-response section: labor demand is a derived demand.

Marginal revenue product: the formula

Marginal revenue product (MRP) is the additional revenue a firm earns from hiring one more unit of a resource. It is built from two pieces you already know:

• Marginal product (MP) is the extra output one more worker produces, measured in units of the good.
• Marginal revenue (MR) is the extra revenue from selling one more unit of output, measured in dollars.

Multiply them: MRP equals marginal product times marginal revenue. Marginal product is measured in physical units and MRP is measured in dollars, so the multiplication converts extra output into extra money. You can check your arithmetic on the MRP calculator.

Here is the shortcut that trips students up. If the firm sells in a perfectly competitive output market, its marginal revenue equals the market price, because it can sell every unit at that going price. In that case MRP equals marginal product times price, and economists call this the value of the marginal product. If the firm is instead a price maker (a monopoly, monopolistic competitor, or oligopolist), it must lower price to sell more, so its marginal revenue is below price. Then you must use MRP equals MP times MR, not MP times price. A price-making firm's MRP curve falls faster, because MRP drops both from diminishing marginal product and from a falling MR.

The MRP curve slopes downward because of the law of diminishing marginal returns: as the firm adds workers, each extra worker eventually adds less output than the one before, so marginal product falls and MRP falls with it. For a price maker, the decline is steeper still, because a falling MR pushes MRP down on top of diminishing returns. That downward-sloping MRP curve is the firm's labor demand curve. Sketch it against a wage line in the factor markets sandbox and watch hiring change as the wage moves.

The hiring rule: MRP equals MRC

A firm keeps hiring as long as each new worker adds at least as much revenue as they cost. Formally, hire while MRP is greater than MRC, and stop where MRP equals MRC. Overshooting that point means the last worker cost more than they brought in, which shrinks profit; stopping short means the firm left profit on the table by not hiring a worker who would have paid for themselves.

Marginal resource cost (MRC) is the cost of employing one more unit of a resource. In a perfectly competitive labor market, the firm is a wage taker: it is so small relative to the market that it can hire all the workers it wants at the going wage without bidding the wage up. So each additional worker costs exactly the market wage, which means MRC equals the wage. The firm's individual labor supply curve is a flat horizontal line at that wage.

Put the two pieces together. In a competitive labor market the profit-maximizing rule MRP equals MRC becomes MRP equals the wage. Graphically, you draw the downward-sloping MRP (labor demand) curve and a horizontal wage line, and the firm hires the quantity of labor where they cross. Raise the wage and the horizontal line shifts up, cutting the MRP curve at a smaller quantity, so employment falls. That is why labor demand slopes downward: a higher wage means fewer workers are worth hiring.

The wage itself is set in the overall market by the intersection of market labor demand (the sum of all firms' MRP curves) and market labor supply (the sum of all workers willing to work at each wage). An individual competitive firm takes that wage as given and simply reads its own hiring off its MRP curve.

Least-cost rule versus profit-maximizing rule

When a firm uses more than one input, say labor and capital, two related rules govern the mix. Keep them separate on the exam, because they answer different questions.

The least-cost rule answers "what input mix produces a given output at the lowest cost?" A firm minimizes cost when the last dollar spent on each input yields the same extra output. That means the marginal product per dollar is equal across inputs: the marginal product of labor divided by the price of labor equals the marginal product of capital divided by the price of capital. If labor gives more output per dollar than capital, shift spending toward labor until the ratios equalize.

The profit-maximizing rule answers "what quantity of each input maximizes profit?" It is stricter. Not only must the marginal product per dollar be equal across inputs, but the marginal revenue product per dollar spent on each input must equal one. Written out, MRP of labor divided by the price of labor equals MRP of capital divided by the price of capital, and both equal one. Setting the ratio to one is the same as saying MRP equals input price for each factor, which is just the MRP-equals-MRC hiring rule applied to every input at once.

The relationship is a nesting one: every profit-maximizing input combination is also least-cost, but not every least-cost combination maximizes profit. A firm can produce some output as cheaply as possible and still be producing the wrong amount. Profit maximization pins down both the mix and the scale.

What shifts labor demand and labor supply

Because MRP is the labor demand curve, anything that changes MRP shifts labor demand. The main determinants are:

• Demand for the product. Since labor demand is derived, a rise in demand for the good raises its price and marginal revenue, which raises MRP and shifts labor demand right. A fall does the opposite.
• Worker productivity. Better training, or technology and capital that make existing workers more productive, raises marginal product, raising MRP and shifting labor demand right. Watch the direction, though: labor-substituting technology that replaces workers instead of complementing them can lower marginal product for those workers and shift labor demand left, the same substitution effect described in the next bullet.
• Prices of other resources. If capital and labor are substitutes, cheaper capital can lower labor demand as firms swap machines for workers. If they are complements, cheaper capital can raise labor demand because the two are used together.
• Number of buyers of the resource. More firms competing to hire increases market labor demand.

Labor supply shifts for reasons that change how many people are willing to work at each wage:

• Population and immigration. More available workers shift labor supply right.
• Migration between markets. Workers moving into a region or occupation increase its supply.
• Preferences and other opportunities. Better pay or conditions in a competing occupation pull workers away, shifting this market's supply left. Changing social norms about who works can shift it right.
• Skills and education. Training changes how many workers qualify for a given labor market.

A clean way to check yourself: a change in the wage moves you along a fixed curve, while a change in any determinant shifts the whole curve. Practice distinguishing shifts from movements in the factor markets sandbox, and if a term is fuzzy, look it up in the glossary.

How this connects to the rest of AP Micro

Factor markets are where the theory of the firm gets reused, so the concepts you carry in matter. Marginal product comes straight from the production and cost material, marginal revenue depends on the market structure you studied in Units 3 and 4, and the whole unit is another application of marginal analysis. If MP and MR are shaky, review the microeconomics hub before pushing further into factor markets. Once the competitive labor market is solid, you are ready for monopsony, where a single dominant employer faces an upward-sloping labor supply curve and MRC rises above the wage, breaking the tidy MRP-equals-wage result you learned here.