Marginal Revenue Product and Value of Marginal Product

TL;DR

Marginal Revenue Product (MRP) measures the extra revenue a firm gets from hiring one more unit of a resource, while Value of Marginal Product (VMP) is the additional revenue from selling the output of one more resource unit assuming perfect competition. MRP considers market power, while VMP does not. Both help firms decide how many resources to hire to maximize profit.

1. The Mental Model

Imagine you're running a business and considering hiring another worker or buying another machine. You want to know how much extra money that new worker or machine will bring in. That's what MRP and VMP help you figure out.

2. The Core Material

In economics, firms decide how much of a resource (like labor or capital) to hire by comparing the cost of that resource to the benefit it brings. The benefits are measured by Marginal Revenue Product (MRP) and Value of Marginal Product (VMP).

What's Marginal Revenue Product (MRP)?

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Marginal Revenue Product (MRP) is the additional revenue a firm earns from hiring one more unit of a variable input (like labor). It's calculated as the product of the Marginal Product of Labor (MPL) and the Marginal Revenue (MR) the firm receives from selling the extra output.

• MRP = MPL × MR

MPL is the extra output produced by one more unit of labor. MR is the additional revenue from selling one more unit of output.

MRP is the more general concept and applies to all market structures (perfect competition, monopoly, oligopoly, monopolistic competition).

What's Value of Marginal Product (VMP)?

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Value of Marginal Product (VMP) is the additional revenue a firm earns from hiring one more unit of a variable input assuming the firm sells its output in a perfectly competitive market. In a perfectly competitive market, the firm is a price taker, meaning Marginal Revenue (MR) is equal to the market price (P) of the good.

• VMP = MPL × P

Since MR = P in perfect competition, in this specific market structure, MRP = VMP. However, for firms with market power (like monopolies), MR < P, so MRP < VMP.

The Hiring Rule

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Firms will continue to hire additional units of a resource as long as the additional revenue generated by that resource (MRP) is greater than or equal to the additional cost of hiring it (the wage rate for labor, or rental rate for capital).

• Hire until MRP = Wage Rate (or Factor Price)

How MRP and VMP Relate

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This diagram shows how MRP and VMP are related and how they guide hiring decisions.

graph TD
    A["Firm's Decision: How much resource (e.g., labor) to hire?"] --> B{"Market Structure?"}

    B -- "Perfect Competition" --> C["MR = P (Market Price)"]
    B -- "Imperfect Competition (Monopoly, Oligopoly)" --> D["MR < P (Marginal Revenue < Price)"]

    C --> E["Value of Marginal Product (VMP)"]
    D --> F["Marginal Revenue Product (MRP)"]

    E -- "VMP = MPL x P" --> G["Resource Hiring Rule: VMP = Wage Rate"]
    F -- "MRP = MPL x MR" --> G

    G --> H["Profit Maximization"]

3. Worked Example

Let's say you own a small t-shirt printing business.

If the daily wage you have to pay a worker is $70:

• For the 1st worker: MRP ($160) > Wage ($70). Hire!
• For the 2nd worker: MRP ($105) > Wage ($70). Hire!
• For the 3rd worker: MRP ($60) < Wage ($70). Don't hire this worker, as they'd bring in less revenue than they cost.

So, you'd hire 2 workers to maximize your profit, as the MRP of the 2nd worker ($105) is greater than the wage ($70), but the MRP of the 3rd worker ($60) is less than the wage ($70). Notice how VMP is always higher than MRP in this example because MR < P (due to market power). If you operated in perfect competition and could sell all shirts for $10 (so MR was also $10), you'd hire 3 workers because VMP for the 3rd worker ($100) is still greater than the wage ($70), but VMP for the 4th worker ($50) is less than the wage.

4. Key Takeaways

• MRP measures the extra revenue from hiring one more unit of a resource, calculated as MPL × MR.
• VMP measures the extra revenue from hiring one more unit of a resource when selling output in perfect competition, calculated as MPL × P.
• For a perfectly competitive firm, MR = P, so MRP = VMP.
• For a firm with market power, MR < P, so MRP < VMP.
• Firms maximize profit by hiring resources until the MRP of the last unit hired equals the resource's cost (e.g., wage rate).
• The law of diminishing marginal returns means that MPL, and therefore MRP/VMP, will eventually decrease as more units of a variable input are added.

Common mistakes you should avoid:
- Confusing MRP and VMP, especially assuming they are always equal.
- Forgetting that VMP only applies directly to perfectly competitive output markets.
- Not understanding that the firm's decision rule (MRP = factor price) comes from profit maximization.
- Mixing up Marginal Product (MPL) with Marginal Revenue Product (MRP).

5. Now Try It

Imagine you manage a pizza shop. A new oven costs $500 per month to rent. Using this new oven, you can make an extra 100 pizzas a month. Each pizza sells for $12, but because you have a popular brand, you know that to sell more, you'll have to slightly drop your effective price for all pizzas, so your marginal revenue from selling these extra pizzas is $10 per pizza.

Calculate the Marginal Revenue Product (MRP) of the new oven and the Value of Marginal Product (VMP) of the new oven. Based on your calculations, should you rent the new oven? What if your firm was in a perfectly competitive market and could sell all extra pizzas at $12 each? What's your decision then?