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Fixed Inputs and Diminishing Marginal Product
In production processes where some inputs, such as land or machinery, are fixed, adding more of a variable input like labor causes total output to increase at a slower and slower rate. This relationship results in the slope of the production function gradually decreasing as more labor is utilized, a key economic principle known as diminishing marginal product.
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Increasing Nature of the Production Function
Fixed Inputs and Diminishing Marginal Product
General Production Function of a Farmer (y=g(h))
A production function describes the relationship between a variable input (X) and the resulting total output (Y), for non-negative values of X. For this relationship to be economically plausible, it must satisfy two key conditions: 1) Zero input results in zero output, and any positive input yields a positive output. 2) The function must be consistently increasing, meaning more input always leads to more output. Based on these conditions, which of the following mathematical expressions could NOT represent a plausible production function?
Plausibility of a Production Model
A relationship between a single input (X) and total output (Y) must meet two core conditions to be considered an economically plausible production model: 1) Output is zero if input is zero, and positive for any positive input. 2) Output consistently increases as input increases. Analyze each mathematical function below (assuming X ≥ 0) and match it to the description that correctly explains its plausibility.
Plausibility of a Proposed Production Function
Consider a production process where the relationship between a single input (X, where X ≥ 0) and total output (Y) is described by the equation Y = -X² + 10X. This equation represents a plausible production function for all positive values of input X because it shows that adding more input initially leads to a significant increase in output.
Evaluating a Production Model's Plausibility
Economic Rationale for Production Model Properties
Critique of a Proposed Production Model
A production process is described by the relationship between a single input (X) and the total output (Y), where X ≥ 0. For this relationship to be considered a viable model of production, it must satisfy two fundamental properties: 1) no input produces no output, and any positive amount of input produces a positive amount of output; 2) the total output must consistently rise as more input is used. Given these properties, which of the following equations represents a plausible production function for all positive values of the input?
Critiquing and Correcting a Production Model
Learn After
A small farm has a fixed amount of land and one tractor. The table below shows the total bushels of corn harvested per season as more farmhands are hired. Analyze the data to determine after which farmhand is hired the farm first experiences diminishing marginal product.
Number of Farmhands Total Bushels Harvested 1 100 2 220 3 360 4 480 5 550 Coffee Shop Productivity
The Logic of Production Constraints
A company operating a factory with a fixed number of machines finds that as it hires more workers, each additional worker contributes less to the total production than the previous one. This situation implies that hiring another worker will cause the factory's total output to fall.
Explaining Production Bottlenecks
A bakery has a single oven (a fixed input) and hires bakers (a variable input). As more bakers are hired, they begin to get in each other's way, leading to each additional baker contributing less to the total number of loaves produced than the one before. Which of the following graphs, with the number of bakers on the horizontal axis and the total loaves produced on the vertical axis, best illustrates this production process?
A pizza parlor has one large oven. The owner wants to understand their production process. Match each element of the pizza parlor's operation to the correct economic term.
In a production process with at least one fixed input, the principle that states that adding more units of a variable input will eventually result in smaller and smaller increases in total output is known as the law of ____.
T-Shirt Shop Production Analysis
Critiquing a Manager's Decision