under what conditions an econoy would be operating inside its production possibility frontier?
When the Opportunity Cost or the tradeoff between the two goods is always at a constant rate.
On a Production Possibility Frontier (PPF), a bowed-out shape is more natural and realistic than a linear one. This curvature reflects the principle of increasing opportunity costs, where reallocating resources to produce more of one good results in progressively larger sacrifices of the other good. As resources are not perfectly adaptable for the production of both goods, the bowed-out shape illustrates the diminishing returns encountered in resource allocation, making it a more accurate representation of real-world production scenarios.
The production possibility curve is not always linear, in fact, it is usually concave down (bowed-in). The shape of the curve depends on the substutability of the goods described by the curve in the question. When goods are perfectly substitutable in production, the PPP (or PPF) is linear.
Linear isoquant [perfect substitutability of factors of production], Input-output isoquant or Leontif isoquant [no substitution or strict complementarity; only one efficient method of production] are exceptions to isoquant convexity to the origin. Kinked isoquant is of limited substitutability at kinks. But if kinks come closer and closer, it will become a smooth curve, convex to the origin.
A linear production possibility curve (PPC) implies constant opportunity costs, meaning that the trade-off between two goods remains the same regardless of how much of each good is produced. This suggests that the inputs to production can be easily substituted for one another without losing efficiency. In contrast to a concave PPC, which indicates increasing opportunity costs, a linear PPC reflects a scenario where resources are perfectly adaptable for producing either good.
When the Opportunity Cost or the tradeoff between the two goods is always at a constant rate.
If the variable x is raised to the power of 1 or 0. No other possibilities.
The production possibility curve is not always linear, in fact, it is usually concave down (bowed-in). The shape of the curve depends on the substutability of the goods described by the curve in the question. When goods are perfectly substitutable in production, the PPP (or PPF) is linear.
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Linear programming can be used to develop an aggregate production plan by optimizing the allocation of resources to meet production goals while minimizing costs. This mathematical technique helps in determining the best combination of production levels for different products to achieve maximum efficiency and profitability.
Wilfred Candler has written: 'Linear programming with stochastic yields' -- subject(s): Linear programming, Management, Production control
A. N. Ahmed has written: 'Experiments in reduction techniques for linear and integer programming' 'A modified production procedure for linear programming problems'
This detergent is the linear alkylbenzene sulfonate.See this link for several production details.
Linear equations can used in many areas. They are particularly useful in determining the most economical delivery patterns in trucking and in distribution. They are also used to establish the most effective patterns for production line loading in large scale production
Volume of Production
Linear expansivity of solids is crucial in various applications, such as engineering and construction, where materials expand and contract with temperature changes. This property is considered when designing bridges, railways, and buildings to prevent structural damage. Additionally, it is important in manufacturing processes, such as metalworking and glass production, where precise dimensions are required. Understanding linear expansivity also aids in selecting materials for electronic components to ensure reliability under varying thermal conditions.
Two possibilities: The line is linear over some of its length and then goes non-linear (or the other way round: Think of a mass, at the end of a string, being swung in a circle. Then the string is cut. The motion of the mass would have been circular (lon-linear) until the instant the string was cut and then linear, as it flies off into a tangent. Or The line is linear from one perspective but not from another: Think of the trajectory of a ball that is thrown up at an angle to the horizon. If seen from above, the ball travels in a straight line (linear) but if seen from the side it follows a parabola (non-linear). Hope that helps.