When the Opportunity Cost or the tradeoff between the two goods is always at a constant rate.
under what conditions an econoy would be operating inside its production possibility frontier?
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.
The intention of the measurement is to capture the value of the total production, which would be market price as estimated by the mechanisms in place to monitor and report GDP, A disadvantage is that it can over or understate true GDP if there is a change in market conditions for some subset of production that does not have another co-linear variable to adjust after the fact.
under what conditions an econoy would be operating inside its production possibility frontier?
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.
A Production Possibility Frontier (PPF) is a straight line when the opportunity cost of producing one good over another remains constant. This typically occurs when the resources used in production are perfectly adaptable to both goods, meaning that shifting resources from one product to another does not change the efficiency of their production. In such cases, the trade-offs between the two goods are linear, reflecting a consistent rate of substitution.
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
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.