Question

In the context of our analysis of the Edgeworth production box, suppose that a new invention changes a constant-returns-to-scale food production process into one that exhibits sharply increasing returns. How does this change affect the production contract curve?

Short answer

A move from a constant-returns-to-scale food production process to one with sharply increasing returns alters the production contract curve from a straight diagonal line to a convex shape. This change reflects the increase in productivity and could offer both economic agents in the trade more advantageous production and trading opportunities.

Step-by-step solution

Understanding the Meaning of Returns to Scale

In the context of production, returns to scale refers to how the output of production changes as all input factors change proportionately. When returns to scale are constant, increasing all input by a certain percentage results in an equal percentage of increase in output. In the case of increasing returns to scale, a certain percentage of increase in input causes a greater percentage increase in output.

Analyzing the Impact of Increasing Returns to Scale on the Production Contract Curve

Previously, when we had constant returns to scale, the contract curve was a straight diagonal line from one corner of the box to the opposite because an equal percentage increase in inputs resulted in an equal percentage increase in output. However, with increasing returns to scale, output increases at a higher rate than input. Therefore, the contract curve would evolve into a convex shape because the production function is now more productive.

The Implication for the Economic Agents

The shift from a straight-line contract curve to a convex one implies a change in the equilibrium points. Now, more output can be produced with the same amount of inputs, allowing both economic agents to potentially reach higher indifference curves. The increase in the returns to scale could result in more beneficial trading opportunities for both economic agents, potentially leading to a more optimal Pareto efficiency.

Key concepts

Returns to Scale

In the realm of production, returns to scale is a fundamental concept that describes the relationship between changes in inputs and the corresponding change in outputs. Imagine you're running a bakery. If you double the amount of flour, sugar, and other ingredients, as well as the number of ovens and bakers, what happens to the number of cakes you can produce? If you can exactly double your output, you're experiencing constant returns to scale. However, if your output more than doubles, you're blessed with increasing returns to scale, possibly due to efficiencies or synergies among the inputs. Conversely, if output less than doubles, it's called decreasing returns to scale.

It's important to know that returns to scale occur when all inputs change by the same proportion. In our bakery analogy, it's not just adding more flour but proportionally increasing everything from space to labor.

Production Contract Curve

Consider the production contract curve as a graphical representation of the various combinations of two goods that two producers can efficiently produce. It's plotted on an Edgeworth production box, which is essentially a square or rectangular diagram illustrating the total amount of resources shared between two producers. The contract curve is found where the production indifference curves of both producers are tangential to each other, indicating that neither producer can increase production of one good without reducing production of the other good.

When returns to scale are constant, this curve is a straight line. However, when there are increasing returns to scale, as in the case of the bakery with a new oven that's much more efficient, the curve bends outward because you can make a lot more cakes without using up as much resources proportionally. This demonstrates that you're getting more output per unit of input, which is a favorable position for any producer.

Increasing Returns to Scale

When a production process benefits from increasing returns to scale, it means that by scaling up all inputs by a certain percentage, the output will increase by an even higher percentage. This scenario might occur due to factors such as improved technology, specialization, or enhanced teamwork leading to a more than proportional increase in output.

For instance, if the bakery invests in a new mixing technology that makes the baking process more efficient, the bakery could see its productivity soar without needing to double its input of ingredients and bakers. This is an example of increasing returns to scale, where technology acts as a magnifier for productivity.

Economic Equilibrium

Economic equilibrium is the point where supply equals demand, and no economic force is pushing change since all consumers and producers are satisfied with the current market conditions. Think of it as a busy market that, after all the haggling, quietens down because everyone has bought or sold what they wanted at prices they find acceptable.

In the context of the production contract curve, economic equilibrium refers to a point on that curve where the allocation of resources cannot be changed without making someone worse off, assuming everything else stays the same. This state of balance in production is crucial for understanding how markets operate and how resources are allocated efficiently.

Pareto Efficiency

Pareto efficiency or Pareto optimality is named after the Italian economist Vilfredo Pareto. It's a quality of economic allocations where no individual can be made better off without making someone else worse off. Picture a situation where you can no longer slice the pie to give someone a bigger piece without taking away from someone else's share. That's Pareto efficiency.

In the bakery example, if you reach a point where you cannot increase the production of cakes without reducing the production of, say, cookies, assuming constant tastes and resources, you've achieved Pareto efficiency in your product mix.