Could a nation be producing in a way that is allocatively efficient, but productively inefficient?

Allocative efficiency occurs when resources are distributed in such a manner that the mix of goods and services produced results in the highest possible level of satisfaction for consumers. In this state, the marginal cost (MC) of the last unit produced is equal to the marginal benefit (MB) derived from its consumption. In other words, resources cannot be reallocated to make someone better off without making someone else worse off, thus achieving a socially optimal scenario.

Productive efficiency is achieved when a firm or nation produces goods and services at the lowest possible cost. It occurs when production takes place at the lowest point on the average total cost (ATC) curve. In other words, a firm or nation is fully utilizing its resources and minimizing waste while producing the maximum output with its given inputs.

A nation can technically achieve allocative efficiency without achieving productive efficiency in some cases. It may be possible that a nation is producing goods and services that maximize the satisfaction of its people, but it is doing so in a way that does not minimize the cost of production to the lowest possible levels. For example, consider a hypothetical nation that produces two goods (A and B) using two types of resources (labor and capital). The nation allocates its resources in such a way that the satisfaction of its people is at its maximum (allocative efficiency). But, suppose there's a lack of competition in the market or there's some other factor restraining the nation from utilizing its resources optimally which results in higher average costs associated with the production of goods A and B. In this situation, the nation would be allocatively efficient but not productively efficient.

It is possible for a nation to be productively inefficient while being allocatively efficient. This occurs if goods and services are produced in such a way that maximizes consumer satisfaction, but the production process is inefficient and not taking place at the lowest possible cost. However, it's important to note that this situation might not be sustainable in the long run, as inefficient production processes may lead to a misallocation of resources, making it more difficult to maintain allocative efficiency.