How is the law of diminishing marginal returns applicable to both production and cost theory?
The law of diminishing marginal return states that the amount of marginal or additional utility derived from consumption of each additional unit of a good decreases as the total amount of that good consumed increases.
One implication of the law of diminishing marginal utility is that as the supply of a good and along with that the total consumption increases the price that consumers are willing to pay for the good decreases. Thus the prices of a good is determined by the marginal utility of the last unit consumed. This is the reason why things like air, which are essential for very survival of life, are available free.
The law of marginal return has no direct implication on cost of production, but to the extent it influences the demand of a good at various prices, it affects the equilibrium level of demand and supply. Thus it effects the quantities that manufacturers are willing to produce, and then the level of production affects the cost of production.