Production

Main activity of a firm. The process of transforming inputs into output.

Production function gives the maximum output for different combinations of inputs.

The standard inputs are Labor ($L$) and Captial ($K$) and the output is $Q$.

Usually, we can write,

A is called the technology factor. $\alpha$ and $\beta$ are positive.

Returns to scale

Measures the responsiveness of output to proportional change in input in all inputs.

Cob-Douglas Production function:

If we increase both inputs $t$ times. The function is then,

Thus, increase in input by a multiple of $t$ gives an $t^{\alpha+\beta}$ multiple of production.

Now, if $\alpha+\beta=1$, then input multiple of $t$ gives output multiple of $t$. This case is called constant returns to scale. Half the input and the output halves as well. CRS.

If $\alpha+\beta>1$, then it is called increasing returns to scale. Input multiple of $t$ gives output multiple greater than $t$.

If $\alpha+\beta<1$, then it is decreasing returns to scale. Input multiple of $t$ gives output multiple less than $t$. We say that the production function returns to scale. DRS.

Marginal product

$MP_2$: the change in output due to unit change in labour, all else held constant.

Cost of production

Cost function. Two inputs $L,K$ with input prices $w$ (wage), and $r$ (price for capital, rent). If $Q$ is the output, the cost function will then be,

$r$ is the interest paid on the rent, but not the whole, since it asset. Similarly for equipment, which can later be sold.

Marginal cost is the increase in cost to produce an additional unit.

Average cost (AC)

Plotting $L(Q)$ against Q.

If the plot is linear, then the marginal cost is constant. In this case, the average cost is equal to marginal cost.

To increase production two fold, cost increases two fold. This holds only if labour and capital are two fold increased