Lecture 7

Profit maximization

Profit maximization

Profit maximization

The Firm’s demand for factors in the long run Section 15.1 The Firm’s demand for factors in the long run

Recap Production and Costs in the Long Run Firm can adjust employment of capital and labor Achieve the least cost method of producing a given quantity of output

Isoquants Geometry of LR production Least costly method Requires labeling vertical axis with K, stands for capital Requires labeling horizontal axis with L, which stands for labor Requires fixed period of time Least costly method Avoid technologically inefficient points which are outside the boundary General observations about isoquants Slope downward Fill the labor-capital plane Never cross Convex to origin

Marginal Rate of Technical Substitution Absolute value of slope of isoquant MPL divided by MPK Amount of capital necessary to replace one unit of labor while maintaining a constant level of output If much labor and little capital employed to produce a unit of output, MRTSLK is small Provides geometric proof that isoquant is convex

Marginal Rate of Technical Substitution The discussion above assumed a one-unit change in labor. More generally, if labor changed by some amount of ∆L, we will have: and we would have:

Choosing a Production Process Minimizing cost necessary for maximizing profit Isocost curve Tracks set of all baskets of inputs employed Assume cost fixed Slope: -PL/PK Firm chooses point where isocost and isoquant curves tangent Means MRTS = PL/PK Tangencies lie along firm’s expansion path

Firm’s Demand in the LR All factors variable Assume fixed technology (the production function), rental rate (PK), and market price (PX). Note that making the assumption that PK is fixed incurs no loss of generosity, as only the relative price matters.

Construction of LR Labor Demand Factor demand vs output demand: The major difference is that a firm, unlike the case of output demand, has no budget constraint. Instead it has an infinite family of isocost lines, and it could choose to operate on any one of them. So we call factor demand “derive” from output demand. In short, we have to consider the optimal decision on the output market.

Construction of LR Labor Demand To be more precise, we need to determine how much to produce before we determine exactly how much factors to hire. Eg: We, again, need to resort to the principle of MR=MC.

Construction LR Labor Demand Substitution and scale effects associated with a factor price change SubE: When the price of an input changes, that part of the effect on employment that results from the firm’s substitution toward other inputs. ScaE: When the price of an input changes, that part of the effect on employment that results from changes in the firm’s output

Substitution and Scale Effects Direction of substitution effect and scale effect Always reduces firm’s employment of labor An increase in the wage rate raises firm’s long-run total cost curve: Could rise and become steeper, causing long-run marginal cost to rise. Could rise and become shallower, causing long-run marginal cost to fall when labor is a regressive factor.

Substitution and Scale Effects Combine effects Labor demand curve always slopes downward The proof is available at the appendix

SR and LR Relationship In LR MRP shifts due to adjustments in capital employment Infinite number of steps

The industry’s demand for factors of production Section 15.3 The industry’s demand for factors of production

Industry’s Demand Sum of individual firm’s demand curve for factor of production Monopsony Upward-sloping supply curve Marginal labor cost (MLC) Employment and wage rate

Industry’s Demand Existence of monopsony Even a firm that is unique in its industry has no monopsony power, provided that firms in other industries compete with it for the use of the factors. Monopsony is rare, especially in the long run.

The distribution of income Section 15.4 The distribution of income

Distribution of Income Payments to factors of production In Figure 15.11, total revenue is A+B+C, of which B+C are paid to workers. C refers to the opportunity costs for workers. B is earned as rent. A is payment to other factors, including the owner’s contribution.

Distribution of Income Returns to scale Decreasing return to scale (DRS) – AC curve is increasing – Price is higher than AC (why?) – positive profit. IRS – negative profit. CRS – zero profit.

Distribution of Income

Distribution of Income Returns to scale Decreasing return to scale (DRS) – AC curve is increasing – Price is higher than AC (why?) – positive profit. IRS – negative profit. CRS – zero profit.

Distribution of Income Who benefits? Recall the tax incidence. Compare the cases of tax and subsidy. Now we talk about rent in the case of factor supply. Bottomline: factors that are supplied relatively inelastically earn more rents and gain more from a rise in demand.