We reviewed the * marginal product of labor* and learned that for the production function for a firm, it is the slope of the tangent line at any point on the function. Remember that the firm’s production function graphs output vs.

*labor*and the economy-wide production function graphs output vs.

*capital*. This is because we are holding the total labor force constant (amount in the labor force = L) in the economy, and we are holding the level of capital constant per firm (K = 1 per firm). To calculate the profit-maximizing condition, we take the revenue function and calculate the point at which the slope of the tangent line (MPL x P) is the same as the slope of the labor costs function (this slope is just the wage rate, W). So, the profit-maximizing condition will be when MPL x P = W.

Using the fact that the first derivative (or slope) of the firm’s production function can be calculated using calculus, we know that the MPL is given by . The profit-maximizing condition for a firm in our economy is when MPL x P = W. If we plug in the formula of MPL that we have using calculus, into the profit-maximizing condition, then after a little manipulation, we get the labor demand function for the entire economy. That is, . And when L^{d } = L, the total labor supply for the economy, then the our macroeconomic model’s labor market is in equilibrium, which looks something like this:

**Marginal Propensity to Consume**

We next talked about the consumption (C) part of the real GDP, Y (recall that Y = C + I + G + NX). From the circular-flow diagram, we know that households spend all of their income on one of three things: (1) Consumption; (2) Savings and; (3) Taxes. The after-tax income is called the **disposable income**** **(Y^{D}) and we are mainly concerned with the effects on total consumption, C, for changes in the disposable income, Y^{D}. To look at that, we divide total consumption spending into two parts:

- Baseline consumption (C
_{0}) - Marginal propensity to consume (C
_{y})

The marginal propensity to consume (MPC) part of the consumption is what determines by how much total consumption will change for changes in disposable income. Everything else that affects consumption (optimism, pessimism, risk, etc.) is lumped into the baseline consumption part it. When we plot the per capital disposable income against the total per capital consumption expenditure, from 1959 to 2006 (both in terms of year 2000 dollars), we get the following graph.

The average slope for the plot is around .35, so we can say that the crude value of the MPC using inflation-adjusted, per capita data from 1959-2006, is .35, and the baseline consumption is $8,850.

Since consumption and disposable income have a linear relationship, we model consumption as: C = C_{0} + C_{y}Y^{D}, where Y^{D} is the disposable (or after-tax) income, and Y^{D} = (1-t)Y.

This is where we stopped. Next week, we will continue on with investment or I component of the real GDP, and talk about present value and how the real interest rate affects investment decisions.

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