Microeconomics: Factor Markets

Definition:

Factor markets: markets for the factors of production (example: labor and capital).

Markets are formed whenever consumers and producers meet to exchange goods or services.

Deriving factor demand:

the demand for goods or services in the product markets creates demand for the factors of production.

An increase (decrease) in demand for good X leads the suppliers to increase their production thereby increasing (decreasing) the demand for the factors of production.

Marginal revenue product:

The demand for the factor of production is formed by multiplying a firm's marginal revenue by its marginal product.

Remember that by taking the derivative of the TR function with respect to Q we are able to find the MR.

$\frac{dTR}{dQ}\approx \frac{\Delta TR}{\Delta Q}$

Marginal product on the other hand is found by taking the derivative of the production function with respect to a factor of production (L or K for example).

$\\ 1. MPK= \frac{\partial F}{\partial K} \\\ \\ 2. MPL= \frac{\partial F}{\partial L}$

Marginal revenue product (MRP): the change in total revenue when one more input is employed. It decreases as more similar inputs are employed due to the principle of diminishing marginal return.

$\\ 1. MRP_L= MR \cdot MPL \\\ \\ 2. MRP_K= MR \cdot MPK$

Notice that the MRP is the factor demand; an increase in product prices, marginal revenue or marginal product increases (rightward shift) the factor demand.

Marginal-factor cost:

Marginal factor cost (MFC) is the extra cost a firm incurs when employing one additional unit of input such as a worker or machine.

In other words, the MFC is derived by taking the derivative of the TC function with respect to a specific input.

$\\ 1. MFC_L= \frac{\partial TC}{ \partial L } \approx \frac{\Delta TC}{\Delta L}\\\ \\ 2. MFC_K= \frac{\partial TC}{ \partial K } \approx \frac{\Delta TC}{\Delta K}$

In a perfectly competitive factor market, the MCF is equal to the price of the input, i.e either wage rate for the labor market or rental rate in the capital market.

Reference: Mayer,David. AP Microeconomics Crash Course. Research & Education Association (2014). p 125-128.

Comments

Econometrics: Bivariate population model

Hello I'm finally back from my extended break. I thought that we should start studying Econometrics. Let's begin by analyzing a simple bivariate regression. Assume that this equation describes the relationship between two variables X and Y. We say that Y is the dependent variable, whereas X is the independent variable. In other words, we assume that Y (the output) depends on X (the input). Epsilon is the error term, it represents other factors that affect Y. The error term must be uncorrelated with the variable X so that we do not need to include them in our regression, and thus the coefficient of X (beta) should not change, even though Epsilon also determines Y. beta-0 is the constant term. It tells us what would be Y if X=0. beta-1 is the effect on Y if X changes by one unit. To see this, assume X=education is a continuous function, let's take the derivative of Y=wage with respect to X: Thus, if education goes up by one unit, we should expect, on average, wage to go up

Macroeconomics: multiplier and crowding out effects

Multiplier effect: whenever any of the components of AD increases, the increase in GDP will be greater than the initial increase in expenditures. The impact on GDP of a particular increase in spending depends on the proportion of the new income that is taken out of the system to the proportion that continues to circulate in the economy. The multiplier effect tells us the impact a particular change in one the components of AD will have on the total income (GDP). Let k denote the spending multiplier, which is a function of MPC and MPS. The larger the marginal propensity to consume, the larger the spending multiplier. Notice that the larger the MPC, the greater the impact a particular change in the spending variables will have on the nation's GDP. The crowding out effect: If government spending increases without an increase in taxes, the government must borrow funds from the private sector to finance its deficit, thereby increasing the interest rate. This increase in interest rate,

Econometrics: OLS estimates

Let X and Y be column vectors and the sample has the size n: The vector beta contains both the coefficient of X as well as the coefficient for the intercept. This is equivalent to writing this equation: We will assume that the expected value of the error term is 0 (this can be done by construction), and that X is uncorrelated to epsilon. Assume the following is for population data. Let's prove that statement: Since we know that the covariance between X and epsilon is 0, it follows that the expected value of X times the error term must also be 0. Since we do not have access to the actual expected value of the distribution, let's use the sample data instead: The hat on the covariance signifies that this is a MM estimator. Let's use the fact that the sample mean of epsilon is also equal to 0, then: Using the estimation for the covariance and that the expected value of the error term equals 0: Then we have: To get this result, you must use the properties of the summation op

Economics and Statistics

Search This Blog