Exercise: Payoff matrix -Oligopoly market-

You are given a payoff matrix for two firms in an oligopoly market.

Find the dominant strategy (if any) for each firm.

What profit would they each earn if they form a cartel (if possible)?

Can the cartel hold in the long run? If not, what is the long run equilibrium?

Payoff Matrix:	Firm A: high prices	Firm A: low prices
Firm B: high prices	A: $1000 B: $1000	A: $1200 B: $800
Firm B: low prices	A: $600 B: $1200	A: $700 B: $700

The dominant strategy for firm A is to charge a low price for its product. You can see that no matter what firm B chooses, firm A is always better off by choosing the low price option (i.e its profit is always bigger than if it had charged a high price).

The strategy for firm B depends on the choices firm A makes. If firm A charges a high (low) price then firm B should charge a low (high) price.

In order to find the point at which the firms would collude (i.e act as one monopolistic firm), find the point(s) where the sum of economic profits is the greatest. Then choose the points that benefit both parties. In our case we see that the sum of the first entries in each column are equal to one another and greater than the rest of the sums in each entry in the matrix. As we will see, the long run equilibrium prevents the firms from colluding.

Since we know that the firm A will charge a low price, it makes sense for firm B to charge a high price in order to maximize its profit. Then, we see that the long run equilibrium is in the upper right entry of the payoff matrix. Firm A has no incentive to form a cartel with firm B.

Reference: Exercise inspired by: Mayer,David. AP Microeconomics Crash Course. Research & Education Association (2014). p 123.

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