Economics Examination



Economics Examination

Answer to Question 1

A)

The difference between a monopoly and a competitive firm lies in the difference in the Revenue function. The revenue function of a monopoly is R(X) = PX(X) X. P(X) is just the inverse of the demand function.

The monopolist firm determines how much to produce by the equating marginal revenue (MR) to marginal cost (MC). The monopolist firm's MR function is the derivative of the Total Revenue function (TR), which is TR = aq - bq^2. So the MR function will be MR = a- 2bq. The MC function is the derivative of the cost function, C = cq + F, so MC = c.

MR = MC

2bq = c

-2bq = c - a

-2q = (c - a)/ b

2q= -(c - a)/ b

q=( a - c)/ 2b

As derived above the quantity that will produce will be (a - c)/ 2b. So we will just plug in the value of the quantity in the equation of price. The answer will be:

P = a - bq

P = a - b ((a - c)/ 2b)

(Gahvari, 2006)

B)

The competitive firm determines how much to produce by the equating marginal revenue (MR) to marginal cost (MC). The competitive firm's MR function is the price function, which is P = a - bq. Price is the marginal amount of money which will be earned with each extra unit of goods sold. So it can be said that MR = a- bq. The MC function is the derivative of the cost function, C = cq + F, so MC = c.

MR = MC

bq = c

-bq = c - a

-q = (c - a)/ b

q= -(c - a)/ b

q= a - c/ b

As derived above the quantity that will produce will be (a - c)/ b. So we will just plug in the value of the quantity in the equation of price. The answer will be:

P = a - bq

P = a - b ((a - c)/ b)

(Gahvari, 2006)

C)

According to the Cournout model firms make simultaneous quantity decisions. One firm has no idea about what the other firm will do, so it gives his best possible quantity decision according to Nash Equilibrium. The duopolists are in a non-cooperative game, and determine the Nash equilibrium given the conditions. The quantity of the goods produced is decided simultaneously and homogenous goods are produces, so therefore the price of the good is determined taking into account the total quantity supplied, p ( q1+ q2 ). In order to find the Nash equilibrium in this case, the best response functions ( best quantity choice for both firms as a function of the other) needs to be calculated. The point of intersection will be the Nash equilibrium (Chen & Chen, 2007).

Suppose the industry demand function is p= a - bq, where q is the total industry output. The cost function of out firm is C = cq + f(Cost of firm 1), and the other firm has a cost function of C= zq (Cost ...