Microeconomics Assignment – Fundamental Concepts, Production Functions, Competitive Edge, Market Theories, And Real World Events

Purpose of PART 1 – Understanding Fundamental Economic Concepts and Factors Affecting Elasticity

1. In a market system where producers cooperate in creating individual and aggregate output levels and prices, it is called a cartel. In the case of a perfect cartel type, the output and price of the whole industry as well as each member firm is determined by a common authority which allows the achievement of joint profits for the individual firms. The resultant profit is distributed in a way which is pre-decided. Each firm’s share from the joint profit may not be in proportion to quota of the supply or the cost that would be incurred. The central administrative authority decides the output quota for each firm such that the cost to the outut produced is mininmized. This is found when the marginal costs of the member firms are equal (Pindyck et al, 2009).

To determine price and output of a cartel, we consider a two member firm. The cartel’s industry demand curve would be its aggregate demand curve as shown by DD in the figure given below. Below the demand curve lies the marginal revenue curve of the cartel. The marginal cost curve of the cartel (MC^T) is the aggregate or horintal aggregate of the MC curves of both firms A and B (MC^A and MC^B). Again, the output of each firm is distributed in a way that the marginal costs are equal (Shapiro,1989). The cartel’s profit is maximized where MR is equal to MC which here is shown as point C. The profit maximizing output is here, OQ* and the price is OP*. We see in the figure that when firm A produces OQ¹ and firm B produces OQ² , the marginal costs of the firm is equal. OQ* is the sum of OQ¹ and OQ² with A’s profit PFTK and B’s PEGH, the sum of which is maximum (Hall et al, 2010).

(a) The given demand function is

P=1,000 – Q_S – Q_T 

Where Q_S and Q_T are the quantities sold by the respective firms and P is the (market) selling price. The total cost functions of manufacturing and selling the component for the respective firms are:

TC_s = 70,000 + 5Q_S+ 0.25Q²_S

TC_{t =} 110,000 + 5Q_T + 0.15Q²_T 

Total profit of S is:

Π_S = PQs-TCs= (1000-Qs-Qt)Qs – 70,000 + 5Q_S+ 0.25Q²_S

=-70000+995Q_S-QsQ_T-1.25Qs²

Taking partial derivative of the above equation with respect to Qs gives us (Varian, 2010):

dPs/dQs= 995-Qt-2.50Qs………………………………… (1)

Similarly we get firm T’s total profit as:

Π _T= P_T-TC_T= (1000-Q_S-Q_T) Q_T – 110,000 + 5Q_T + 0.15Q²_T

=-110000+995Q_T-Q_S Q_T -1.15Q_T² 

On taking partial derivatives with respect to Qt we obtain as follows:

dPt/dQ_T = 995-Q_S-2.3Q_T…………………………………………(2)

We see the first equation are functions of Q_S and Q_T

Setting both equation 1 and 2 to zero yields:

2.50Qs+Qt=995

Qs+2.30Qt=995

As we solve the two equations we get, Q_S*=272.32 units and Q_T*=314.21 units. On substituting these two values in the demand equation we get the equilibrium selling price of P*=$413.47 per unit and the profits obtained are:

Π _S=$ 22695 and

Π _T=$3536.17.

1. b) Now if both the firms decide to form a cartel then total industry profits would be:

 π = πs+πt

=PQ_S-TC_S+PQ_T-TC_T

π= (1000-Qs-Qt) Qs – 70,000 + 5Q_S+ 0.25Q²_S + (1000-Qs-Qt) Qt – 110,000 + 5Q_T + 0.15Q_T²

= 180000+995Qs-1.25Qs²+995Qt-1.15Q²-2QsQt

To maximize this total profit we take partial derivative with respect Qs and Qt respectively:

dPR/dQs= 995-2.50Qs-2Qt

dPR/dQt=995-2.30Qt-2Qs

Setting these equal to zero we obtain:

995-2.50Qs-2Qt=0

995-2.30Qt-2Qs=0

.On solving we get Qs*=170.57units and Qt*=284.39units. Substituting these in the price functions and profit function gives P*=$545.14 per unit and PR*=$46291.43

The Marginal costs for each firm would be:

MCs= d(TCs)/dQs= 5+0.5Qs

MCt= d(TCt)/dQt= 5+0.3Qt

The marginal cost function as obtained before, on substituting values we get: MCs*=MCt*=$90.29

Reference

Pindyck, R. Rubinfeld, D. & Mehta, P. (2009). Microeconomics. South Asia: Pearson

Hall, R., & Lieberman, M., ( 2010). Economics: Principles and applications, USA: CengagE learning

Shapiro, C. (1989). Theories of Oligopoly behavior. Available at: https://www.sciencedirect.com/science/article/pii/S1573448X89010095 [Accessed 9 March 2017]

Varian, H. (2010). Intermediate microeconomics. New Delhi:Affiliated East-West Press