Unraveling Market Dynamics: A Business Economics Case Study

In the intricate realm of business economics, navigating the complexities of market equilibrium and deciphering the strategic choices of rival firms poses a significant challenge. Our exploration today centers around a compelling scenario featuring two competitors, A and B, engaged in the production of identical products within a market steered by the forces of demand and supply. This analysis not only sheds light on the intricacies of market dynamics but also provides valuable insights for those seeking business economics homework help. Join us on this journey as we unravel the strategic intricacies that define the delicate balance in the business landscape. 

Question:

Consider a market with two competing firms, A and B, producing identical products. Both firms have a marginal cost (MC) of $50 per unit. Firm A has a fixed cost of $1,000, while Firm B has a fixed cost of $800. The market demand curve is given by P = 200 - 2Q, where P is the price and Q is the total quantity produced in the market.

a) Calculate the equilibrium price and quantity in this market.

b) Determine the individual quantity produced by each firm at the equilibrium and their profits.

c) If Firm A could somehow lower its fixed cost to $600, analyze the impact on the market equilibrium, individual quantities produced by each firm, and their profits.

Go ahead, take your time to work through it. I'm here when you're ready for the answers!

Let's break down the question step by step:

a) Equilibrium Price and Quantity:

The equilibrium occurs where the quantity demanded equals the quantity supplied. In other words, it's where the market demand equals the sum of the quantities supplied by each firm.

The demand curve is given by P=200−2Q, and the total quantity supplied by both firms is the sum of their individual quantities, QA​ and QB​. The marginal cost for both firms is $50.

Equating demand and supply:

200−2Q=QA​+QB​

Since the firms are identical, we can assume QA​=QB​, and thus,

200−2Q=2Q

Solving for Q:

4Q=200

Q=50

Now that we have the quantity, we can find the price by substituting Q back into the demand curve: P=200−2(50)=100

So, the equilibrium price is $100, and the equilibrium quantity is 50 units.

b) Individual Quantity and Profits at Equilibrium:

Since QA​=QB​=50, we can find the individual quantity for each firm. Then, we can calculate profits using the following formula:

CostProfit=(P−MC)×Q−Fixed Cost

For Firm A:

ProfitA​=(100−50)×50−1,000=2,500−1,000=1,500

For Firm B:

ProfitB​=(100−50)×50−800=2,500−800=1,700

c) Impact of Lower Fixed Cost for Firm A:

If Firm A lowers its fixed cost to $600, its new profit becomes:

 ProfitA​=(100−50)×50−600=1,900

Now, re-evaluating the equilibrium, the market demand remains the same, but Firm A's supply curve shifts upward due to the lower fixed cost. The new equilibrium quantity (Q) is where 200−2Q′=2Q′, and solving for Q′=66.67 (approximately). The new equilibrium price remains $100.

The new individual quantity for Firm A is 66.67 units, and for Firm B, it's 50−(66.67−50)=33.3350−(66.67−50)=33.33 units.

The new profits are:

ProfitA′​=(100−50)×66.67−600≈2,333.33

ProfitB′​=(100−50)×33.33−800=833.33

So, lowering Firm A's fixed cost increases its profit but decreases Firm B's profit. The overall market quantity increases, but the price remains the same.