if the total cost function of a firm under perfectly competitive market is given by: TC= 3Q2 + Q + 90. then find the optimum level of output and the corresponding profit when the price of the products is birr 25? if you are the advisor of the firm, what do you suggest? and why?
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To find the optimum level of output and corresponding profit, we need to determine the quantity that maximizes the firm's profit. In a perfectly competitive market, profit is maximized when marginal cost equals marginal revenue.
1. To determine marginal cost (MC), we differentiate the total cost (TC) function with respect to quantity (Q):
MC = d(TC)/dQ = 6Q + 1
2. To determine marginal revenue (MR), we use the fact that in a perfectly competitive market, price equals marginal revenue:
MR = price = $25
3. Setting MC equal to MR gives us the equation:
6Q + 1 = 25
4. Solving for Q:
6Q = 24
Q = 4
So, the optimum level of output is 4.
To find the corresponding profit, we need to calculate total revenue (TR) and subtract total cost (TC):
TR = price * Q = $25 * 4 = $100
Profit = TR - TC = $100 - (3Q^2 + Q + 90) = $100 - (3(4)^2 + 4 + 90) = $100 - (48 + 4 + 90) = $100 - 142 = -$42
The corresponding profit is -$42, meaning the firm is making a loss.
As an advisor, I would suggest the following:
1. Analyze the market demand: Determine if there is sufficient market demand for the firm's products at the current price. If the market demand is low, it may be challenging to generate profits.
2. Evaluate cost-cutting measures: Identify areas where costs can be reduced. This could include optimizing production processes, negotiating better supplier deals, or reducing overhead.
3. Consider product differentiation: Explore ways to differentiate the firm's products from competitors. This could involve improving product quality, offering unique features, or targeting a specific niche market.
4. Monitor competition: Stay updated on competitors' pricing strategies and market trends. Understanding the competitive landscape can help identify opportunities and make informed decisions.
5. Review pricing strategy: Assess if the current price is appropriate given the cost structure and market conditions. Price adjustments may be necessary to improve profitability.
Remember, these suggestions are based on the assumption that the firm wants to maximize profit. Depending on the firm's goals and objectives, strategies and recommendations may vary.