Write the equation of the tr curve and then plot the

Question

Question 1:

Consider a linear industry demand equation: P = 20 - 2Q, where P is the unit price in dollars and Q is quantity in million units. The cost structure in the industry is given by the constant unit and marginal costs: TC = 10Q. Assume that the industry is monopolized by only one company.

(Hint: In solving this assignment, you may use algebra and graph. Further, you may also construct a table similar to the one you did for Assignment #1 to solve the problems).

1. Write the equation of the TR Curve and then plot the TR curve (with Q along the horizontal axis and TR along the vertical axis) for this company in Figure 1. Comment on the shape of the TR curve.
2. Plot the TC curve (with Q along the horizontal axis and TC along the vertical axis) for this company in Figure 1. Comment on the shape of the TC curve. Is it a short-run cost curve or a long-run cost curve? Explain your answer.
3. Given the TR and TC information given in the first two questions, calculate Total Profit (TP) at each level of output and then plot the TP curve in the same Figure 1. Plot the TP (Total Profit) curve (with Q along the horizontal axis and TP along the vertical axis) for this company. Comment on the shape of the TP curve.
4. If the goal of this monopolist is to maximize profit, what will be its optimal output Q*_p  based on the TP curve. Show this solution in Figure 1.
5. What will be the optimal price (P*_p) charged by the monopolist at output Q*_p?
6. What will be the amount of Total profit (TP) earned by the monopolist at Q*_p?
7. If the goal of this monopolist is unconstrained sales revenue maximization, what will be its optimal output Q*_us? Show this solution in Figure 1.
8. What will be the price (P*_us charged by the monopolist at output Q*_us?
9. What will be the amount of Total Profit (TP) earned by the monopolist at Q*_us?
10. If the goal of this monopolist is constrained sales revenue maximization, what will be its optimal output Q*_cs, assuming the minimum profit constraint is Min TP = $8 million? Show this solution in Figure 1.
11. What will be the price (p*_cs) charged by the monopolist at output Q*_cs?
12. What will be the amount of Total Profit (TP) earned by the monopolist at Q*_cs?

Question 2:

Assume that the MNK Company produces and sales DVD Players. It has a maximum capacity production U=100,000 units per year. Assume its current production (Q_tr*) is running at the rate of 80% of its production capacity. Assume that the company experiences a cost structure of MC=AC= $50 at the current estimated production rate. The company has a total capital investment K = $500,000. The Company has as its goal a target rate of return on invested capital at R₀ = 20%.

1. What is the estimated current production rate Q*_tr for the company at the 80% capacity rate?
2. If the company follows the target-return pricing strategy, what will the price P*_tr that the company will charge to its customers at the Q_tr* production rate?
3. What will be the Lerner Index of Monopoly Power under this solution?
4. What will be an estimate of the implied Elasticity of Demand in this industry under the target- return pricing scheme?
5. If the company follows the Markup pricing strategy, what will the price P_ms* that the company will charge to its customers, assuming it wants a 20% markup over unit costs?
6. What will be the Lerner Index of Monopoly Power under this solution?
7. What will be an estimate of the implied Elasticity of Demand in this industry under the markup-pricing scheme?
8. Which of the above two pricing strategies will give the higher degree of market power to the firm in this industry? Explain your answer.