Question 1: A homogeneous products duopoly faces a market demand function given by Q = 10 - 2P, where Q = Q1 + Q2. Both firms have a constant marginal cost MC = 2. 1. Suppose the two firms set their quantities simultaneously by guessing the other firm's quantity choice. Derive the equation of each firm's reaction curve and then graph these curves. 2. What is the Cournot equilibrium quantity and price in this market for each firm? 3. What would the equilibrium price in this market be if it were perfectly competitive? 4. What is the Bertrand equilibrium price in this market?
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- (a) Elucidate price and output determination under any two non-collusive models of Oligopoly. (b) Consider a market structure comprising two identical firms (A and B), each with the cost function given by: Ci = 30Qi , where Qi for i = {A, B} is output produced by each firm. Market demand is given by: P = 210 − 1.5Q, where Q = QA + QB (i) Find Cournot equilibrium. (ii) What will be the outcome if the firms decide to collude? Compare it with the results under the Cournot equilibrium.Consider a product market with three consumers A, B and C with demand function PA = 6 – QA, PB = 6 – 2QB and PC = 12 – QC respectively, where P is the price in dollars and QA, QB and QC are the quantities demanded by Consumer A, B and C respectively. The marginal cost of the product is constant at $4. (i) If the product is public good, analyse the product and determine the optimal quantity of the product in the market.(ii) How will your answer be different if the product is a private good instead? (Hi there, may I requst for a detailed step by step explanation as i struggle with this topic. Thank you)Suppose that the elasticity of demand at a given price level is E(p)=.8. What does that mean? Select both the correct answer to elastic, unit, or inelastic as well as what the company should do to increase revenue. Since 0The profit maximizing condition for a purely competitive firm is when. Price elasticity of demand is positive. Price average total costs O Price - average total costsSuppose we have a product with the following conditions: The consumer's maximum willingness to pay is 8 A firm's minimum willingness to accept is 1 The market price is 7 a. What is the consumer surplus? CS = b. What is the producer surplus? PS = c. What is the total surplus TS =You are the principal economist at a firm that produces some output y based on the following function: y = f(x1, x2) = x ³ x ² 1. Calculate the marginal product (MP) of both inputs at some arbitrary input bundle (x₁, x₂). Interpret the sign of both. 2. Using your answer in the previous part, calculate OMPT₂/0x₁. Interpret what this means. 3. Calculate the technical rate of substitution between ₁ and x2, i.e., MP/MP₂. 4. Does this production function exhibit increasing, decreasing, or constant returns to scale? Show. 1 5. Lay out a brief, realistic example of x₁, x2, y that fits the dynamics that you calculated.Suppose the representative firm of the economy has a production function of the form F(K, N) =AK0.5N 0.5 . The marginal product of labor is then given by MP N = 0.5AK0.5N −0.5 . The current capitalstock is K = 40. (a) Holding fixed capital at 40, draw a graph of output as a function of labor. What are some importantfeatures of this graph? (b) If A = 4 what is the Labor Demand Curve, ND(w), as a function of the real wage w? (c) Suppose labor is supplied inelastically with NS(w) = 10. What is the equilibrium wage w, employmentlevel N, and full employment output Y ? (d) Suppose that productivity unexpectedly increases to A = 6. What is the new equilibrium wage w,employment level N, and full employment output Y ?Let's tackle each part of the question step by step:1. **Monopoly Market:** A) To find the profit-maximizing output and price, we first need to find the monopolist's marginal revenue (MR) function. MR is the derivative of total revenue (TR) with respect to quantity (Q). TR is simply the product of price (P) and quantity (Q). \[TR = P \times Q = (120 - Q) \times Q = 120Q - Q^2\] Taking the derivative of TR with respect to Q: \[MR = \frac{dTR}{dQ} = \frac{d(120Q - Q^2)}{dQ} = 120 - 2Q\] Setting MR equal to marginal cost (MC) to maximize profit: \[MR = MC\] \[120 - 2Q = 20\] \[100 = 2Q\] \[Q = 50\] Now, substitute \(Q = 50\) into the demand function to find the price: \[P = 120 - Q = 120 - 50 = 70\] So, the profit-maximizing output is 50 units, and the price is $70. B) To find the total profit, we need to subtract total costs from total revenue: \[TR = P \times Q = 70 \times 50 = 3500\] \[TC = 20Q 200 = 20(50) 200 = 1000\] Total profit: \[Total\ Profit = TR - TC = 3500 - 1000 = 2500\]2.…A market demand function is given by the equation QD = 180 – 2P. Find the value of consumer surplus if price is equal to 65. Illustrate your demand curve and the area of consumer surplus. Identify the area of consumer surplus, the price at which demand is zero, the level of demand if price was zero and the slope (show calculation if required).In a Cournot setting, what should be the produced quantity and realized price in a duopoly with firms A and B that is characterized by P=140-Q and constant marginal costs of $20?.The supply and demand equations of a good are given by the following formulas P=2Qs +48 P= -6QD+ 160 Find the equilibrium price and quantity. The equilibrium quantity is. (Type an integer or a decimal.) ***2. Consider the production functions given below: a. Suppose that the production function faced by a bread producer is given by Q = 4KL, where MPK = 4L and MP, = 4K. i. Do both labor and capital display diminishing marginal products in the short run? Explain. ii. Find the marginal rate of technical substitution for this production function. (Hint: The MRTS MPL MPK iii. Does this production function display a diminishing marginal rate of technical substitution? iv. Graph isoquants for Q = 20, and Q = 40. Put capital (K) on the y-axis and labor (L) on the x- axis. Label the isoquants with their quantities. v. What are the returns to scale for this firm? Explain. 20 19 18 17 16 15 14 13 12 11 10 9 0 1 2 3 4 5 6 00 9 10 11 12 13 14 15SEE MORE QUESTIONS