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- K Given the input-output matrix below, find the output matrix if final demand changes to 400 for water, 180 for electric power, and 700 for agriculture. Industry: Water Electric Power Agriculture Other Water 120 120 240 720 The output matrix is X = (Round to two decimal places as needed.) Industry Electric Power 400 200 100 300 8 Agriculture Final Demand 180 240 120 60 260 170 500Consider a competitive market for red lentils with 100 identical farmers in Horsham Victoria, a competitive market price of $5 and the following MC for each farmer: MC = $0.05Q Also consider the following market demand function: QD a) Calculate the optimal level of production (in tonnes) for each farmer (show workings) = = 1000 - 40P b) Assuming 100 lentil farmers of equal size how many tonnes of lentils in total will be supplied in the entire market? (show all workings) c) Consider that the government now imposes a 25% tax on producers, calculate i) the new equilibrium level of output for each firm (hint - think about how this affects each farmer's marginal cost), and ii) new total supply in the entire market (show all workings)2. Consider a market where demand is described by QD = 140 – 6P. An individual firm in this market can supply quantity q = P – 2 in the short run, for any price above 2. (Quantities are in thousands of units per year, prices are in US dollars per unit.)
- 3. Suppose the total cost of q units produced by an increasing-cost industry is given by C(q) = q +8q On the demand side, the aggregate willingness to pay for q units of the good is WTP(q) = 100 g - 2q² a) Find the aggregate supply and aggregate demand functions. b) Derive the equlibrium assuming the market is competitive. c) Find the maximum amount consumers are willing to pay for the equilibrium output. What is the consumers' surplus equal to? d) Find the total cost of the equilibrium output. What is the average cost equal to? What is the profit of the industry equal to? e) Calculate the total surplus or welfare in equilibrium.2. The supply Qs = s(P, Pm) has the functional form of: Qs = -12 + 0.5P - 2Pm initially, the materials cost Pm_0 = 7. Find the optimal quantity to supply if the price is P=76 and P=80. At P=76, Q_0 = . At P=80, Q_0 = . 3. Now, the cost of materials changes to Pm_1 = 9. Find the optimal quantity to supply if the price is P=76 and P=80. At P=76, Q_1 = At P=80, Q_1 = Draw the second supply curve and show how supply shifted.2. A refrigerator manufacturer is planning capacity expansions. They have determined that their capacity cost follows the equation below, where f(y) = kya, is the cost of a plant that can produce y units annually. f(y) = 0.0107y⁰.62 They have determined that when a = 0.62, using a = u/(e" - 1) gives a value u = 0.89. Their demand for refrigerators is growing at a rate of 5000 units annually, and they use a 16% interest rate for discounting. At the optimal capacity addition level, what does each capacity installation cost?
- Question 2. The price - demand equation and the cost function for the production of HDTVS are given respectively by x = 6000 – 30 p and C(x) = 72000+ 60 x where x is the number of HDTVS that can be sold at a price of $p per TV and C(x) is the total cost (in dollars) of producing x TVs. A. Express the price p as a function of the demand x, and find the domain of this function. B. Find the marginal Revenue at a production level of 1500 and interpret the result c. Sketch a graph of Revenue and Cost functions. Indicate interval in which Profit occurs and loss occurs.The demand and supply functions for a particular commodity are D(x) = 80e-0.001x and S(x)= 30e0.001r , where x is the number of units of the product, D(x) is the price that results in a consumer demand of x units and S(x) is the price that results in a producer supply of x units. a. Find the equilibrium point using your calculator and identify the equilibrium units and price. Give your answers to the nearest whole unit and nearest dollar. The value of x at equilibrium is units. The value of p at equilibrium is b. Determine the consumers' surplus.Suppose that all firms in a constant-cost industry have the following long-run cost curve:c(q) = 4q2 + 100q + 100The demand in this market is given by QD = 1280 - 2p. Suppose the number of firms in the market is restricted to 80a. Derive the supply curve with this restriction. Find the market equilibrium price and quantity with the restriction.b. If firms are allowed to buy and sell these permits in an open market, what will be the rental price of permits? Will firm’s that own permits make profit? Briefly explain.c. How much deadweight loss is generated by the permit system? Provide a graph showing the region of this deadweight loss.d. Suppose the government abandons the permit system and simply imposes a fixed fee on firms in the market. If the fee is set equal to the permit price you found in c., what will be the equilibrium price, quantity, number of firms and deadweight loss?
- 1) Suppose you have a job analyzing a perfectly competitive market. The aggregate demand is D Q (p)= 72- 3 And the cost function for the (identical) firms is C(g)= 6q2+54 (a) Consider first a short scenario, and setup and solve the profit maximization problem over quantity. Write the quantity an individual firm will produce as a function of the sale price. (b) Solve for the price, quantity, and profits for each individual firm and then also for aggregate quantity in equilibrium when the number of firms is fixed at N = 32 (show your work) (c) Will these firms shutdown in the short run? Explain. (d) Imagine now that that we are in the long run. What will be the equilibrium in this market if the free entry assumption holds? Solve for the equilibrium price, individual quantity, Aggregate quantity, number of firms, and individual firm profit. (e) Explain why N is different from the number of firms in the long run.31) What is total fixed cost at the profit-maximizing quantity? 32) When the process of entry and exit has ended in a competitive market, are firms’ profits positive, negative, or zero? Why is this true? 33) When a single firm can supply a good or service to an entire market at a lower cost than could two or more firms, the industry is known as a?A local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are aweekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of$5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price ? and demand ? is linear. Use the research department’s estimates to express ? as a function of ? and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of ?. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function interms of ?. e) Determinethe Marginal costand interpret the…