3. Suppose the total cost of q units produced by an increasing-cost industry is given by C(q) =q² +8q On the demand side, the aggregate willingness to pay for q units of the good is WTP(q) = 100 q-29² 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.
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- 3. The industry producing and selling wooden pallets is comprised of 100 identical firms each of which has a short-run total cost function given by C's = 0.5g² + 10g + 5, where q is output of (standardized) wooden pallets per day. (a) What is the equation of the short-run supply curve for each firm? (b) What is the equation of the short-run supply curve for the market as a whole? 31.The price p in dollars of a certain commodity and the quantity x sold obey the demand equation p= -1/5x + 200 where 0<=x <=1000. Suppose that the cost C in dollars of producing x units is C= the square root of x divided by 10 + 400. Assuming that all items produced are sold, find the cost of c as a function of the price p.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 –- 2 g a) Find the aggregate supply and aggregate demand functions. b) Derive the equlibrium assuming the market is competitive.
- Consider 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)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 500The 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.
- 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.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.THIS EXERCISE FOR MATHEMATICAL ECONOMIC : Question (1): Suppose the estimated quantity demand for potato chips is Q = 140 – 15p and the quantity supply function for potato chips is Q = 115 + 10p. Find the equilibrium price and quantity for the number of bags of potato chips. Suppose that the main costs of producing potato chips are labor and potatoes. On a per unit basis, the cost of producing and manufacturing a bag of potato chips rises by $1.50. The firms are citing higher labor costs and fewer potatoes are grown due to the poor climate. What will be the new equilibrium price and quantity? Whichever curve you think a shift will occur, derive the new function. Suppose that a health news piece has been published indicating the ill effects of consuming potato chips. The news has been published after the firms incurred the higher costs of production. Consumers are being advised to consume popcorn or pretzels instead of potato chips. How would that affect the market for potato…
- The demand and supply functions a firm producing a certain product are given respectively by: and , where p is the price per unit and quantities are in millions per year. How much consumer surplus (CS1) do consumers receive when price is P1 = $60?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.)A retail chain will buy 900 cordless phones if the price is $30 each and 800 if the price is $40. A wholesaler will supply 350 phones at $40 each and 1400 at $70 each. Assuming that the supply and demand functions are linear, find the market equilibrium point and explain what it means.