Give correct answers.
Suppose that initially a competitive industry with many identical firms is in the long-run equilibrium. Each firm has a cost function of C0 (q) =1+q2. Discovery of a new production technique lowers the variable cost, and this makes each firm's total cost function C(q) =1+0.25q2.
A. Calculate the initial long-run equilibrium price (p0) and the new long-run equilibrium price (p1).
B. Suppose that market demand is linear and given by p = 4 ? 0.1Q, where p is the market price and Q is the total quantity demanded. Calculate the number of firms in the industry before and after the change in technology?
A perfectly competitive firm has a Cobb-Douglas production function f (X1, X2) = X1X2. Suppose that input prices are w1 = 1 and W2 = 1. The firm wants to find the cheapest way of producing y = 32. a. Suppose that in the short run the quantity of input factor 2 is fixed at X2 = 8. Solve the firm's short-run cost minimization problem to derive the optimal input quantity x1. b. Derive the corresponding costs Cs of producing y = 32 in the short run. c. Now consider the long run, in which both input factors are variable. Set up the Lagrangian function for this firm's long-run cost minimization problem. d. Derive the first-order conditions of the above long-run cost minimization problem. e. Solve the above first-order conditions to derive the optimal input quantities x1 and X2. f. Derive the corresponding costs c* of producing y = 32 in the long run.(b) Explain how the fiscal stimulus affect the economy, the potential multiplier effect of this stimulus considering the US current situation, and the potential limitations (if any) of the US policy mix adopted. (20 marks, 300 words max)1. A perfectly competitive industry has a large number of potential entrants. Each firm has the same cost function such that the long-run average cost of the firm is minimized ar the output level 20. The average cost of producting 20 unit is $10 per unit. a. Find the long-run market supply curve. Explain your answer clearly. b. Assume that the market demand function is given by Q = 1500 - 50 * P. Find the long-run equilibrium price and quantity. c. Find the number of firms in this market. d. Suppose that market demand shifts to Q = 2000 - 50 * P. What would happen to long-run supply curve, equilibrium price and equilibrium quantity and the number of firms in the market. Explain your answer clearly.Problem 1 Consider a competitive industry with a large number of firms, all of which have identical cost functions c(y) = y' + 1 for y > 0 and c(0) = 0 (this simply means that the firm only pays the fixed cost when producing positive levels of output). Suppose initially that the demand in the industry is given by D(p) = 52 - p. 1. Derive the supply curve for an individual firm. Make sure you write it in the form: 0 for p ? Si(p) = ?? for p 2?? 2. If there are N firms in the industry, what will be the industry supply, S(p)? Use a form similar to part (a). What is the minimum price at which a positive output will be sold in this market? 3. Suppose initially, N = 40. Compute the equilibrium market price and quantity. How much output is each individual firm producing and how much profit does each firm make? 4. Is N = 40 a long-run equilibrium? How can you tell? What will happen to the number of firms and market price in the long run (increase or decrease) and why? 5. Compute the long-run equilibrium price, market quantity, and number of firms. What is the output of each individual firm? 6. Suppose now that a fixed fee of 1 is imposed on each firm in this market. The fee is collected from any firm that produces y > 0 and is the same regardless of output (hence it is "fixed"). What will happen to the market price, market quantity, output per firm, and number of firms in the long- run? Problem 2 All firms in a competitive industry have the following (long-run) total cost curve: C(y) = y' - 10y + 36y 1. Assume that there are many firms in this market. Compute the long-run price in this market. How much output does each firm produce. 2. Suppose the market demand is given by QD = 111 - p, where p is the market price and Qp is the quantity demanded. Find the equilibrium quantity and number of firms
