Consider an industry with n firms with outputs y¹,..y", facing an input price vector W= (W1₁,..wn). The total industry output is Y = 19. The firms' cost functions are Ci(w, y) = a(w) + 0¹ (w) [y] (to avoid confusion, note that [y] is y to the power 3), j = 1..n, where a (w) and (w) are functions of input prices. The industry aggregate costs are C = -1 C (w, y). When can the aggregate costs be written as some function of input prices and total industry output (namely, when can it be written as C = a(w) + 0(w)Y)? (a) when a; (w) = 0 for all firms (b) when (w) is the same (0 (w) = 0(w)) for all firms (c) when 3 = 1 for all firms (d) when 3 = 1 and 0¹ (w) = 0(w) for all firms
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- 3.(9N10.8) Suppose that the long-run total cost function for the typical mushroom producer is given by: ( , ) 2 cqw wq q =-+ 10 100 where q is the output of the typica1 firm and w represents the hourly wage rate of mushroom pickers. Suppose also that the demand for mushrooms is given by Q = -1,000P+ 40,000 where Q js total quantity demanded and P is the market price of mushrooms. A. If the wage rate for mushroom pickers is $1, what will be the long-run equilibrium output for the typical mushroom picker? B. Assuming that the mushroom industry exhibits constant costs and that all firms are identical, what will be the long-run equilibrium price of mushrooms, and how many mushroom firms will there be? ( , ) 2 C. Suppose the government imposed a tax of $3 for each mushroom picker hired (raising total wage costs, w, to $4). Assuming that the typical firm continues to have costs given by: cqw wq q =-+ 10 100 how will your answers to parts (a) and (b) change with this new, higher wage rate?If the demand function faced by a firm is:Q = 90 – 2PTC = 2 + 57Q – 8Q2 + Q3 Determine the best level of output for the above question by the MR and MCapproach.Question 2: Determine the best level of output for a perfectly competitive firm that sells its product at P = $4 and faces TC = 0.04Q3– 0.9Q2 + 10Q + 5. Will the firm produce this level ofoutput? Why? Question 3: Suppose that the production function is given as follows:TPL = 10L + 5L2 + L3Find the total product, Marginal product and average product when L = 5. Question 4: Find the optimum level of output and profit from the cost functionTC = 50 + 6Q2 and price P = 100 – 4QAlso derive marginal cost and marginal revenue.1. Let a firm’s cost function be c(y1, y2) = F + αy1y2 + y21 + y22, where α is some constant.a) What restriction on α is required to guarantee that this cost function exhibits economies ofscope?b) What restriction on α is required to guarantee that this cost function exhibits cost complementarities in both goods? Note that you’ll need to verify cost complementarities for y1 andy2.2. Given the industry demand function X(p) = 100 − 2p, consider the following scenarios:• The market is a perfectly competitive market. Assume there are identical firms with marginalcost of 12 in this perfectly competitive market.• The market is dominated by one monopolist with a marginal cost of 12. This monopolist isable to achieve 1st degree pricing.• The market is dominated by one monopolist with a marginal cost of 12, but the monopolistis able to achieve only 2nd degree pricing. Assume the menu offers only 2 choices:(Q∗1 = 30, p∗1 = 35), and (Q∗2 = 60, p∗2 = 20).• The market is dominated by one monopolist…
- Consider a firm with a total cost function TC = q^2 + 20q + 225. a) In a diagram, measuring quantity along the horizontal axis, draw the firm’s Marginal Cost and Average Cost curves. Suppose that the government introduces a $10 per unit seller tax. b) What is the firm’s new total cost function? In the same diagram as above, illustrate how the tax affects the firm’s MC and AC curves. Does the tax affect the firm’s MC? Does it affect the firm’s minimum efficient scale? Suppose instead that the government introduces a new licensing fee that raises the firm’s recurring fixed cost to 400. C) In a new diagram draw the firm’s MC and AC before and after the introduction of the licensing fee. Does the fee affects’ the firm’s MC? Does it affect the firm’s minimum efficient scale?a) when w1 = 8 and w2 = 9, derive the supply function y(p) for Pot & Gold Inc b) Suppose that Pot & Gold Inc has to pay a quasi-fixed cost of $50. When w1 = 8 and w2 = 9, derive the supply function y(p) for Pot & Gold IncSuppose there are 500 identicsl competitivd firms producing widgets and assume the total cost curve for each firm is given as, TC= 5q2+wq+10 and marginal cost is given as MC=10q + w where w is the widget maker's wage and q is the firm's output. If w=$50 what is the equation of the firms short run supply curve? 1) what is the average firm's profit (losses) at the new price of $61? 2) is the average firm in the short-run or long run? given it's profit(losses) should the firm continue to operate? 3) what would you predict, based on the perfectly competitive model of markets, will happen in this industry in the long run?
- 4. Assess which of the following is true and which is false.A firm’s profit equation is given by π = -100 + 160Q – 20Q2. Therefore,a) The firm’s fixed cost is 100.b) The firm’s fixed cost is 40 and variable cost is 20.c) Marginal profit is Mπ = 160 – 20Q.d) The firm’s profit-maximizing output is Q = 4.e) Marginal profit is Mπ = 160 – 40Q and it is positive for quantities that are lower than theprofit-maximizing quantity.Demand for microprocessors is given by P = 35 – 5Q , where Q is the quantity of microchips (in millions). The typical firm’s total cost of producing a chip is Ci = 5qi, where qi is the output of firm i. a) Does the typical microchip firm display increasing, constant, or decreasing returns to scale? What would you expect about the real microchip industry? In general, what must be true about the underlying technology of production for competition to be viable?1. Imagine that there is an industry for a particular product where the demand for this product is given by P = 100-X. There are two factors of production, capital K and labor L; the price of each will be $1 throughout. The firms all have identical technology, which is given by a fixed coefficients production function: where Y is the level of output and a is some constant from (0, 1). Each firm has fixed costs of 16. (a) Suppose there are precisely six firms in this industry; they can exit if they are unprofitable, but no firms can enter. What is the long-run equilibrium in this case? (Even though there are only six firms, they all entertain competitive conjectures about their effect on various prices.) (b) Suppose there is free entry into this industry. What is the long-run equilibrium? 2. Suppose one firm in a general equilibrium economy has a technology with free disposal Prove that Walrasian equilibrium prices are nonnegative.
- Suppose that the steel firm’s costs are shown below: Complete the table and determine the optimal output to be Price of steel is P175 per unit. Output (Q) TFC TVC TC MC TR MR Profit/Loss 0 500 0 1 500 50 2 500 90 3 500 140 4 500 200 5 500 270 6 500 350 7 500 450 8 500 600 9 500 800Nicole wants to examine first if she wants to enter the market for Chanel bags and she assumes that the market is under perfect competition. She observed that all the firms that are producing Chanel bags have the same LR cost function and is given by C = 200 + 20q + 0.5q2. All firms present in the market has a fixed cost of $200 if it produces a positive output, otherwise the LR cost is zero if there is zero production. The market demand for Chanel bags is QD = 1000 - 2p, where p is the price of one umbrella. Currently, Nicole counted that there are 22 firms in the industry and that the market is a constant cost industry.(c) Suppose that the demand for the Chanel Bag shifts to QD = 1600 - 2p. Assuming that the industry is in the LR equilibrium, solve for the market clearing condition and the number of firms present.2. Consider a manufacturing firm with total cost function: TC = 250,000 + 40Q + 0.01Q2, and market demand function: P = 940 – 0.02Q (a) Determine the firm’s profit function. (b) Determine the firm’s OPTIMAL output level. (c) Find the market price of the output at optimal operation?