Question Three a) Suppose the average total cost (ATC) of a firm is given as 4 ATC = Q +-2 Find the output(Q) that minimizes marginal cost b) Consider the following average revenue and cost functions AR = 60 – 6Q TC = 10Q2 – 6Q + 30 Suppose the government imposes a per-unit tax on output Q such that tax function is given as T = tQ where t is the tax rate. Determine: i) The output that maximizes profit ii) Tax rate t that maximizes tax revenue iii) Total tax T iv) Maximum profit and price level
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- Wonopoly and natural resource prices Suppose that a firm is the sole owner of a stock of a natural resource. a. How should the analysis of the maximization of the discounted profits from selling this resource (Equation 17.63 be modified to take this fact into account? b. Suppose that the demand for the resource in question had a constant elasticity form q(t)=a[p(t)]b . How would this change the price dynamics shown in Equation 17.67? c. How would the answer to Problem 17.7 be changed if the entire crude oil supply were owned by a single firm?Suppose a tax is set at t’ in the figure. How many units of emissions are ABATED and is abatement achieved cost effectively? Suppose a regulation has just been implemented requiring that coal-fired power plants pay a tax of $80 on each unit of emissions (1 unit is 1 metric ton). Before the tax was imposed, a plant called Old River Power had an emissions level of 100 units. Given a marginal abatement cost function of 200 – 2E, under the tax policy what will Old River Power pay the regulator in emissions taxes?A firm faces the following average revenue (demand) curve:P = 120 − 0.02Qwhere Q is weekly production and P is price, measured in cents per unit. The firm’s costfunction is given by C = 60Q + 25,000. Assume that the firm maximizes profits.i. What is the level of production, price, and total profit per week?ii. If the government decides to levy a tax of 14 cents per unit on this product, what will be thenew level of production, price, and profit?b. The United States currently imports all of its coffee. The annual demand for coffee by U.S.consumers is given by the demand curve Q = 250 – 10P, where Q is quantity (in millions ofpounds) and P is the market price per pound of coffee. World producers can harvest and shipcoffee to U.S. distributors at a constant marginal (= average) cost of $8 per pound. U.S.distributors can in turn distribute coffee for a constant $2 per pound. The U.S. coffee market iscompetitive. Congress is considering a tariff on coffee imports of $2 per pound.i. If there…
- a. A firm faces the following average revenue (demand) curve:P = 120 − 0.02Qwhere Q is weekly production and P is price, measured in cents per unit. The firm’s cost function is given by C = 60Q + 25,000. Assume that the firm maximizes profits. i. What is the level of production, price, and total profit per week?ii. If the government decides to levy a tax of 14 cents per unit on this product, what will be the new level of production, price, and profit?A Los Angeles firm uses a single input to produce a recreational commodity according to a production function f(x)=4x1/2, where x is the number of units of input. The price of the commodity is $100 per unit, and the input cost is $50 per unit. The fixed costs are zero. A: Write down the firm’s profit function. C:Find the profit maximizing amounts of input and output. What is the maximum profit? C:Suppose that the firm is taxed at $20 per unit of its output (note it is a quantity tax) and the price of its input is subsidized by $10 per unit. What is the new input and output levels? What is the new maximal profit?Glen Eira City Council wants to impose a tax to fish and chips shops. It is considering two types of tax:- a lump sum of 500$ on each fish and chips owner- a tax of 2$ per kg of fish and chips sold, paid by each fish and chips owner(a) Which cost curve would shift as a consequence of each type of tax? (AFC, AVC, (b) Consider the following table of long-run total cost for three different fish andATC, MC)?
- Show the effect of a 25% profit tax on the accounting profit of all firms in a competitive industry. Consider all time periods.. An electricity producer has a constant marginal cost of production equal to $40 per megawatt. The residual demand for its electricity is given by P (q) = a−bq, where P is the price and q is the quantity of power generated by this producer. The producer knows the slope, b, but he vertical intercept of the residual demand curve, a is unknown. Assume A and B are greater than zero. If you get stuck, you may answer any of the following questions for special case where a = 80 And b = 0.5 for partial credit. (a) What is the marginal revenue, M R(q), for this producer? b) What is the optimal q for this producer? (c) What is the electricity producer’s optimal price? (d) What is the electricity producer’s optimal bid in a uniform price Auction? e) Suppose b is equal to zero. Would the producer have an incentive to submit a bid above its marginal cost? Explain.Suppose the demand for a product X produced by a company AAA is given by the following function: QX = 2000 - 250*PX. At what price per item of the product X (EUR) can this copmany maximize its total revenues? Fill in the Table gaps: Demand function Price function Total Revenue (EUR) Marginal Revenue (EUR) Quantity Price per product (EUR) Q = 2000 - 250P P = ? TR = Q*P MR = dTR/dQ = 0 Q = ? P = (2000 - Q)/250 250P = 2000 - Q TR = Q*(2000 - Q)/250 MR = 8 - 2*Q/250 Q/125 = 8 P = (2000 - 1000)/250 P = (2000 - Q)/250 TR = 8*Q - Q^2/250 8 - Q/125 = 0 Q = 1000 P = 4 Alternative solution Demand function Total Revenue (EUR) Marginal Revenue (EUR) Price per product (EUR) Q = 2000 - 250P TR = Q*P MR = dTR/dP = 0 2000 - 500*P = 0 TR = (2000 - 250P)*P MR = 2000 - 2*250*P 500*P = 2000 TR = 2000P - 250P^2 MR = 2000 - 500*P P = 4
- A 62 metre length of rope is cut into pieces whose lengths are in arithmetic progressionwitha common difference of d metres. Given that the lengths of the shortest and thelongest pieces are 0.5 and 3.5 metres respectively, find d.(C) For a firm’s product, the demand function isp = 72 2 0.04qand the average cost function isc¯ =500q+ 30 At what level of output would profit be maximized?Assume inverse demand function for game console in an imaginary country is P=1200-4Q and the total cost function is TC=400+4Q2. Government put $120 of specific tax on production. If the market is competitive what is the incidence of tax on consumer? If the market is monopolist what is the incidence of tax on consumer?Demand for a company’s product is given by the following equation: Q=1000-0.5P. You are also given that its total cost function TC=100+1000Q. Compute the profit maximizing price and quantity B. A firm earns an accounting profit of K150, 000 per year in project A. The firm could earn K150, 000 and K120, 000 in investments B and C, respectively. How much economic profit is the firm earning assuming the three projects are mutually exclusive?