Economics Problem Solving - Assignment Example

Economics Problem Solving Name Tutor Unit Code Question 1 a) If both firms enter the market, and they collude, they will set MR = MC1 to fix the profit-maximizing output. (MC1 < MC2) MR = 100 – 0.5Q = 15 + 0.4Q = MC1 Q = 94.44 Since the firms are in a cartel, they will split the output equally among themselves; Firm A = 47.22 and Firm 2 = 47.22 b) P = 100 – 0.5(94.44) = $52.77 c) The profit for Firm 1 will be: = (47.22) (52.77) - (15 + 0.4(47.22)) = $2457.91 The profit for Firm 2 will be: = (47.22) (52.77) - (10 + 0.2(47.22)) = $2472.35 d) Total industry profit will be: $2457.91 - $2472.35 = $4930.26 e) Profit-maximizing rule for a two plant firm: MC1 = MC2 = MR Question 2: Incremental Reasoning Incremental reasoning entails the estimation of how a decision alternative will impinge on the business costs and revenues. In particular, incremental reasoning reflects on the change in total revenue and total cost resulting from changes in output, price, and investment, among others. It is a general business judgement that every business activity/job should generate some profit. Therefore, special orders that do not cover the costs incurred and make a profit are generally refused. However, incremental reasoning shed more light on making such decisions. In this case, the firm has an annual production capacity of 18,000 units. The budgeted costs and revenue are based on 14,000 units. Therefore, 4,000 more units can be produced without affecting the average variable cost. The special order from the new customers involves 5,000 on an all or nothing deal. The 1,000 units will entail production of additional units that will effectively raise the labour cost by 50 per cent. Therefore, the overall expected costs, revenue and profit will be: Cost/Revenue Amount ($) Labour 70000+35000=105000 Raw material 70000 Fixed cost 50000 Revenue 210000+70000=280000 Profit 55000 If the order is accommodated, the firm will generate additional profits of 35,000 (55,000-20,000). This shows that there is idle capacity that can be utilised to generate more revenue. Therefore, the firm should accommodate the purchase order in its entirety. Question 3 a) Marginal cost function = -0.21 + 0.0014Q b) The marginal cost curve crosses the average variable cost curve at the minimum point of the average variable cost curve. Thus, the average variable cost reaches its minimum when the marginal cost = 0. 0 = -0.21 + 0.0014Q 0.0014Q = 0.21 Q = 150 units Minimum AVC = 125 – 0.21(150) + 0.0007(1502) = 109.25 c) A profit-maximizing perfectly competitive firm is expected to produce the level of output where P = MR = MC. Therefore: 125 = -0.21 + 0.0014Q 0.0014Q = 125 + 0.21 Q = 90 units Profit = Total Revenue – Total Cost Profit = (125*90) – ((109.25*90) + 3500) Profit = -2082.50 d) 115 = -0.21 + 0.0014Q 0.0014Q = 115 + 0.21 Q = 83 units Profit = Total Revenue – Total Cost Profit = (115*83) – ((109.25*83) + 3500) Profit = -3022.75 e) 100 = -0.21 + 0.0014Q 0.0014Q = 100 + 0.21 Q = 72 units Profit = Total Revenue – Total Cost Profit = (100*72) – (109.25*72) Profit = -4166 Question 4 a) MC = -0.04 + 0.0001 b) The marginal cost curve crosses the average variable cost curve at the minimum point of the average variable cost curve. Thus, the average variable cost reaches its minimum when the marginal cost = 0. 0 = -0.04 + 0.0001Q 0.0001Q = 0.04 Q = 400 units AVC = 20 – 0.04(400) + 0.00005(4002) = 4.08 c) A profit-maximizing perfectly competitive firm is expected to produce the level of output where P = MR = MC. Therefore: 23.60 = -0.04 + 0.0001Q 0.0001Q = 23.60 + 0.04 Q = 23.60 units Profit = Total Revenue – Total Cost Profit = (23.60*236.4) – ((4.08*236.4) + 500) Profit = 4114.53 d) 14.94 = -0.04 + 0.0001Q 0.0001Q = 14.94 + 0.04 Q = 36.4 units Profit = Total Revenue – Total Cost Profit = (14.94*36.4) – ((4.08*36.4) + 500) Profit = -104.70 e) 10 = -0.04 + 0.0001Q 0.0001Q = 10 + 0.04 Q = 100.40 units Profit = Total Revenue – Total Cost Profit = (14.94*100.40) – ((4.08*100.40) + 500) Profit = -304.80 Question 5 a) Forecasted demand Q = 1000(-100P) (0.2M) (-500Pr) b) The inverse demand function expresses P as a function of Q; Q = 1000 – 100p + 0.2(30000) – 500(5) Q = 4500 – 100P P = 45 – 0.01Q c) Marginal revenue is the derivative of total revenue; TR = (45 – 0.01Q) Q = 45Q – 0.01Q2 MR = 45 – 0.02Q d) Estimated marginal cost function = -0.08 + 0.0002Q e) To maximise the profits, the firm will produce; 5 = -0.08 + 0.0002Q 5.08 = 0.0002Q Q = 25,400 units Question 6 I. In the absence of an external market, production is determined by adding up the two marginal cost functions vertically and setting the sum (MCS) equal to marginal revenue: P = 100 – Q; MR = 100 − 2Q MCS = MCP + MCM = 2Q + Q = 3Q MR = 100 − 2Q = 3Q = MCS; Q = 20 at P = 80 The transfer price is set equal to the marginal cost of manufacturing the optimal level of output: PT = MCP = (2) (20) = 40 II. The production division should manufacture the quantity that sets its marginal cost equal to the competitive price: P = 52 = 2Q so QP = 26 The transfer price is equal to the competitive market price: MCS = PT + MCM = 52 + Q MCS is set equal to marginal revenue to establish the number of units that will be purchased by the marketing division and the price at which they will be sold: MR = 100 − 2Q = 52 + Q = MCS and QM = 16 at P = 84 Question 7 The barometric firm's demand function (QDL) constitutes the horizontal difference between the market demand function and the followers' aggregate marginal supply function: QDL = QDM – QMS = 800 – 0.50P – 2 - 0.50P = 798 – P The barometric firm's marginal revenue function is: P = 798 – QDL so MR = 798 – 2QDL The barometric firm will produce the quantity of output that equates its marginal cost with the marginal revenue associated with its demand function: MC = 600 = 798 – 2QDL = MR so QDL = 99 and P = 699 The follower firms take the price determined by the barometric firm as given and produce a quantity that equates their aggregate marginal supply with price: P = 699 = 2QF = MC so QF = 349.5 and total output is 449.5. Question 8 The horizontal sum of the marginal revenue functions (MRS) for the two markets is calculated as follows: PA = 200 – 0.5QA so MRA = 200 − QA and QA = 200 − MRA PB = 120 – 0.5QB so MRB = 120 − QB and QB = 120 − MRB Q = QA + QB = 200 – MRS + 120 – MRS = 320 − 2MRS MRS = 160 – 0.5Q This horizontally summed marginal revenue function applies when marginal revenue is below 120. When marginal revenue is above 120, only the marginal revenue function for market A is relevant. Setting the firm's marginal cost function equal to MRS yields: MRS = 160 – 0.5Q = 20 + 0.20Q = MC so Q = 200 and MRS = 60 Substituting MRS = 60 into the marginal revenue function for the two markets yields QA= 140 and QB = 60. Substituting these quantities into the demand functions yields PA = 130 and PB = 90. References Gans, J. King, S. Stonecash, R. and Mankiw, G.N. (2011). Principles of Economics. 5th edn. Cengage Leraning. Sexton, R.L. and Fortura, P. (2006). Exploring Economics. Nelson Education Limited. 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