# Essays on Economics Problem Solving Assignment

The paper “ Economics Problem Solving” is a convincing variant of the assignment on macro & microeconomics. If the order is accommodated, the firm will generate additional profits of 35,000 (55,000-20,000). This shows that there is an idle capacity that can be utilized to generate more revenue. Therefore, the firm should accommodate the purchase order in its entirety. Question 3 Marginal cost function = -0.21 + 0.0014Q 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 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 = -2082.50 115 = -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 = -3022.75 100 = -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 MC = -0.04 + 0.0001 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 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 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 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 Forecasted demand Q = 1000(-100P) (0.2M) (-500Pr) 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 Marginal revenue is the derivative of total revenue; TR = (45 – 0.01Q) Q = 45Q – 0.01Q2 MR = 45 – 0.02Q Estimated marginal cost function = -0.08 + 0.0002Q To maximise the profits, the firm will produce; 5 = -0.08 + 0.0002Q 5.08 = 0.0002Q Q = 25,400 units Question 6 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 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.