# Microeconomics and mathematics (with answers) 5 Cost, revenue and profit

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1 Microeconomics and mathematics (with answers) 5 Cost, revenue and profit Remarks: = uantity Costs TC = Total cost (= AC * ) AC = Average cost (= TC ) MC = Marginal cost [= (TC)'] FC = Fixed cost VC = (Total) variable cost AVC = Average variable cost (= VC ) TC = FC + VC Revenues TR = Total revenue (= AR * ) AR = Average revenue (price) (= TR ) MR = Marginal revenue [= (TR)' Profit = π π = TR - TC 5.1 Total and average cost Fixed cost = 1200 Average variable cost = Calculate total cost if 300 units are produced Graph total cost as a function of ( = 0,100,200,...600) Graph average cost as a function of ( = 100,200,...600). 5.2 Cost, revenue, profit, break-even point A firm has fixed cost of 300, variable cost of 10 per unit and sells a unit at the price of Graph total cost (FC, VC), total revenue and show profit/loss ( = 0,10,...100) in the same diagram Calculate the break-even point (π = 0):, cost and revenue 5.23 Calculate the quantity where profit is 60. UESTI05.DOC Page 1 (of 5) 5 Cost, revenue and profit 1st June 2012

2 5.3 Profit, break-even point 5.31 Express profit (= TR - TC) as a function of by using additionally: Fixed cost (FC) Average variable cost (AVC) Average revenue (AR) 5.32 Calculate profit (loss) by using the the equation obtained in FC = 240 AVC = 5 AR (= Price) = 8 = Use the equation obtained in 5.31 and the numbers of 5.32 to calculate if we target a profit of Calculate the break-even point using the equation obtained in 5.31 and the numbers of Demand and revenue 8 P Demand (= Price, AR) Find the demand function (P =...) Find the total revenue function Find the marginal revenue function Calculate average revenue, total revenue and marginal revenue if = 3 = Demand and revenue 5.51 Demand: P = 50-5 Find the total revenue and the marginal revenue functions. UESTI05.DOC Page 2 (of 5) 5 Cost, revenue and profit 1st June 2012

3 5.5 cont Calculate marginal revenue if = 2 = Graph demand, marginal revenue and total revenue as follows: P MR TR Which relation exists between MR = 0 and TR? 5.6 Fixed cost, demand and profit 10 A firm has only fixed cost of 20. Demand: P = We suppose that the firm can choose. Which results in the highest profit and how much is this profit? 5.7 Cost Total cost = Find the equation for average cost and for marginal cost. UESTI05.DOC Page 3 (of 5) 5 Cost, revenue and profit 1st June 2012

4 5.8 Cost Average cost = Find the equation for marginal cost Output = 30. Calculate total cost, average cost and marginal cost Another firm wants to buy from us an additional unit for the price of 350. Would you sell the additional unit? 5.9 Cost TC 30 Total cost Find the equation for total cost (TC) Find the equation for average cost and for marginal cost Marginal revenue and price elasticity of demand (e) 24 AR MR MR Demand (= AR, Price) Calculate the price elasticity of demand (e) if MR = 0 (at the point = 4). (Formula for e = d dp * P ) UESTI05.DOC Page 4 (of 5) 5 Cost, revenue and profit 1st June

5 5.11 From marginal revenue to total revenue and average revenue Marginal revenue = 20-5 Find - by integration - the equation for total revenue (c = 0), then the equation for average revenue From marginal cost to total cost and to average cost; fixed and variable cost Marginal cost = Find - by integration - the equation for total cost Which part of total cost is fixed, which part is variable? Find the equation for average cost Calculate total cost, average cost and marginal cost if = 20. Suppose that c = From marginal cost and marginal revenue to total cost and total revenue; profit Marginal cost = (Fixed cost c = 50) Marginal revenue = 20 - (c = 0) Find - by integration - the equations for total cost and total revenue Calculate profit if = 3. Answers. Click here! UESTI05.DOC Page 5 (of 5) 5 Cost, revenue and profit 1st June 2012

6 Answers Microeconomics and mathematics 5 Cost, revenue and profit 5.1 Total and average cost 5.11 TC = *300 = / Total cost Average cost Cost, revenue, profit, break-even point 5.21 Graph TC TR 1500 TR TC 800 Loss Profit Variable cost Fixed cost 5.22 Break-even point: = 16-6 = = 50 Cost/revenue: *50 = ( = 60): = 16 = 60 ANSWER05.DOC Page 1 (of 5) 5 Cost, revenue and profit 13/06/2016

7 5.3 Profit, break-even point 5.31 = TR - TC = AR* - FC - *AVC = - FC + (AR - AVC) 5.32 = (8-5) = - 30 ( Loss) = (8-5) - 3 = = Break-even point ( = 0): 0 = (8-5) - 3 = = Demand and revenue 5.41 P (= AR) = TR = AR* = MR = (TR)' = AR TR MR = = Demand and revenue 5.51 TR = P* = MR = (TR)' = MR (if = 2): 50-10*2 = 30 MR (if = 5): = Page If MR = 0, TR is at its maximum. 5.6 Fixed cost, demand and profit TC = 20 TR = *P = MR = (TR)' = 24-6 If MR = 0 then = 4 (if = 4): TR - TC = 24*4-3* = 28 ANSWER05.DOC Page 2 (of 5) 5 Cost, revenue and profit 13/06/2016

8 5.5 cont Graph demand, marginal revenue and total revenue: P MR P (=AR) MR 10 TR TR (TR)' = MR = Cost AC = TC 10 = MC = (TC)' = Cost 5.81 TC = AC* = MC = (TC)' = TC = 6* *30 = 5558 AC = = (or AC = 6* = 185.3) MC = 12* = No, I would not sell because MC > MR (P). ANSWER05.DOC Page 3 (of 5) 5 Cost, revenue and profit 13/06/2016

9 5.9 Cost 5.91 TC = = AC = TC = MC = (TC)' = Marginal revenue and price elasticity of demand (e) P = 24-3 (Demand) 3 = 24 - P = P d dp = P = 24-3*4 = 12 P = 12 4 = 3 d dp * P = * 3 = - 1 e = From marginal revenue to total revenue and average revenue TR = I(20-5)d = AR = TR = From marginal cost to total cost and to average cost; fixed and variable cost TC = I( )d = c Fixed part: c Variable part: AC = c TC = * = 4187 AC = = 209 (or: = 209) MC = * = 466 ANSWER05.DOC Page 4 (of 5) 5 Cost, revenue and profit 13/06/2016

10 5.13 From marginal cost and marginal revenue to total cost and total revenue; profit TC = I( )d = TR = I(20 - )d = Profit = TR - TC ( = 3): TR = 20* = 55.5 TC = 10* * = 44 = = 11.5 Back to questions. Click here! ANSWER05.DOC Page 5 (of 5) 5 Cost, revenue and profit 13/06/2016

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