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# The following problem relates firm output decisions, market supply, and market equilibrium in a perfectly competitive market (further referred as PCM), that is, a market in which consumers and producers are price-takers.

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Introduction

Answer Key for Additional Exercise on Costs The following problem relates firm output decisions, market supply, and market equilibrium in a perfectly competitive market (further referred as PCM), that is, a market in which consumers and producers are price-takers. Question 1. Complete the following table for a single firm in the short run. Table 1. Cost accounting table for the firm. Letters in the brackets refer to logic used (see below). Answers are given in italic font. OUTPUT (Q) [unit] TC [\$] AVC [\$/unit] ATC [\$/unit] MC [\$/unit] 0 300 - - - 1 400 100 (d) 400 (b) 100 (e) 2 450 (f) 75 (d) 225 (b) 50 3 510 (g) 70 170 (b) 60 (e) 4 590 72.5 (d) 147.5 (b) 80 (e) 5 700 (f) 80 (d) 140 (b) 110 6 840 (h) 90 (d) 140 140 (e) 7 1020 102.85 (d) 145.71 (b) 180 (e) 8 1250 (f) 118.75 (d) 156.25 (b) 230 9 1540 137.78 (d) 171.11 (b) 290 (e) 10 1900 (f) 160 (d) 190 (b) 360 Solution 1: First we need to recall some relationships between various measures of cost accounting in the short run1 and definitions. We will number newly introduced formulas by bold numbers in brackets and then refer to them by number, for convenience. We remember that (1). Definition for average total cost is (2) and for average variable cost - (3). If we divide both sides of equation (1) by quantity produced Q, and account for definitions (2) and (3) we get (4). Also, with definition (3), we can rewrite (1) ...read more.

Middle

TR (p*Q) Profit (TR-TC) <= [unit] [\$] [\$/unit] [\$/unit] [\$/unit] AVC<MC? [\$/unit] [\$/unit] [\$] [\$] => 0 \$300 \$0 (\$300) <= 1 \$400 400 100 100 FALSE 60 -40 \$60 (\$340) 2 \$450 225 75 50 FALSE 60 10 \$120 (\$330) 3 \$510 170 70 60 FALSE 60 0 \$180 (\$330) 4 \$590 147.5 72.5 80 TRUE 60 -20 \$240 (\$350) 5 \$700 140 80 110 TRUE 60 -50 \$300 (\$400) 6 \$840 140 90 140 TRUE 60 -80 \$360 (\$480) 7 \$1,020 145.71 102.86 180 TRUE 60 -120 \$420 (\$600) 8 \$1,250 156.25 118.75 230 TRUE 60 -170 \$480 (\$770) 9 \$1,540 171.11 137.78 290 TRUE 60 -230 \$540 (\$1,000) 10 \$1,900 190 160 360 TRUE 60 -300 \$600 (\$1,300) With the price equal to \$60 situation is not much different from p=\$50. Now MC(Q) = MR(Q) at Q=3. Nevertheless, although a small marginal profit is earned for second unit (see "Mprofit" marginal per-next-unit profit column in Table 3 above or same-name curve on "Unit Costs" graph to the right), the total profit for any number of units produced is still less than just fixed costs loss of -\$300 (which is well seen from "Profit" column in Table 3 and also vaguely seen from the lowest dashed curve "Profit" on "Totals" graph). This outcome is in perfect agreement with previous-page story, since the price = MR line on "Unit Costs" graph is clearly below any point of AVC(C) curve. So, at no output level the manager would be able to reduce loss from fixed costs. Thus, heavily-hearted, he orders to stop production before even starting it. ...read more.

Conclusion

on page 3). By the definition of the perfectly competitive market the entry in the market for new firms is easy, so they will tend to enter so to enjoy economic profits (non-existent in other, presumably in-long-equilibrium industries). Entry of new firms will shift the supply curve out (to the right), which will lead to price decrease down to the level of the typical firm's minimum ATC. After that the long-run equilibrium will be reached. 1 "Short run" is the time-related characteristic of the problem at hand, defined in terms of character of inputs to the production process. We have a "short run" analysis at hand, if at least one of the inputs is "fixed". If we have production function Q=F(L,K), and the time period we look in the problem is one month, then (a) labor L is a variable input (also called "factor of production"), since we typically can change the number of workers within the month by hiring/firing process, especially with hourly paid workers; (b) capital K would be typically a fixed input, since, for example, the lease for business premises is signed usually for not less than a year, thus we cannot change amount of capital within the time-frame in the problem, hence for purpose of this problem capital K is a fixed input/factor. NOTE: if we are asked to perform analysis for the year or two-year time-span, we would talk about "long run" analysis, since the manager will be able to decide (within that time frame) whether to enter in the premises lease altogether again. This makes capital - and thus all the inputs in problem - a variable input - in the long-run analysis. ECON 2010-500, Fall 2003 Answer Key for Additional Exercise on Costs Page 1 of 7 ...read more.

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