<p>Solutions – Assignment 1 – Managerial Economics</p><p>1. (a) </p><p>= 10,000 (0.20) + 15,000 (0.30) + 20,000 (0.40) + 25,000 (0.10)</p><p>= $17,000</p><p>(b) </p><p>= [(10,000  17,000)2 (0.20) + (15,000  17,000)2 (0.30) + (20,000  17,000)2 (0.40) + (25,000  17,000)2 (0.10)].5 = [21,000,000].5</p><p>= $4,583</p><p>(c) </p><p>= 4,583 / 17,000 </p><p>= 0.270</p><p> n 2. (a) Expected(Enrol) A =  Ei Pi i3</p><p>= E1P1  E2 P2  E3 P3 = 8000(.25) + 12000(.5) + 16000(.25) = 2000 + 6000 + 4000  E A = 12000 n Expected(Enrol) B =  Ei Pi i3</p><p>= E1P1  E2 P2  E3 P3 = 8000(.3) + 10000(.4) + 16000(.3) = 2400 + 4000 + 4800  E B = 11200</p><p> n  2 c) Standard deviation  A  (Ei  E A ) * Pi i3 = (8000 12000) 2 *(.25)  (12000 12000)2 *(.5)  (16000 12000)2 *(.25) = (4000) 2 *(.25)  (0)2 *(.5)  (4000) 2 *(.25) = 4000000  4000000</p><p> A  2828.43</p><p> n  2 c) Standard deviation  B  (Ei  E B ) * Pi i3 = (8000 11200) 2 *(.3)  (12000 11200)2 *(.4)  (16000 11200)2 *(.3)</p><p> B  3250</p><p> d) Coefficient of Variation of A</p><p> A   A / E A = 2818.43 / 12000</p><p> A  0.234870 Coefficient of Variation of B</p><p>   B / EB = 3250/11200 = 0.29 3. ANS:</p><p>(a) ED = %Q / %P</p><p>= (Q2  Q1)/(Q2 + Q1)</p><p>= (P2  P1)/(P2 + P1)</p><p>Q1 = 150 P1 = $5.18 Q2 = 200 P2 = $4.38</p><p>= 1.71</p><p>(b) A 1 percent increase in price will result in a 1.71 percent decrease in demand for charcoal.</p><p>4. ANS:</p><p>(a) </p><p>QA1 = 10,000 PB1 = $3.49 QA2 = 8,000 PB2 = $2.59 (b) </p><p>ED = 2.2 Q1 = 8,000 P1  2.98 Q2 = 10,000</p><p>P2 = $2.69</p><p>5. ANS:</p><p>(a) </p><p>Q1 = 23,000 P1 = $375 P2 = $325</p><p>Q2 = 27,312.5 units</p><p>(b) Price effect</p><p>%QD = ED%P</p><p>= +0.1714 (= 17.14%)</p><p>Income effect</p><p>%Q = EY%Y</p><p>Y2 = 7,000 Y1 = 6,750 = + 0.0909 (= 9.09%)</p><p>Net effect = Price effect + Income effect = 0.1714 + 0.0909 = 0.2623</p><p>Using the INITIAL QUANTITY (Q1 = 23,000) as the base in computing the percentage change yields:</p><p>Q2 = Q1 (1 + Net effect)</p><p>= 23,000 (1 + 0.2623)</p><p>Using the AVERAGE QUANTITY [(Q1 + Q2)/2] as the base in computing the percentage change yields:</p><p>Q2 = 29,934 units</p><p>Presto – </p><p>A table or spreadsheet for Presto output (Q), price (P), total revenue (TR), marginal revenue (MR), total cost (TC), marginal cost (MC), total profit (π), and marginal profit (Mπ) appears as follows:</p><p>Total Marginal Total Marginal Total Marginal Units Price Revenue Revenue Cost Cost Profit Profit 0 $60 $0 $60 $100,000 $5 ($100,000) $55 1,000 55 55,000 50 105,500 6 (50,500) 44 2,000 50 100,000 40 112,000 7 (12,000) 33 3,000 45 135,000 30 119,500 8 15,500 22 4,000 40 160,000 20 128,000 9 32,000 11 5,000 35 175,000 10 137,500 10 37,500 0 6,000 30 180,000 0 148,000 11 32,000 (11) 7,000 25 175,000 (10) 159,500 12 15,500 (22) 8,000 20 160,000 (20) 172,000 13 (12,000) (33) 9,000 15 135,000 (30) 185,500 14 (50,500) (44) 10,000 10 100,000 (40) 200,000 15 (100,000) (55)</p><p>B. The price/output combination at which total profit is maximized is P = $35 and Q = 5,000 units. At that point, MR = MC and total profit is maximized at $37,500. The price/output combination at which total revenue is maximized is P = $30 and Q = 6,000 units. At that point, MR = 0 and total revenue is maximized at $180,000. Using the Presto table or spreadsheet, a graph with TR, TC, and π as dependent variables, and units of output (Q) as the independent variable appears as follows:</p><p>C. To find the profit-maximizing output level analytically, set MR = MC, or set Mπ = 0, and solve for Q. Because</p><p>MR = MC</p><p>$60 - $0.01Q = $5 + $0.001Q</p><p>0.011Q = 55</p><p>Q = 5,000</p><p>At Q = 5,000,</p><p>P = $60 - $0.005(5,000)</p><p>= $35 π = -$100,000 + $55(5,000) - $0.0055(5,0002)</p><p>= $37,500</p><p>(Note: 2π/Q2 < 0, This is a profit maximum because total profit is falling for Q > 5,000.) To find the revenue-maximizing output level, set MR = 0, and solve for Q. Thus,</p><p>MR = $60 - $0.01Q = 0</p><p>0.01Q = 60</p><p>Q = 6,000</p><p>At Q = 6,000,</p><p>P = $60 - $0.005(6,000)</p><p>= $30</p><p>π = TR - TC</p><p>= ($60 - $0.005Q)Q - $100,000 - $5Q - $0.0005Q2</p><p>= -$100,000 + $55Q - $0.0055Q2</p><p>= -$100,000 + $55(6,000) - $0.0055(6,0002)</p><p>= $32,000</p><p>(Note: 2TR/Q2 < 0, and this is a revenue maximum because total revenue is decreasing for output beyond Q > 6,000.)</p><p>D. Given downward sloping demand and marginal revenue curves and positive marginal costs, the profit-maximizing price/output combination is always at a higher price and lower production level than the revenue-maximizing price- output combination. This stems from the fact that profit is maximized when MR = MC, whereas revenue is maximized when MR = 0. It follows that profits and revenue are only maximized at the same price/output combination in the unlikely event that MC = 0. In pursuing a short-run revenue rather than profit-maximizing strategy, Presto can expect to gain a number of important advantages, including enhanced product awareness among consumers, increased customer loyalty, potential economies of scale in marketing and promotion, and possible limitations in competitor entry and growth. To be consistent with long-run profit maximization, these advantages of short-run revenue maximization must be at least worth Presto's short-run sacrifice of $5,500 (= $37,500 - $32,000) in monthly profits.</p>