Answers BBEM 4103 Managerial Economics Test I Question

Answers BBEM 4103 Managerial Economics Test I

Question 1 • Managerial economics can be best described as applied microeconomics because it applies microeconomics theory with quantitative tools to achieve company’s objectives. • It integrates economic theory into the management’s decision making process. • It integrates economics theory with techniques of quantitative analysis such as mathematical economics, optimization analysis, regression analysis, costing, linear programming, and risk analysis.

Question 2 Given the total revenue (TR) and total cost (TC) functions of Firm XY are as follow: TR=1400 Q-6 Q 2 TC=1500+80 Q a. Write the firm’s profit (π) function. π = TR-TC π = (1400 Q-6 Q 2)-(1500+80 Q) π = 1400 Q-6 Q 2 -1500 -80 Q π = 1320 Q-6 Q 2 -1500 b. Calculate the marginal profit of the firm based on the answer in part (a). π’ = 1320 -12 Q c. Determine the optimum output or Q* that could optimize the firm’s profit. 1320 -12 Q=0 -12 Q=-1320 Q*=110

Question 2 (cont. ) d. Verify whether the answer in part (c) contribute to the firm’s optimization effort. S. O. C π’ = 1320 -12 Q π’’ = -12 Yes, Q*=110 contribute to the firm’s optimization effort since (-ve) value indicate maximum. e. Calculate the firm’s total cost (TC) Substitute Q*=110 into total cost function. TC=1500+80 Q TC=1500+80(110) TC=10, 300 f. Calculate the firms total revenue (TR) Substitute Q*=110 into total revenue function. TR=1400 Q-6 Q 2 TR=1400(110)-6(110)2 TR=154, 000 -72600 TR=81, 400

Question 2 (cont. ) g. Calculate the firm’s total profit. Substitute Q*=110 into the profit function π = 1320 Q-6 Q 2 -1500 π = 1320(110)-6(110)2 -1500 π = 145, 200 - 72, 600 - 1500 π = 71, 100

Question 3 (a) Maximize the company’s profit subject to the constraint. To maximize the profit, we need to differentiate the profit function π=-60+140 Qx+100 Qy-10 Qx 2 -8 Qy 2 -6 Qx. Qy and solve for Qx* and Qy*. However, the constraint function 20 Qx+40 Qy=200 put limitation that the total quantity produced by the firm must equal 200 units.

Question 3 (cont. ) Step 1: Find Qx from the constraint function. 20 Qx+40 Qy = 200 20 Qx = 200 -40 Qy Qx = (200 -40 Qy)/20 Qx = 10 - 2 Qy Substitute Qx = 10 - 2 Qy into the profit function (which is also known as the objection function of the firm) π=-60+140 Qx+100 Qy-10 Qx 2 -8 Qy 2 -6 Qx. Qy π=-60+140(10 - 2 Qy )+100 Qy-10(10 - 2 Qy )2 -8 Qy 2 -6(10 2 Qy ) Qy

Question 3 (cont. ) π=-60+140(10 - 2 Qy )+100 Qy-10(10 - 2 Qy )2 -8 Qy 2 -6(10 - 2 Qy ) Qy Expand the new profit function. π=-60+140(10 - 2 Qy )+100 Qy-10 (10 - 2 Qy ) - 8 Qy 2 - 6(10 2 Qy ) Qy π = -60+1400 - 280 Qy +100 Qy – 10(100 – 20 Qy + 4 Qy 2) - 8 Qy 2 – 6(10 Qy - 2 Qy 2) π = -60+1400 - 280 Qy +100 Qy – 1000 + 200 Qy – 40 Qy 2 - 8 Qy 2 – 60 Qy + 12 Qy 2 π = 340 + 160 Qy – 36 Qy 2 Differentiate the profit function to maximize the company’s profit subject to the constraint: π’= 160 – 72 Qy

Question 3 (cont. ) c. What is the optimum quantity of Y? Then, substitute Qy* = 2. 22 in the constraint function to obtain Qx* Set the first derivative = 0 and solve for the optimum X and Y quantity. Qx = 10 - 2 Qy π’= 160 – 72 Qy Qx = 10 – 2(2. 22) b. What is the optimum quantity of X? 160 - 72 Qy = 0 Qx* = 5. 56 units -72 Qy = -160/ -72 Qy* = 2. 22 units

Question 3 (cont. ) d. Calculate the company’s total profit. Given: π=-60+140 Qx+100 Qy-10 Qx 2 -8 Qy 2 -6 Qx. Qy Substitute Qy* = 2. 22 and Qx* = 5. 56 into the profit function: π=-60+140(5. 56)+100(2. 22)-10(5. 56)2 -8(2. 22)26(5. 56)(2. 22) π= -60 + 778. 4 + 222 - 309. 136 - 39. 427 - 74 π= RM 517. 837

Question 4 (a) • R = 12. 6 + 22 W – 4. 1 X + 16. 3 Z (b) • R 2 = 0. 3175 • R 2 is the coefficient of determination. It is used to determine how well the regression line fits the data. • It shows that 31% of changes in the dependent variable (R) can be explained by the independent variables W, X, and Z.

Question 4 (cont. ) (c) • F-ratio = 4. 660 • Another test of overall explanatory power of the regression is the analysis of variance (ANOVA), which uses the F-statistics or F-ratio. • The meaning of F-ratio cannot be simply interpreted based on the given value. • Student needs to use F-distribution table to compare the calculated F values with the critical value from table.

Question 4 (cont. ) (d) • The Standard Error (S. E) of Intercept = 8. 34, W = 3. 61, X = 1. 65, and Z = 4. 45. • Standard error of estimation is a measure of the dispersion of the data points from the line of best fit (simply known as the regression line) • The smaller the S. E of estimation, the closer the data points are to the regressed line. • In other words, S. E of estimation is used to indicate the accuracy of a regression model.

Question 4 (cont. ) (e) • If W, X, and Z are all equal to 0, • R = 12. 6 + 22 W – 4. 1 X + 16. 3 Z • R = 12. 6 + 22(0) – 4. 1(0) + 16. 3(0) • R = 12. 6 (f) • If W = 10, X = 5, and Z = 30, R = ? • R = 12. 6 + 22(10) – 4. 1(5) + 16. 3(30) • R = 701. 1

Question 5 (a) • Given y = (3 x 4 + 5)6. Find the derivative using chain rule. • Let y = u 6 and u = 3 x 4 + 5. Then, y’ @ dy/du = 6 u 5 and u’ @ du/dx = 12 x 3 • Apply the Chain rule: y’ @ dy/dx = dy/du. du/dx • y’ = 6 u 5. 12 x 3 • y’ = 72 x 3 u 5 • @ • y’ = 6(3 x 4 + 5)5. 12 x 3 • y’ = 72 x 3(3 x 4 + 5)5

Question 5 (cont. ) b) y = (4 x 2 – 3)(2 x 5) – y’ = (4 x 2 – 3)(10 x 4) + 2 x 5 (8 x) – y’ = 40 x 6 – 30 x 4 + 16 x 6 – y’ = 56 x 6 – 30 x 4 c) y = 7 x 9 (3 x 2 – 12) – y’ = 7 x 9 (6 x) + (3 x 2 – 12)(63 x 8) – y’ = 42 x 10 + 189 x 10 – 756 x 8 – y’ = 231 x 10 – 756 x 8