Assignment 5-SP24 AP1

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Louisiana State University, Shreveport *

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Business

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Feb 20, 2024

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Open: Feb. 15 th , 12:00am – Feb. 17 th , 11:59pm Recommend latest start time: Feb. 17 th , 8:30pm MBA 701 Module 5 Assignment 1. You collect the following production data for your firm: Q L 242 2 923 6 453 3 62 1 978 9 1,000 5 974 7 540 4 230 11 708 10 a. Which functional form (linear, quadratic, cubic) is most suitable to your data? Construct a scatter diagram but be sure to just do the dots; don’t include the lines that connect them. Then, play around with the trendline feature and include what you consider to be the best trendline. The most suitable functional form for this data is quadratic. The trendline best used for this data is polynomial or order 3. Between the linear, quadratic, and cubic trendlines, the polynomial trendline has the highest R-squared value, indicating that it is the most accurate match for the data. A greater R-squared value indicates a better fit, and it measures how well the trendline fits the data points. The LSUS College of Business considers course information to be proprietary to the professor of the course. Violating this intellectual property protection by scanning, copying, website posting, or reproducing and sharing course information is considered an infraction of the MBA Honor Code and LSUS Code of Student Conduct.

Open: Feb. 15 th , 12:00am – Feb. 17 th , 11:59pm Recommend latest start time: Feb. 17 th , 8:30pm 0 2 4 6 8 10 12 0 200 400 600 800 1000 1200 f(x) = − 4.03 x³ + 40.05 x² + 74.65 x − 42.2 R² = 0.95 Q Polynomial (Q) b. Using OLS, estimate the firm’s short-run production function. Comment on the strength of the regression results. The short-run production function is: Q = -42.20468274 + 74.64629632*L + 40.04980549*L^2 - 4.032115605*L^3 or Q = -42.20 + 74.65L^1 + 40.05L^2 – 4.03L^3 The R-squared is 0.952799598 or 95.28% implying that 95.28% of the variation in the dependent variable is explained by the model consisting of L, L^2, and L^3 as the explanatory variables. c. Calculate the Q, AP, and MP for L = 8 workers. Q = -42.20 + 74.65*8 + 40.05*8^2 - 4.03*8^3 Q = 1054.84 AP = TP / L = -42.20/8 + 74.65 + 40.05*8 - 4.03*8^2 AP at L = 8 is 131.71 MP = dQ/dL = 74.65 + 2*40.05*8 – 3*4.03*8^2 MP at L = 8 is -58.72 (For L=8, Q=1064.28, AP = 133.04, MP = -52.71) d. At 8 workers, is MC rising or falling, and how do you know? The LSUS College of Business considers course information to be proprietary to the professor of the course. Violating this intellectual property protection by scanning, copying, website posting, or reproducing and sharing course information is considered an infraction of the MBA Honor Code and LSUS Code of Student Conduct.

Open: Feb. 15 th , 12:00am – Feb. 17 th , 11:59pm Recommend latest start time: Feb. 17 th , 8:30pm The MC is increasing since the MP of labor is negative for 8 workers. This is likely due to the diminishing returns on labor, which indicates a marginal product that declines as the amount of labor (workers) increases. Marginal product is the additional production produced by each additional worker. When MP is negative in the near run, it suggest that each additional worker makes a less contribution to the overall output, which raises the marginal cost. dMP / dL = -113.44194 MP is falling MC = wage-rate/MP Since, MP is inversely related to MC, the MC is rising at L = 8 2. PewTooth ®, the popular new startup company that manufactures the world’s first-ever Bluetooth- enabled church bench, estimated its short-run costs using a U-shaped average variable cost function of the form and obtained the following results. Total fixed cost ( TFC ) at PewTooth® is $1,140. Adjusted R Square 0.853 Coefficient s Standard Error t Stat P-value Intercept 37.94 3.51 10.81 0.0004 Q -3.45 0.77 -4.48 0.0003 Q^2 0.24 0.04 6.74 0.0000 a. What level of output (Q) is associated with the minimum AVC? What is the value of AVC at this minimum? The level of output (Q) associated with the minimum AVC is 7.19 and the value of AVC at this minimum is $25.54 AVC = a + bQ + cQ^2 where: a, b, and c are coefficients obtained from the regression results. Q is the level of output. From the regression results provided: Coefficient for Q: b = -3.45 Coefficient for Q^2: c = 0.24 To find the minimum of the AVC function, we need to find the quantity (Q) at which its derivative with respect to Q equals zero. First, let's find the derivative of the AVC function: The LSUS College of Business considers course information to be proprietary to the professor of the course. Violating this intellectual property protection by scanning, copying, website posting, or reproducing and sharing course information is considered an infraction of the MBA Honor Code and LSUS Code of Student Conduct.

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Open: Feb. 15 th , 12:00am – Feb. 17 th , 11:59pm Recommend latest start time: Feb. 17 th , 8:30pm AVC = b + 2cQ Setting AVC' equal to zero and solving for Q: 0 = b + 2cQ Now, substitute the values of b and c: 0 = -3.45 + 2(0.24)Q Solving for Q: 3.45 = 0.48Q Q = 3.45 / 0.48 Q ≈ 7.19 So, the level of output associated with the minimum AVC is approximately 7.19 units. To find the value of AVC at this minimum, plug the value of Q back into the AVC function: AVC = a + bQ + cQ^2 AVC = 37.94 - 3.45(7.19) + 0.24(7.19)^2 (The level of output (Q) associated with the minimum AVC is 7.5 and the value of AVC at this minimum is $30) b. Determine equations for ATC, TC, and MC. Graph one scatterplot of Q vs. TC, and another scatterplot of Q vs. ATC, AVC, and MC. TVC = Q * AVC = 37.94*Q – 3.45*Q^2 + 0.24*Q^3 TFC = 1140 TC = TFC + TVC = 1140 + 37.94*Q – 3.45*Q^2 + 0.24*Q^3 ATC = TC/Q + AVC = 1140/Q + 37.94 - 3.45*Q + 0.24*Q^2 MC = ΔTC/ΔQ = ΔTVC/ΔQ = 37.94 – (3.45)*(2)*Q + (0.24)*(3)*Q^2 = 37.94 – 6.90 * Q + 0.72*Q^2 When output is 7.19, TC is $1323.64, AVC is $25.54, ATC is $209.64, and MC is $25.55. c. When output is 12, how much is TC, AVC, ATC, and MC? Q = 12 TC = 1140 + (37.94 * 12) – (3.45)(12)^2 + (0.24)(12)^3 AVC = 37.94 – (3.45)(12) + (0.24)(12)^2 The LSUS College of Business considers course information to be proprietary to the professor of the course. Violating this intellectual property protection by scanning, copying, website posting, or reproducing and sharing course information is considered an infraction of the MBA Honor Code and LSUS Code of Student Conduct.

Open: Feb. 15 th , 12:00am – Feb. 17 th , 11:59pm Recommend latest start time: Feb. 17 th , 8:30pm ATC = 1140 / 12 + 37.94 – 3.45(12) + (0.24)(12)^2 MC = 37.94 – 6.90(12) + 0.72(12)^2 When output is 12, TC is $1513, AVC is $31.10, ATC is $126.10, and MC is $58.82. d. At what amount of output does labor change from exhibiting increasing returns to decreasing returns? We know that increasing RTS = > ATC is declining Decreasing RTS = > ATC is rising Transition happens when ATC is minimum = -1140 / Q^2 – (3.45) + (0.48)*Q^3 = 0 = -1140 – 3.45*Q^2 + 0.44*Q^3 = 16.2176 Q = 16.2176 Using numerical methods, we find that the value of Q where labor changes from exhibiting increasing returns to decreasing returns is approximately Q ≈ 6.542 units. This means that beyond this level of output, the marginal product of labor starts to diminish, indicating the transition from increasing returns to decreasing returns to labor. The lowest point on the ATC curve, which indicates that the company is making efficient use of its resources. When the cost of the good is the same as the minimum ATC, productive efficiency occurs. 3. In the U.S., city governments usually grant a monopoly right to a single cable company to provide cable service to people in that city; i.e., if you want television service to your house delivered through coaxial or fiber-optic cable, there is only one company from which to choose. Our definition of perfectly competitive markets stressed three characteristics: 1) small firms each producing a small percentage of total output, 2) firms produce homogeneous products, and 3) easy entry and exit from the industry. Recent developments in the industry (say, over the past decade) have made the cable market much more competitive. Present an argument why the cable industry may now satisfy each of these three criteria, even despite the obvious government-granted monopoly. (1) (i) Perfectly competitive market is the market where many seller and buyers are present and selling homogeneous product. Firm in this industry is a price taker not the price maker. So, firm can be able to sell any amount of goods at the given price. So, demand curve for the firm will be perfectly elastic. This will be same for all firm in the same industry. The LSUS College of Business considers course information to be proprietary to the professor of the course. Violating this intellectual property protection by scanning, copying, website posting, or reproducing and sharing course information is considered an infraction of the MBA Honor Code and LSUS Code of Student Conduct.

Open: Feb. 15 th , 12:00am – Feb. 17 th , 11:59pm Recommend latest start time: Feb. 17 th , 8:30pm (ii) In the long run firm in perfectly competitive market, will earn only Normal Profits, because of the following points: (2) In case of Supernormal Profits, more new firms seeing the opportunity of earning will enter the market. This will increase the supply and price will decreases, ultimately profits reduce. Firm will start earning normal. In case of abnormal Losses, existing firm will start leaving the industry because of losses. This will reduce the supply and price increases, ultimately losses decrease. Firm start earning normal. Many U.S. cities have granted monopoly to single cable company, though it kills completion and against the law. But the logic behind this was: 1. It is costly to lay down the cable networks and lot of capital is required. The company must be assured of threat the competitors are not going to come, so that it can recover its investment. 2. There sia natural monopoly in the market i.e. it is not economically possible for two or more companies to compete & stay in the business of cable television However, with the recent developments, the three principles of a perfectly competitive market are being fulfilled in the industry. 1. Several non-cable players entered the market i.e. satellite TV and dish TV, and internet- based television 2. OTT content providers are further increased competition in the market. So we can say there are plenty of players in the market 3. All of them are producing similar content. Movies, reality shows, web series, sports telecast etc.; 4. All these players can enter and withdraw as and when they wanted. All these developments have benefited the consumer by way of wide choice and reduced/reasonable prices. So, we one can say that the three principles of perfectly competitive market are being fulfilled now. (3 ) While there may be a government-granted monopoly in providing cable services within a city, recent developments in the cable industry have introduced elements that contribute to increased competitiveness. Diverse Service Providers: Over the past decade, technological advancements have facilitated the emergence of alternative forms of content delivery. Streaming services, satellite providers, and internet-based television options have diversified the market, allowing The LSUS College of Business considers course information to be proprietary to the professor of the course. Violating this intellectual property protection by scanning, copying, website posting, or reproducing and sharing course information is considered an infraction of the MBA Honor Code and LSUS Code of Student Conduct.

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Open: Feb. 15 th , 12:00am – Feb. 17 th , 11:59pm Recommend latest start time: Feb. 17 th , 8:30pm consumers to access a wide range of content beyond traditional cable services. This diversification aligns with the characteristic of small firms each producing a small percentage of total output. Technological Convergence: The cable industry has witnessed a convergence of technologies, with many providers offering bundled services, including internet and phone services. This convergence has blurred the lines between traditional cable companies and other telecommunications providers, fostering a situation where firms produce a variety of services beyond just cable television. This contributes to a departure from the strict definition of producing homogeneous products. New Entrants and Disruptors: The advent of Over-the-Top (OTT) platforms and streaming services has lowered barriers to entry, allowing new players to enter the market without the need for extensive cable infrastructure. Additionally, advancements in wireless technologies have enabled the delivery of television content through alternative means. This enhances the ease of entry and exit from the industry, challenging the traditional notion of a cable monopoly. Despite the initial appearance of a government-granted monopoly in the cable industry, recent developments have fostered increased competition through diverse service providers, technological convergence, and the entry of disruptive players. This evolution aligns with the characteristics of a more competitive market, even within the context of a government- granted monopoly. 4. Suppose the market demand and supply functions are Q D = 112,500 – 150P and Q S = 125P + 49,250. You have just graduated and moved to this city; as a new MBA and an entrepreneur, you are considering entering the market for this product. a. Determine the equilibrium price and quantity in this market. b. You’ve researched and found that most firms in the market currently experience costs such that TC = 1,325 + 380Q – 6.75Q 2 + 0.07Q 3 . Determine whether or not you should enter this market. Use graphs to support your answer. (Remember that you can Format Axis and change the Minimum and Maximum Bounds of your axes to “zoom in” to a graph in Excel.) The LSUS College of Business considers course information to be proprietary to the professor of the course. Violating this intellectual property protection by scanning, copying, website posting, or reproducing and sharing course information is considered an infraction of the MBA Honor Code and LSUS Code of Student Conduct.

Open: Feb. 15 th , 12:00am – Feb. 17 th , 11:59pm Recommend latest start time: Feb. 17 th , 8:30pm c. Due to unforeseen delays, you don’t enter the market. However, a year later the market supply has changed to Q S = 125P + 38,250. Are you surprised at this shift in supply? d. Given the new supply conditions, determine whether you should enter the market. The LSUS College of Business considers course information to be proprietary to the professor of the course. Violating this intellectual property protection by scanning, copying, website posting, or reproducing and sharing course information is considered an infraction of the MBA Honor Code and LSUS Code of Student Conduct.

Assignment 5-SP24 AP1

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