The estimation of a Cobb-Douglas production function for 20 firms of a given industry yields: q₁ = 16.907 + 0.322k₁ + 2.777l₁ R² = 0.915 DW = 2.032 RSS = 0.461 Use a = 5%
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- 1. The estimation of a Cobb-Douglas production function for 20 firms of a given industry yields: = 16.907 + 0.322k₁ + 2.777l₁ R² = 0.915 DW = 2.032 RSS=0.461 Use a = 5% Var ß= 0.166070 0.031857 0.216639 -0.857446 -0.057229 4.939971/ where : fitted values of naturals logaritrhms of output (output express in 1000 tons); k₁: natural logaritrhms of capital output (output express in 1000 tons) l: natural logaritrhms of labour (labour is in hours) RSS: residual sum of squares t: firm index Var ß: variance - covariance matrix of estimates a. Evaluate the statistical significance of the coefficients.10K L%. 1). Consider the production function Q = (a) What is the output when K = 100000 and L = 243? (b) Use the marginal analysis to estimate Q(99995, 243) and Q(100000, 245). (c) Use a calculator to compute these two values of Q to three decimal places and compare these values with your estimates in (b). (d) How big must AL be in order for the difference between Q(100000, 243+AL) and its linear approximation Q(100000, 245) + -DAL, to differ by more than two units?It is estimated that a grocer’s daily profit from the sale of two brands of cherry juice is given by thefunction:P(x,y) = (x - 30)(70 - 5x + 4y) + (y – 40)(80 + 6x – 7y) centswhere x is the price per can of Brand V Juice and y is the price per can of Brand Triple V Juice. CurrentlyBrand V Juice sells for 50 cents per can and Brand Triple V Juice sells for 52 cents per can.i. Use marginal analysis to estimate the change in the daily profit that will result if the grocer raises theprice of Brand Triple V by one cent per can while keeping the price of Brand V unchanged.ii. Find a stationary point of the daily profit function. Classify this stationary point.
- 21. The estimation of a Cobb-Douglas production function for 20 firms of a given industry yields: 4. 16.907+0.322k; +2.777li R2 = 0.915 DW = 2.032 RSS = 0.461 Use α = 5% 4.939971 Var ẞ=0.216639 0.031857 -0.857446 -0.057229 0.166070/ where fitted values of naturals logarithms of output (output express in 1000 tons); ki: natural logarithms of capital output (output express in 1000 tons) l: natural logarithms of labour (labour is in hours) RSS: residual sum of squares 1: firm index Var ẞ: variance-covariance matrix of estimates Evaluate the statistical significance of the coefficients.1. Exercise 9.1 A study of 86 savings and loan associations in six northwestern states yielded the following cost function. 2.38 0.006153Q 0.000005359Q² 19.2X1 C + + (2.62) (2.84) (3.16) (3.50) where C = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times 100 percent. Q = output; measured by total assets ($ million) X1 = ratio of the number of branches to total assets ($ million) Note: The number in parentheses below each coefficient is its respective t-statistic. Which of the variable(s) is (are) statistically significant in explaining variations in the average operating expense ratio? (Hint: t0.025,7€ 1.99 .) Check all that apply. X1 Q2 What type of average cost-output relationship is suggested by these statistical results? Quadratic Linear Cubic Based on these results, what can we conclude about the existence of economies or diseconomies of scale in savings and loan associations in…A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p = 75 – 0.1D units (D is the demand or quantity sold per month and p is the price in dollars). The fixed cost is $1,000 per month and the variable cost is $30 per unit produced. Solve, a. What is the maximum profit per month related to thisproduct? b. What is the range of profitable demand during a month?
- Q4 A business manager determines that t months after production begins on a new product, the number of units produced will be P thousand,where P(t) =6?2 + 5? /(? + 1)2 production in the long run (i) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture.Turbulence makes it difficult to directly measure the thickness of the slick at the source (where x = 0),but for x > 0,it is found that y =0.5(x2 + 3x)/ x3 + x2 + 4x Required:a)Assuming the oil slick is continuously distributed,how thick would you expect it to be at the source?The cost, in millions of dollars, of building a three-story high school in NewYork State was estimated to be: 2C x x x x 1.7 0.14 0.0001 20 400where x is the number of thousands of square feet. Suppose that you arecontemplating building a for-profit three-story high school and estimate thatyour total revenue will be $0.2 million dollars per thousand square feet.(a) What is minimum area for a three-story high school in New YorkState, that this model covers? (b) What is the variable cost of building a three-story high school in NewYork State? (c) What is the fixed cost of building a three-story high school in NewYork State? (d) Determine the profit function,P x( ), for building a three-story highschool in New York State? . (e) Determine,P(250) , for building a three-story high school in New YorkState, and interpret the result. (f) How many thousands of square feet should a three-story high schoolbuilding in New York State be in order to break even?A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p = 77 – 0.12D units. The fixed cost is $800 per month and the variable cost $25 per unit produced. What number of units, D*,should be produced per month and sold to maximize the profit per month related to the product? Round your answer to 2 decimal places.
- calculate the Reaction functionsProfit Analysis Unendo, is a large computer game manufacturer. They have estimated that the demand function for their game "Star Wars Battlefront III" is as follows... STAR WARE BATTLEFRONT p = 86 - 0.05q where p is the price of a game and q is the number of game produced and sold per week. They estimate that their cost function in dollars is ... Clq) = 179 + 5000; where the fixed cost is $5000 and the marginal cost is $17 per game Unendo wishes to maximize the weekly profit of producing and selling the game. Find the maximum profit they can earn. (Round your answer to 2 decimal places, if necessary).s) Suppose that a company has fixed costs of 300300 dollars and variable costs of 0.75x+14200.75x+1420 dollars per unit, where x is the number of units produced. Suppose further that the selling price of its product is 1550-0.3x1550-0.3x dollars per unit. In each part, assume that the number of units produced/sold must be a whole number and round to the nearest one. (a) Find the break-even points. The larger number of units at which break- even occurs is , with corresponding revenue dollars. and The smaller number of units at which break- even occurs is , with corresponding revenue dollars. (b) Find the maximum revenue. (c) What price will maximize profit? (Recall that profit is the difference between revenue and cost)