Q2. The economist for the ABC Truck Manufacturing Corporation has calculated a production function for the manufacture of their medium-size trucks as follows: Q= 1.3*(L^0.75)*(K^0.3) Where Q is the number of trucks produced per week, L is the number of labor hours per day and K is the daily usage of capital investment. 1. Does the equation exhibit increasing, constant or decreasing returns to scale? Why? 2. Calculate the marginal product of labor and marginal product of capital using the below data? 3. How many trucks will be produced per week with the following amounts of labor and capital? Labor Capital 100 50 120 60 150 75 200 100 300 150

Q2. The economist for the ABC Truck Manufacturing Corporation has calculated a production function for the manufacture of their medium-size trucks as follows: Q= 1.3(L^0.75)(K^0.3) Where Q is the number of trucks produced per week, L is the number of labor hours per day and K is the daily usage of capital investment. 1. Does the equation exhibit increasing, constant or decreasing returns to scale? Why? 2. Calculate the marginal product of labor and marginal product of capital using the below data? 3. How many trucks will be produced per week with the following amounts of labor and capital? Labor Capital 100 50 120 60 150 75 200 100 300 150

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.7P

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A second firm's production function is given by the equation Q = 12L.5K.5. Input prices are $36 per labor unit and $16 per capital unit, and P = $10. a. In the short run, the firm has a fixed amount of capital, K = 9. Create a spreadsheet to model this production setting. Determine the firm's profit - maximizing employment of labor. Use the spreadsheet to probe the solution using your spreadsheet's optimizer.
Suppose a Cobb-Douglas Production function is given by the function: P(L,K)=8L^0.7K^0.3Furthemore, the cost function for a facility is given by the function:C(L,K)=300L+500KSuppose the monthly production goal of this facility is to produce 20,000 items. In this problem, we will assume LL represents units of labor invested and KK represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs?Units of Labor LL = (Show your answer is exactly 1 decimal place)Units of Capital KK = Incorrect (Show your answer is exactly 1 decimal place)Also, what is the minimal cost to produce 20,000 units? (Use your rounded values for LL and KK from above to answer this question.)The minimal cost to produce 20,000 units is $ Hint: Your constraint equation involves the Cobb Douglas Production function, not the Cost function. When finding a relationship between LL and KK in your system of…
Given the production function Q=30K0.7 L 0.5 the input price are w=30 a Determine the equation for the expansion d r=20 What is the different efficient input combination for an output rate of Q = 200 ? for Q=500?
How would you determine that a two-input Cobb-Douglas production function has decreasing returns to scale (DRS), increasing returns to scale (IRS) or constant returns to scale (CRS) depending on whether α1 + α2 is larger than, smaller than, or equal to one?
Bloomswood Hotel is situated in Forkland, a picturesque town in the mountain region of a country. Allen Grabos works as a gourmet chef at the hotel that caters mostly to tourists. In a conversation with his wife, Delia Grabos, Allen claims that he is underpaid. The hotel makes up to $500,000 per year but his annual salary is only around $28,000 a year. Delia, however, is of the opinion that since new hotels and inns are expected to open in Forkland, the salaries paid to hotel staff in the area should increase. (1) Which of the following, if true, will weaken Delia's argument? A. Due to an increase in the number of fatal accidents recently in Forkland, tourism in the area was adversely affected. B. Tourism revenues in Forkland have been increasing consistently for the past 5 years. C. Spring and summer are the peak tourist seasons in Forkland. D. Bloomswood sold one of its seaside resorts because tourism in that part of the country declined substantially. E. Bloomswood…
You are working to model your production function and you are interested in the equation of the line tangent to the production function at a specific level of production. You know that the equation of the tangent line will be first derivative of the production function. Given this information, Previously, a consultant had estimated that your production function could be estimated as f(x) = -1,000 + 26 hours - 0.2 hours^2 Given that you firm is planning to use 97 hours in the production process, what is the value of the equation of the tangent line at 97?
The Cobb-Douglas production function can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form: Q=γ[δK−ρ+(1 - δ)L−ρ]−ν/ρ�=�[δK−ρ+(1 - δ)�−ρ]−ν/ρ where γ is an efficiency parameter that shows the output resulting from given quantities of inputs; δ is a distribution parameter (0 ≤ δ ≤ 1) that indicates the division of factor income between capital and labor; ρ is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the production process; and ν is a scale parameter (ν > 0) that indicates the type of returns to scale (increasing, constant, or decreasing). Complete the following derivation to show that when ν = 1, this function exhibits constant returns to scale. First of all, if ν = 1: Q� = = γ[δK−ρ+(1 - δ)L−ρ]−1/ρ�[δK−ρ+(1 - δ)�−ρ]−1/ρ = = γ[δK−ρ(−1/ρ)+(1 - δ)L−ρ(−1/ρ)]�[δK−ρ(−1/ρ)+(1 - δ)�−ρ(−1/ρ)] = = Then, increase the…
The chief economist for Argus Corporation, a large appliance manufacturer, estimated the firm’s short-run cost function for vacuum cleaners using an average variable cost function of the form AVC = a + bQ + cQ2 where AVC = dollars per vacuum cleaner and Q = number of vacuum cleaners produced each month. Total fixed cost each month is $180,000. The following results were obtained: Dependent Variable AVC R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS 19 0.7360 39.428 0.0001 PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE VARIABLE INTERCEPT 191.93 54.65 3.512 0.0029 Q -0.0305 0.00789 23.866 0.0014 Q2 0.0000024 0.00000098 2.449 0.0262 Quetsion: At what level of output will average variable cost be at a minimum? What is the minimum average variable cost?
The chief economist for Argus Corporation, a large appliance manufacturer, estimated the firm’s short-run cost function for vacuum cleaners using an average variable cost function of the form AVC = a + bQ + cQ2 where AVC = dollars per vacuum cleaner and Q = number of vacuum cleaners produced each month. Total fixed cost each month is $180,000. The following results were obtained: DEPENDENT VARIABLE: AVC R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 19 0.7360 39.428 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 191.93 54.65 3.512 0.0029 Q -0.0305 0.00789 23.866 0.0014 Q2 0.0000024 0.00000098 2.449 0.0262 d) If Argus Corporation produces 10,000 vacuum cleaners monthly, what is the estimated average variable cost?
Please explain why the law of diminishing returns applies only in the short-term period.
Refer to Figure 11-1. Diminishing marginal returns is illustrated in the per-worker production function in the figure above by a movement up along any of the production functions. from Production function 1 to Production function 2. from Production function 1 to Production function 3. from Production function 2 to Production function 1.
You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi:Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled c. At the end of the year it is expected that output will double with purchase of new equipment and machinery. The production function is estimated to be Q = 60L.30K.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? d. Assume Kia Head Office is considering hiring more laborers either at their Gwadar plant or alternatively at the Karachi plant. What will be your advice if workers’ marginal product is 40 at wage of Rs=5/hour in Karachi and marginal product is 28 at wage of Rs=4/hour in Gawdar?