A country's production is described by the function f(x, y) = 30x y units, when x units of labor and y units of capital were used. a) Compute Jz and f.- b) What is the marginal productivity of labor and the marginal productivity of capital when the amounts expended on labor and capital are 100 units and 30 units, respectively? c) In order to increase the country's productivity, should the government have encouraged capital investment rather than increasing expenditure on labor?
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- USE R LANGUAGE TO SOLVE THE equation The output of a production process, Q is given by the function2K^(-3)L^(5/2)/2K log4 6L^2where K and L denote capital and Inbour. Calculate the output when the capital and labour are 10 and 20 units, respectively.Prof. Smith and Prof. Jones are going to produce a new textbook. The production function for the book is: ?=?1/2?1/2?= is the number of pages in the finished book?= is the number of working hours spent by Smith?= is the number of working hours spent by JonesSmith's labor is valued at 3 TL per working hour and Jones's labor is valued at 12 TL per working hour. After having spent 900 hours preparing the first draft, Smith cannot contribute any more to the book. Jones will revise the Smith's draft to complete the book.a) How many hours will Jones have to spend to produce a finished book of 300 pages?b) What is the marginal cost of the 300th page of the finished book?Suppose the production function for widgets is given byq = kl - 0.8k2 - 0.2l2where q represents the annual quantity of widgets produced, k represents annual capital input, and l represents annual labor input.a. Suppose k = 10; graph the total and average productivity of labor curves. At what level of labor input does this average productivity reach a maximum? How many widgets are produced at that point?b. Again assuming that k = 10, graph the MPl curve. At what level of labor input does MPl = 0?c. Suppose capital inputs were increased to k = 20. How would your answers to parts (a) and (b) change?d. Does the widget production function exhibit constant, increasing, or decreasing returns to scale?
- A farmer has 1 acre of land. If he uses X pounds of fertilizer he can harvest √x tons of wheat. What is his production function if he has A acres of land and can just replicate the same production process on each piece of land? XXX A * A VXA √XALet S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used () and the amount of capital used () by the following function: S- 20 L0 C0.7 In this formula L represents the units of labor input and Cthe units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 50,000 tons of steel at minimum cost. If your answer is zere, enter "p" Min 40 120 s.t. 20 S0000 (b) Solve the optimization problem you formulated in part a. Hint: When using Excel Solver, start with an initial >oand C0 Do not round intermediate calculations. Round your answers to the nearest whole number 2991 2318 Cost S 397448 ide FeedbackQ1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.
- Q1 a) Given a production function depicting the response of paddy rice tofertilizer application,Y = 3X+ 9X2 - X3(i) Calculate the exact MPP and APP.(ii) At what level of fertilizer input(X) does MPP, APP and TPP reachtheir maximum values?(iii) At what level of fertilizer input will r = 0? And what is the valueof TPP at that level?(iv) If the farmer increases the amount of fertilizer in his riceproduction in his area of diminishing returns, explain whether ornot total production will increase or decrease.b) Explain the economic significance of farm records.Q2 a) What are the major objectives of agricultural marketing?b) Explain how one can evaluate the efficiency of a marketing situation.Suppose the production function is given by O = 5K - 2L What is the marginal product of the 6th capital when 5 units of capital and 10 units of labor are employed? A5 b. 4 C. 11 d. 45Question 13 5 pts For the production function y = 4x1+ 3x2, which of the two inputs is more productive when x1 is 10 and x2 is 10? X1 X 2 neither; for this situation, they have equal marginal products cannot tell from the above information Question 14 5 pts Given the production function y = x1 1/3 x,1/3, what is the marginal physical product of x2 when x1 is 5 and x2 is 5? O 0.75 37 0.19 O 1.11
- 1. Consider the production function Q=K³/ª L/4 Further suppose that capital is fixed at 16 units. Answer the following questions: a. Find Q when L =16 units. What is the output (Q) when L increases to 81 units? e b. Find the average product of labor when L when L increases 81 units? 16 units. What is the average product of labor %3D c. Find the marginal product of labor when L 16 units. What is the marginal product of labor when L increases 81 units? d. Show that doubling all the inputs doubles the output.Please don't copy ans Economics You are the owner of a motorbike company that currently has two different factories, an old one and a new one. The old factory uses an old technology that requires large amounts of labor to produce motorbikes. The production technology for the old firm is given by Fo(L) = m*L^1/2 . The new factory uses a much more modern production technology given by Fn(L) = n*L^1/2 . a. What are costs as a function of output for each individual factory? b. Suppose that you want to produce 1000 motorbikes. How many motorbikes will you produce at the old factory and how many will you produce at the new factory? c. Derive an expression for the total cost of producing y motorbikes (assuming that you always divide production between the factories in the optimal way). How does this cost function compare to the individual factory cost functions? d. It turns out that you can upgrade your old factory to make it just as efficient as the new factory. To pay…Question 15 Consider the following figure (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a level of K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; five units of labor is shown as reference in the horizontal axis; the corresponding production for this level of labor is 200; the graphs slope is initially increasing, then there is an inflexion point to the left of five levels of labor; after this inflexion point, the slope of the graph is decreasing; a line that passes through zero and is tangent to the graph is also shown; this line is tangent to the graph for a level of labor that is to the left of 5.) Denote by APL(L,K)=f(L,K)/L the so-called average product of labor (here f is the production function of the firm). From the…