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- Question 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 1.11Consider the following production function for shirts: q = v6 L3/4K/4, where L is worker-hours, and K is sewing machine-hours. a. Compute the marginal products of labor and capital, the average product of labor, and the marginal rate of technical substitution of labor for capital (i.e. how many units of capital are needed to make up for the loss of one unit of labor)? b. Are there diminishing returns to labor (that is, does the marginal product of labor decrease when labor L increases)? What about to capital? Is there diminishing marginal rate of technical substitution (MRTS)? с.Consider the following production function: q = 9LK + 6L² – Assuming capital is measured on the vertical axis and labor is measured on the horizontal axis, determine the value of the marginal rate of technical substitution when K= 30 and L= 10. MRTS = -. (Enter a numeric response using a real number rounded to two decimal places.) 20 tv MacBook Air F6 FB 10 F3 23 2$ & з 4 6 7 8 { [ E Y U P D F G J K > C V N M command option - .. .- B
- Suppose the production function is Cobb-Douglas and f(x1,x2)) = x11/2x3/221. Write an expression for the marginal product of x1.2. Does marginal product of x1 increase for small increases in x1, holding x2 fixed? Explain3. Does an increase in the amount of x2 lead to decrease the marginal product of x1? Explain4. What is the the technical rate of substitution between x2 and x1?5. What is the type of returns to scale of this production function? (Increasing, decreasing,constant)Consider a firm that produces output (y) using only two inputs (A and B). The firm has a perfect substitutes production technology and a production function of the formf(A, B) = 5A + 8B. %3D Suppose the firm is currently using 200 units of input B. What is the marginal product of inputA when A 100? 500 What is the marginal product whenA 150? 750 Give your answers to two decimal places.What is the marginal physical productivity (MPP) of the inputs given the function Q = 12x + 2x1x2 + 2x²? Select one: O a. MPPT₁ 24x1 + 2x1 MPP₂ = 2x1 + 4x₁ O b. MPPT₁ = 24+ 2x₂ + 2 MPPT₂ = 2x1 + 4x2 OC. MPPT₁ MPPT2 O d. MPPT₁ MPPT - 24x₁ + 2x1 2x2 + 4x2 Time 24x₁ + 2x₂ 2x₁ + 4x2 Next p
- Suppose that this conveyor-manufacturing firm has another location and would like you to evaluate the input mix decisions at this new location. Here is all you know about the newlocation. The marginal rate of technical substitution is currently 0.5. The marginal product of labor at its target level of output is 60 rollers per hour. What is the marginal product of capital? Ifthe rental rate for capital is $24 per hours at this location and the wage paid to labor is $12 per hour, could this location be minimizing the costs of producing its target level of output? Explain briefly.QUESTION 2The total production of a good y is determined by the production function y = 3L2/3K1/3, where L is labour input and K capital input.The reward (factor prices) for labour and capital are, l = 27 en r = 2, respectively.The producer needs to produce 9000 units of good y.How much units of labour will he hire if he wants to miminize his total costs? 1587,4839,953000515,23What is the marginal physical productivity (MPP) of the inputs given the function Q=18x21+2x1x2+2x22 ? Select one: a. MPPx1=36x1+2x1MPPx2=2x1+4x1 b. MPPx1=36x1+2x1MPPx2=2x2+4x2 c. MPPx1=36+2x2+2MPPx2=2x1+4x2 d. MPPx1=36x1+2x2MPPx2=2x1+4x2
- (04.Suppose we are given (he constant returns to scale (CES) production function q= { ßa + aa }1/a a. Show that the marginal product of Beta is (g/B) and marginal product of Alpha (q/a)** b. Show that RTS = (2/B); I lence or otherwise shov that the ò =-1/(1-a) 1-aY-2x11 y2-3X12 Q 4. ( A) Consider the following production functions: y2 are products and x is the use of input i in the production of productj. The total use of x is a function of y, and y2 given by: x1 =;+ where yi and %3D a) Find the product transformation rate. b) What will be the shape of production possibility curve? c) Are the productive competitive OR1. Let y = f(x1, x2)=x11/2+ X1X2 be a firm's production function, where x20, x220. - a. Write down the firm's production possibility set, and its input requirement set.“ b. Is this production function concave, quasi-concave? c. Is this production function homogenous, homothetic? + d. Find its returns to scale when x1=1, and x2=1.e
