Suppose a firm’s production function is ? = ?2?. a) Determine the labor and capital demand functions. b) Are capital and labor normal or inferior inputs in this production process?
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Suppose a firm’s production function is ? = ?2?.
a) Determine the labor and capital demand functions.
b) Are capital and labor normal or inferior inputs in this production process?
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- 1. A firm can manufacture a product according to the production function Q = F(K,L) = K³/4L¹/4 a. Calculate the average product of labour, when the level of capital is fixed at 16 units and the firm uses 16 units of labour. How does the average product of labour change when the firm uses 81 units of labour? b. Find an expression for the marginal product of labour when the amount of capital is fixed at 16 units. Then, illustrate that the marginal product of labour depends on the amount of labour hired by calculating the marginal product of labour for 16 and 81 units of labour. c. Suppose capital is fixed at 16 units. If the firm can sell its output at a price of £100 per unit and can hire labour at £25 per unit, how many units of labour should the firm hire to maximise profits?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.Q)solve it correctly The marginal products of capital (MPK) and labor (MPL) are, respectively, MPK = 2000 units; MPL = 1500 units. The input prices are: PK = $10/unit; and PL = $150/unit. To minimize production costs, the firm should A. increase both capital and labor B. decrease both capital and labor C. increase capital; decrease labor D. decrease capital; increase labor E. do nothing; costs are minimized
- 6. The Miller Company is trying to determine the combination of inputs to produce a specific volume of bar stools ordered. The production function for the firm is given: Q = 14LK? The wage of a worker is $80/day and the price of a machine is $240/day. If they need to produce 4,536 bar stools per day: a. What is the optimal combination of Labor and Capital, i.e. find the cost-minimizing combination of inputs to produce 4,536 bar stools? b. What is the total cost of using the inputs found in part a?2) The general Cobb-Douglas production function for two inputs is given by: q = f (k, l) = AKªL® where 0 0, f¡ > 0, frk 0. b.) Show that = a and ɛg,i Eq,k B (Note that ɛ's are elasticities). || C.) Show that, for this Cobb-Douglas function, production is CRS if a + ß = 1.1. 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
- The production function of a firm is x= A* l^a* k^(1-a-b)*e^b. l is labor, k is capital, e is energy, x is output (sold at price p) a) What is the interpretation of A? b) Under what condition(s) does the production function exhibit constant returns to scale} Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing? c) Setup the profit maximization problem for the firm. d) Find the optimality conditions for all the inputs in the production function. e)Find the input demand functions for labor, capital, and energy f) Find the optimal supply function for x. g) Setup the cost minimization problem Show the relevant Technical Rates of substitution. (I mainly have concerns for d), e), f) questions)The production function of a firm is x= A* l^a* k^(1-a-b)*e^b. l is labor, k is capital, e is energy, x is output (sold at price p) a) What is the interpretation of A? b) Under what condition(s) does the production function exhibit constant returns to scale} Is it homogeneous? Are the marginal products of inputs increasing, constant, or decreasing? c) Setup the profit maximization problem for the firm. d) Find the optimality conditions for all the inputs in the production function. e)Find the input demand functions for labor, capital, and energy f) Find the optimal supply function for x. g) Setup the cost minimization problem Show the relevant Technical Rates of substitution.Consider 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.
- A firm uses the inputs of Iron and labor to produce Cars. Suppose that the quantity of labor is fixed. The quantity of Iron and the number of Cars produced is given by the following table: Tons of Iron per week Number of Cars per week 0 0 10 50 20 100 30 170 40 220 50 250 60 260 70 250 80 200 What is the average product of Iron when 40 tons are used? What is the marginal product of the 60th ton Iron? Does this production function exhibit diminishing marginal returns? If so, at what quantity of Iron do they start to occur?Suppose the production function is Cobb-Douglas and f(x1;x2)=x11/2x23/2 Write an expression for the marginal product of x1. Does marginal product of x1 increase for small increases in x1, holding x2 fixed? Explain Does an increase in the amount of x2 lead to decrease the marginal product of x1? Explain What is the the technical rate of substitution between x2 and x1? What is the type of returns to scale of this production function? (Increasing, decreasing, constant)A firm uses 3 factors of production. Its production function is f(x, y, z) = min{x3/y, y2, (z4 − x4)/y2}. If the amount of each input is multiplied by 6, its output will be multiplied by A.) 216 B.) 36 C.) 6 D.) 0.16 -the Answer is 36, Please explain in detail why this is