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Consider the following production function
TPL = 12L2 – 0.8L3
- Find the value of L that maximizes APL
- Find the value of L that maximizes MPL
Given function:
TPL = 12L2 – 0.8L3
Step by step
Solved in 4 steps with 2 images
- Consider the following production function TPL = 12L2 – 0.8L3 Find the value of L that maximizes TPL Find the value of L that maximizes APL Find the value of L that maximizes MPLSuppose the two factors are perfect complements and the production function is given by y=min { 13x1,2x2} Where x1=300, X2=50 What will be level of production and draw corresponding iso quant?Sam Malone is considering renovating the bar stools at Cheers.The production function for new bar stools is given byq = 0.1k 0.2l0.8 where q is the number of bar stools produced during the renovation week, k represents the number of hours of bar stoollathes used during the week, and l represents the number ofworker hours employed during the period. Sam would like toprovide 10 new bar stools, and he has allocated a budget of$10,000 for the project.a. Sam reasons that because bar stool lathes and skilled barstool workers both cost the same amount ($50 per hour),he might as well hire these two inputs in equal amounts.If Sam proceeds in this way, how much of each input willhe hire and how much will the renovation project cost?b. Norm (who knows something about bar stools) arguesthat once again Sam has forgotten his microeconomics.He asserts that Sam should choose quantities of inputs sothat their marginal (not average) productivities are equal.If Sam opts for this plan instead, how much of…
- What is the marginal physical productivity (MPP) of the inputs given the function Q=12x21+2x1x2+2x22?Suppose that a certain factory output is given by the Cobb-Douglas production function ?(?, ?) = 60?^1/3?^2/3 units, where K is the level of capital and L the size of the labor force need to maximize the factory’s output. (a) Determine whether the Cobb-Douglas production function is concave, convex, strictly concave, strictly convex or neither.Does the value of λ change if the budget changes from $4600 to $5600?What condition must a Cobb-Douglas production function q = cKαW β satisfy toensure that the marginal increase of production is not affected by the size of thebudget?
- What is the marginal Physical Productivty (MPP) of the inputs given the function Q= 18x21+2x1x2+2x22 ?Answer the Constrained Optimization: Cobb-Douglas Production Function:3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product of Capital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combination of K and L that the firm should use to produce the maximum possible output. Do not solve the problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it facesConsider the following production function: Q = 100L0.5K0.5 subject to the budget constraint 5L + 10K = 75; where L is labour and K is capital. Derive the capital to labour ratio.
- If the economy uses inputs efficiently, then (pls select all that applies) Group of answer choices a) MRTS = 1. b) MRTS must be equal to the slope of a firm’s isoquant curve. c) the ratio of input marginal products must be equal to the ratio of input prices. d) the quantity of one output cannot be increased without decreasing the quantity of the other. e) every firm’s MRTS is equal to every consumer’s MRS. f) every firm’s MRTS is equal to the ratio of input prices. g) MRTS = MRT. h) outputs are on PPThe production function y= K0.5 L0.5 shows that the inputs are perfect substitutes. True or false.Suppose the productionfunction is given by Q = 5K + 3L. What is the average product of capital when10 units of capital and 10 units of labor are employed? 5 8 3 30