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 MPL
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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 MPL
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- Suppose 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…How does a consumer’s optimal choice of goods change if all prices and the consumer’s income double? (Hint: focus on the budget constraint. You don’t have to, but you can use an example to support your answer).5. Output is produced according to a production process given by: Q = 4LK, where L is the quantity of labor input and K is the quantity of capital input. If the price of K is $10 and the price of L is $5, then what is the cost-minimizing combination of K and L capable of producing 32 units of output?
- How do you create a concave production possibilites curve graph?Consider an individual who receives utility from consumption, c, and leisure, l. The individual has L time to allocate to work, n, and leisure. The individual’s consumption is a function of how much he works. In particular, c = root n. The individual’s maximization problem is max U =ln(c)+θl subject to c = √n n+l=L where θ > 0. Solve the maximization problem. Hint: Substitute both constraints into the objective function.(i) Find the rate of change of the function f(x) =x + 2/ 1 − 8x with respect to x when x = 1.(ii) The number of units Q of a particular commodity that will be produced with Kthousand dollars of capital expenditure is modeled by Q(K) = 500 K2/3Suppose that capital expenditure varies with time in such a way that t months from nowthere will be K(t) thousand dollars of capital expenditure, whereK(t) =2t4 + 3t + 149 / t + 2 (a) What will be the capital expenditure 3 months from now? How many units will be producedat this time?(b) At what rate will production be changing with respect to time 5 months from now?Will production be increasing or decreasing at this time?
- 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 PPWhat is the marginal Physical Productivty (MPP) of the inputs given the function Q= 18x21+2x1x2+2x22 ?Given a production function of this nature; AX1aX2b determine the Marginal Rate of Technical Substitution.
- What is the marginal physical productivity (MPP) of the inputs given the function Q=12x21+2x1x2+2x22?Q5The rate of change of the function f(x) =x + 2 /1 − 8xwith respect to x when x = 1. (i) The number of units Q of a particular commodity that will be produced with K thousand dollars of capital expenditure is modeled by Q(K) = 500 K^2/3. Suppose that capital expenditure varies with time in such a way that t months from nowthere will be K(t) thousand dollars of capital expenditure,whereK(t) =2t4 + 3t + 149 /t + 2 Required:(a) What will be the capital expenditure 3 months from now? How many units will be producedat this time? (b) At what rate will production be changing with respect to time 5 months from now?Will production be increasing or decreasing at this time?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.