6. Optimize the Cobb-Douglas production function given the following parameters. The maximum 12 and the price of about of money available to spend is $1, 200 where the price of K = L = 6. That is P = 12 and P = 6. The function is given as q = K0.4L°.6. Using the Lagrangian method, what are the optimal values of Ko and Lo?
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- 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?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.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.
- (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-adoubt EXERCISE 11.6 Suppose capital and labour are perfect complements in a one- to-one ratio. That is, suppose that Q = min (L, K). Currently, the wage is w=5 and the rental rate is r = 10. What is the minimum cost and method of produc ing Q = 20 units of output? Suppose the wage rises to w' = 20. If we keep total cost the same, what level of output can now be produced and what method of production (input mix) is used? PVERSam 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…
- Very short answer ...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?If output is produced according to Q = 4LK, the price of K is $10, and the price of L is $40, then the cost minimizing cost minimizing combination of K and L capable of producing 64 units of outputlis L O and K 64 (please put your answers in numerical value with no comma or decimal place)
- .(a) A firm has production function q(k,l) = k'/³1²/3, where k denotes the capital used and I denotes the labour employed. Suppose that each unit of capital costs v dollars and each unit of labour costs w dollars, so that the capital and labour costs are vk + wl. Use the Lagrange multiplier method to determine the values of k and I that minimise the cost of producing Q units of the firm's good. Find the corresponding minimised value, C, of this cost and the value, X*, of the Lagrange multiplier corresponding to the optimising values of k and l. Show that d* =A firm face the production function:Q=120L+200K-L2-2K2It can buy L at N5 a unit and K at N8 a unit with a budget of N70. Use any method ofyour choice to find the maximum output the firm can produce.Both capital and labor are variable inputs. Suppose the wage rate of labor is 16 (per hour) and the rental price of capital is 20 (per hour). The downward sloping smooth curves that bend in towards the origin are a firm's isoquants. The downward sloping straight lines are isocost lines. If the ferm plans to produce 20 units of output lper hour), its minimized cost is Capital slope=-0.8 (6,5.5) (4,5) (2,3) q=30 q=20 q=10 Labor O 180 O 160 O 164 O 122