Problem 7: For each of the following parts of this question, you are to calculate (i) MPL, (ii) MPK, and (iii) MRTSLK: (a) OOO Q = 10L0.5K0.5 Q = 18L² + 14K³ - L²K. Q = 17L +9K+0.6L0.4K0.5 Regarding the production function part (a) only: Q = 10L0.5K0.5. Do labor and capital have diminishing returns to output? Are there diminishing MRTSLK?
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- 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.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.Ben's swim coach estimates that his time, t, in the 100-yard butterfly at a big upcoming meet as a function of the number of yards he swims per week, y, is t = 50+8e-0.00005y Based on this production function, his coach also estimates that if Ben swims 20,000 yards per week, his time will be 52.94 seconds, and he will finish tenth place. If he swims 40,000 yards per week, his time will be 51.08 seconds, and he will come in third. If he swims 60,000 yards per week, his time will be 50.40 seconds, and he will win the meet. Use calculus to determine Ben's marginal productivity of time given the number of yards he practices. Is there diminishing marginal productivity of practice yards? Ben's marginal productivity of swim time given y practice yards (MP) is (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ MPy character.)
- The output (Q) of a production process is a function of two inputs (L and K) and K is given by the following relationship: Q = 0.50LK− 0.10L2− 0.05K2 The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is interested in maximizing output subject to a cost constraint of $500. Use the lagrangian optimization techniques to find the following: How many units of L and K should be used by the firm? What is the total output of this combination? What is the marginal rate of substitution between L and K?A T-shirt screener can screen t-shirts (q) in two different ways. He can either use a fast screening machine (F) or a slow screening machine (S). Screen use is defined in terms of ”hours” running. His production function is f(F, S) = 10F + 6S. (a) The screener wants to be able to produce 120 shirts. List three feasible and efficient production plans (combinations of inputs) for doing this. (b) Graph the screener’s isoquant curve for q = 120. (c) The hourly cost of using the fast machine is $800 and the hourly cost of the slow machine is $200. What is the cost minimizing (optimal) combination of inputs for producing 120 shirts? (d) Suppose the screener must now produce 400 shirts. What is the cost minimizing combination of inputs?The cost of controlling carbon dioxide emissions [C(E)] at a firm goes up rapidly as the amount of emissions (E) increase. Let's assume the relationship is defined by the function below. C(E)= 5000+ 40E +2E² E20 where E is measured in tonnes per year and C is measured in dollars per year. a) Determine the Marginal Cost function for controlling carbon dioxide emissions and find the marginal cost at 50 tonnes of emissions: b) Determine the Average Cost Function for controlling carbon dioxide emissions and find the tonnes of emissions at minimum average cost. c) The government is charging a tax of $270 for every tonne of carbon dioxide emitted. At, 50 tonnes of emissions, is it profitable for the firm to control emissions on its own or pay the carbon tax?
- The per-unit cist of an item is its average total cost=(=total cost/quantity). Suppose that a new cell phone application costs $100,000 to develop and only $0.70 per unit to deliver to each cell phone customer. What will be the per-unit coat of the application if it sells 100 units? What will be the per-unit coat of the application if it sells 1,000 units? What will be the per-unit cost of the application if it sells 1 million units?Does the output maximization level of input use exist for the following function? If yes, then what is the exact input-use level? y = x1 + 0.1x12 - 0.05x13 + x2 + 0.1x22 - 0.05x23100VKL, where q is 4. The production function for puffed rice is given by q = the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. (a) Calculate the q = 1,000 isoquant for this production function and show it on a graph. (b) If K = 10, how many workers are required to produce q =1,000? What is the average productivity of puffed-rice workers? (c) Suppose technical progress shifts the production function to q = 200 VKL. Answer parts (a) and (b) for this new situation.
- Q4 A business manager determines that t months after production begins on a new product, the number of units produced will be P thousand,where P(t) =6?2 + 5? /(? + 1)2 production in the long run (i) A ruptured pipe in a North Sea oil rig produces a circular oil slick that is y meters thick at a distance x meters from the rupture.Turbulence makes it difficult to directly measure the thickness of the slick at the source (where x = 0),but for x > 0,it is found that y =0.5(x2 + 3x)/ x3 + x2 + 4x Required:a)Assuming the oil slick is continuously distributed,how thick would you expect it to be at the source?10K L%. 1). Consider the production function Q = (a) What is the output when K = 100000 and L = 243? (b) Use the marginal analysis to estimate Q(99995, 243) and Q(100000, 245). (c) Use a calculator to compute these two values of Q to three decimal places and compare these values with your estimates in (b). (d) How big must AL be in order for the difference between Q(100000, 243+AL) and its linear approximation Q(100000, 245) + -DAL, to differ by more than two units?The table shows the quantity of gold bars (in thousands) and the extraction cost per gold bar (in dollars) for the Acme Company. Use these data to answer the questions below. Quantity of Gold Bars (thousands) Extraction Cost ($ per bar) 0 30,000 1 35,000 2 40,000 3 45,000 4 50,000 5 55,000 Instructions: Enter your answers as a whole number. a. If the user cost is $10,000 and the current price of a gold bar is $55,000, how many bars (in thousands) should Acme Company extract and sell this year in order to maximize profits? bars b. Now suppose that the user cost decreases by $5,000 such that the new user cost is $5,000, but the price remains the same. How many bars (in thousands) should Acme Company extract and sell this year in order to maximize profits? bars Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.