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- Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function. S = 20L0.30c0.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 60,000 tons of steel at minimum cost. Min s.t. = 60,000 L, C 20 (b) Solve the optimization problem you formulated in part (a). (Hint: When using Excel Solver, start with an initial L> 0 and C > 0. Round your answers to the nearest integer.) $ at (L, C) =The production of a product is characterised by the function f(x, y) = 16x/4y3/4, where x is the number of units of labour and y is the number of units of capital needed to produce f(x, y) units of the product. Each unit of labour costs £50 and each unit of capital costs £100. You are given a budget of £500,000 and are asked to calculate the number of units of labour that maximise the production. Enter your answer as an integer. Answer: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.Consider the following production function with inputs L and K: Q = (L 0.5 + K0.5)2. The input prices are r = 2 and w = 1. 1) What is the optimal use of labor and capital? 2) Consider a technological advacement such that Q = 2(L 0.5 + K0.5)2 and w = r = 1. What is the optial level of K and L? Any change in K/L? What is the new cost?Suppose that widgets can be produced using two different production techniques, A and B. The following table provides the total input requirements for each of five different total output levels:(Photo)Assuming that the price of labor (PL) is RO 2 and the price of capital (PK) is RO 3, calculate the total cost of production for each of the five levels of output using the optimal (least cost) technology at each level. How many labor hours (units of labor) would be employed at each level of output? How many machine hours (units of capital)? (Graph the total cost of production as a function of output. (put cost on the Y-axis). Which technology is the cheapest at all levels of output. Select one:a. None of the other three answersb. Technology Bc. Neither A Nor Bd. Technology A
- The demand and supply of pizza is defined by the following equations: Qd = D(P, Y ) = 1 + Y − 2P Qs = D(P, PM) = 2 P/PM where, Qd is quantity demand, P is the price of each pizza sold, Y is the average income of consumers, Qs is the quantity supplied, and Pm is the price of inputs used in the production of pizza. (a) List the endogenous and exogenous variables of this model (b) Find the equilibrium price Pe and quantity Qe of pizza as a function of the exogenous variables. (c) Use a simple demand and supply diagram to show what happens to the equilibrium price and quantity when there is an increase in one of the exogenous variables.Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amount of capital used (C) by the following function. 2040.30 0.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. min s.t. S = $ L, C≥ 0 = 55,000 (b) Solve the optimization problem you formulated in part (a). What is the optimal solution value (in dollars)? Hint: Use the Multistart option as described in Appendix 8.1. Add lower and upper bound constraints of 0 and 5,000 for both L and C before solving. (Round your answers to three decimal places.) at (L, C) =An economy depends on two basic products, wheat and oil. To produce 1 metric ton of wheat requires 0.25 metric tons of wheat and 0.33 metric tons of oil. Production of 1 metric ton of oil consumes 0.08 metric tons of wheat and 0.11 metric tons of oil. Find the production that will satisfy a demand for 540 metric tons of wheat and 870 metric tons of oil. The input-output matrix is A= 0.25 0.08 0.33 0.11 .
- Given that TC=2000+100Q-10Q2+Q3 where Q is level of output and maximum level of MP is 15 units, answer the following question based on the given information. A. Determine the TFC ,TVC,AVC,AFC,AC and MC functions b. Calculate the level of output at which AVC and AC reaches its minimum c Draw the relationship between production and cost curve and What relationship do you observe between production and cost curves? Why is this so? G At 5 units AVC,APL is 10,what is the maximum APL?Toyota hired you as a manager for its operation in Pakistan. Suppose that the following is the short-run production function at their assembly plant in Pakistan: Q = 7L + 0.6L2 – 0.1L3 where L = Labor (Number of workers), Q is quantity of output (Cars assembled) per week Find the labor value when the MPL is Maximum. Find the value of MPL at its maximum. Assume Toyota Head Office is considering hiring more laborers either at their Quetta plant or alternatively at the Karachi plant. What will be your advice if workers’ marginal product is 400 at wage of Rs=100/hour in Karachi and marginal product is 350 at wage of Rs=800/hour in Quetta? At the end of the year it is expected that output will double with purchase of new equipment and machinery. The long-run production function is estimated to be Q = 60L+ 50K + 200 where L is labor and K is capital. Suppose initial L1 = 15 and K1 = 20 When inputs are…The AVC and the AC curve can intersects each other at any point True/False