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Cost Minimization1. An orange goes through four major steps on its way from grove to grocery store at the Sunkist Citrus Processing Plant in the southern San Joaquin Valley: washing, waxing, grading (inspection), and packaging. The facility's production technology can be represented by the following production function:q=F(L,K)=10L^(1/2)K^(1/2)Where q denotes the amount of boxes of oranges produced in an hour, L denotes the number of workers, and K denotes the capital (machinery) used in production. The wage rate for a factory worker is $20/hour and the rental rate of capital is $80/hour.A. What are the cost minimizing quantities of labor and capital when the factory produces 100 boxes of oranges each hour? What are the facility's total costs under this scenario? Use the Method of Lagrange Multipliers.B. Calculate the values for MPL and MPK when evaluated at the optimal solution in Part A. Then calculate the MRTS and verify (numerically) that the tangency rule holds.C. Illustrate the optimal input combination found in Part A using a diagram that contains both an isoquant and isocost curve.D. If the factory's manager decides to increase output to 140 boxes per hour and capital remains fixed (since the decision is made abruptly), how much labor will the facilityrequire in order to produce at minimum cost? What will the facility's total costs be?E. How will the optimal level of labor and capital be affected in the long run if Sunkist decides to maintain production at 140 boxes? What will resultant total costs be?
Compute Florence's MRS of all other goods for travel. (In other words, compute her MRS with travel on the horizontal axis.
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Suppose an economy of two firms and two consumers. The two firms pollute. Firm 1 has a marginal savings function of MS1(e) = 5-e where e is the quantity of emissions from the firm.
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Recent increases in rents have caused the citizens of Elmville to vote for a rent ceiling of $1200. Assuming all rental units in Elmville are identical and the supply and demand for rental units are given by Qs = -1000 + 20P Qd = 50000 - 10P
Suppose that technophiles are willing to pay $400 now for the latest iPhone, but only $300 if they have to wait a year. Normal people are willing to pay $250, and their desire to purchase does not vary with time. Ignore the time value of money a..
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