A firm can produce output using two inputs: capital (K) and labor (L). The level of production that the firm can achieve can be written in terms of the amount of inputs used in the following way: Y = [A¯¹n Kª/n + B−1/n La/n] n/a, where A=7, B=14, a=1-n and n is a parameter that takes values strictly between 0 and 1. If the amount of capital used by the firm is equal to 78, how much labor the firm needs to hire in order to produce an amount of output of 120? Solve the problem by first formulating an equation.
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- Suppose a tax is set at t’ in the figure. How many units of emissions are ABATED and is abatement achieved cost effectively? Suppose a regulation has just been implemented requiring that coal-fired power plants pay a tax of $80 on each unit of emissions (1 unit is 1 metric ton). Before the tax was imposed, a plant called Old River Power had an emissions level of 100 units. Given a marginal abatement cost function of 200 – 2E, under the tax policy what will Old River Power pay the regulator in emissions taxes?When a thousand dollars are spent on labor and y thousand dollars on equipment, the output of a certain factory is Q units, where Q(x, y) = 240x³/85/8 Suppose $200, 000 is available for both labor and equipment. (a) How should the money be allocated between labor and equipment to generate the largest possible output? What is the largest pos- sible output? (b) Use the marginal productivity of money to estimate the change in the maximum output of the factory that will result if money available for labor and equipment is increased to $210, 000.Does the minimum efficient scale necessarily have to be where the marginal cost is minimal? Can taxes be Pareto improving? How?
- The total cost of producing x items of product A and y items of product B isC(x, y) = 22x2 + 8y2 − 5xyIf the firm is committed to producing 20 items in total, write down the constraint connectingx and y . Hence fi nd the number of each type that should be produced to minimise costs(b) Identify the wage-rental ratio in a diagram with k on the horizontal axis and y and W(k) on the vertical axis. (c) The elasticity of substitution in production is defined as: FLFK OKL = F(K,L)FLK dk w Show that the elasticity of the (w) function, defined as is equal to oKL: dw k1. Pekan Nenas has 20 competitive pineapple orchards, all of which sell pineapples at the world price of RM2 per pineapple. The following equations describe the production function and the marginal product of labor in each orchard: where Q is the number of pineapples produced in a day, L is the number of workers, and MPL is the marginal product of labor. (a) (b) (c) Q = 100L - L² MPL = 100 - 2L, (d) What is each orchard's labor demand as a function of the daily wage W? What is the market's labor demand? Pekan Nenas has 200 workers who supply their labor inelastically. Solve for the wage W. How many workers does each orchard hire? How much profit does each orchard owner make? Calculate what happens to the income of workers and orchard owners if the world price doubles to RM4 per pineapple. Now suppose that the price is back at RM2 per pineapple but a flood destroys half the orchards. Calculate how the flood affects the income of each worker and of each remaining orchard owner. What…
- The Southern Mail produces local newspapers. The company can rent its equipment andhire workers at competitive rates. Equipment needed for this operation can be rented at R4per hour, and labour can be hired at R3 per worker hour. The production function usingavailable technology can be expressed as: Q = 2L0.5 K0.5 a) Determine the firm's optimal ratio of labour to capital.b) Determine the cost-minimizing level of capital and labour in the long run if thefirm wants to produce 160 units. Calculate the cost.c) Graphically illustrate this using isoquant and isocost lines.10. Extension of the Cobb-Douglas Production Function-The Cobb-Douglas produc- tion function (Equation 7.16) can be shown to be a special case of a larger class of linear homogeneous production functions having the following mathematical form:" Q = y[@K* + (1 – a)L°]W/P where y is an efficiency parameter that shows the output resulting from given quantities of inputs; a is a distribution parameter (0 sas 1) that indicates the division of factor income between capital and labor; p is a substitution parameter that is a measure of substitutability of capital for labor (or vice versa) in the pro- duction process; and v is a scale parameter (v > 0) that indicates the type of re- turns to scale (increasing, constant, or decreasing). Show that when v = 1, this function exhibits constant returns to scale. [Hint: Increase capital K and labor L each by a factor of A, or K* = (A)K and L* = (1)L, and show that output Q also increases by a factor of A, or Q* = (A)(Q).]a) Given that a firm has a production technology, y= (X² + X²)², derive the MRTS12
- A plant with a marginal abatement function described by MAC = 75-5E is polluting the town's water supply. Emissions are measured in tons per year. a) Government regulators propose that the company pay a tax equal to $30 per ton of emissions. How many tons will the firm abate when faced with this tax, and how much better off will it be compared to if it does no abating. b) Suppose that, instead of the tax, the government offers to pay the firm $30 for each ton of emissions it abates. How many tons will the firm abate, and how much better off will it be compared to if it does no abating? c) If damages caused by the firm's emissions is described by the function MD = 5E, what tax rate would encourage the firm to abate to the socially efficient level of emissions? Compute the private and social compliance cost and the net benefit accruing to society from the socially efficient emissions tax. %3DThe outputs of firms 1 and 2 are given by Q = 3L and Q2 =4L respectively 0.6 0.6 where the L's stand for labour (measured in hours). If the total labour supply is 350 what would be the total output (Q, + Q2) if (a) labour was split equally between the two firms. (b) labour was allocated efficiently between the two firms. MacBook AirGreen et al. (2005) estmate the supply and demand curves for Californa processod tomatoes. The supply function is: \[ \ln \left(Q_{s}\right)=0.200+0.550 \ln (p) \] whereQis the quantify of processing tomatoes in milions of tons per year andpis the price in dollars per ton. The demand function is: \[ \ln \left(Q_{d}\right)=2600-0.200 \ln (p)+0.150 \ln \left(p_{1}\right) . \] wherep1is the price of tornato paste (which is what processing tomatoes are used to produce) in dollars per ton. Supposept=$119Determine how the equilerium price and quantity of processing tomatees change if the price of tomato pasise tails by16%. If the price of tomato paste fals by18%, then the equaborium price will by 5 (Enter a numene response using a real number rounded to two decimal places)