Assume a firm is attempting to minimize cost by selecting units of capital and units of labor in order to produce am least as large as some specified output quota. Cost-minimizing choices are provided in the following table for a ba and new scenario. Baseline New Wage rate $50 $50 Rental rate $50 $50 Output quota Units of labor employed 66 99 44 66 Units of capital employed 44 66 Using the table, how did the new event affect the firm's total cost? O Total cost remained unchanged. O Total cost decreased. O Total cost increased. O Cannot be determined.
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- Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r,respectively. Initially, the firm faces market prices of w=$5 and r=$15. Assume the firm has a cost budget of$1,500.a. Using the isoquant-isocost model, graphically show the optimal level of employment for this firm in thelong run.b. Suppose the government now imposes a minimum wage of $10 for workers. Using the same graph aspart a, graphically show the impact of the minimum wage on the optimal level of employment in thelong run.c. Refer to the initial situation described in part a. Now suppose a new innovation causes the price ofcapital to fall to $10. Using a new isoquant-isocost model, graphically show how this change impacts theoptimal levels of employment and capital in the long run. Clearly identify the resulting scale andsubstitution effects caused by the lower cost of capital. Could you please answer this question using the graphs please.According to the Wall Street Journal, Mitsubishi Motors recently announced a major restructuringplan in an attempt to reverse declining global sales. Suppose that as part of the restructuring planMitsubishi conducts an analysis of how labour and capital are used in its production process. Priorto restructuring Mitsubishi’s marginal rate of technical substitution is 0.15 ( in absolute value). Tohire workers. Suppose that Mitsubishi must pay the competitive hourly wage of US$ 15. In thestudy of production process and markets where capital is procured, suppose that Mitsubishidetermine that its marginal productivity of capital is 0.5 small cars per hour at its new targetedlevel of output and that capital is procured in a highly competitive market. The same studyindicates that the average selling price of Mitsubishi’s smallest car is US$ 9500. Determine therate at which Mitsubishi can rent capital and marginal productivity of labour at its new targetedlevel of output. To minimize costs…Cowles Foundationfor Research in Economicsat Yale UniversityCowles Foundation Discussion Paper No. 2021ARE WE APPROACHING AN ECONOMIC SINGULARITY?INFORMATION TECHNOLOGY AND THE FUTUREOF ECONOMIC GROWTHWilliam D. NordhausSeptember 2015An author index to the working papers in theCowles Foundation Discussion Paper Series is located at:http://cowles.yale.edu/This paper can be downloaded without charge from theSocial Science Research Network Electronic Paper Collection:http://ssrn.com/abstract=2658259Electronic copy available at: http://ssrn.com/abstract=2658259Are We Approaching an Economic Singularity?Information Technology and the Future of Economic GrowthWilliam D. Nordhaus1September 1, 2015AbstractWhat are the prospects for long-run economic growth? The presentstudy looks at a recently launched hypothesis, which I label Singularity.The idea here is that rapid growth in computation and artificialintelligence will cross some boundary or Singularity after whicheconomic growth will…
- A firm uses a single input to produce a commodity according to itsshort-run production function f(x) = 4√x, where x is the number of units ofinput. The commodity sells for $100 per unit. The input cost $50 per unit.(a) Write down a function that states the firm’s profit as a function ofthe amount of input.(b) What is the profit maximizing amount of input and output?(c) Suppose the firm is taxed $20 per unit of its output and the priceof its input is subsidized by $10, explain in detail how this will affect the newinput and output levels?Imagine a firm that employs two types of workers – some with computer skills and others withno technology related skills. (i) Explain how a firm’s production function is related to its marginal product of labour, howa firm’s marginal product of labour is related to the value of its marginal product and how afirm’s value of marginal product is related to its demand for labour. (ii) Explain how the wage can adjust to balance the supply and demand for labour whilesimultaneously equalling the value of the marginal product of labour.Q5 A firm's production function is Q is equal to 5L2Ka) Find out the MPL and MPb) Does this production function exhibit constant, increasing, or decreasingreturns to scale?c) What is the marginal rate of technical substitution of L for K for thisproduction function Q6.Suppose the firm sells its output according to the following demand scheduleMarginalTotal Product Total Revenue eLabor Product Price Revenue Product$3.50192c2.80182.30291.80391.65471.5021.4053Fill in the remaining two columns of the table. How many workers wilhired at a wage of $72
- Q.1.20 An upward-sloping labour supply curve illustrates that ceteris paribus; (a) the quantity of labour supplied and the hours of work per week aredirectly related.(b) the quantity of labour supplied and the price of labour used to produceoutput are inversely related.(c) individuals use higher income to buy back leisure time.(d) a greater quantity of labour would be supplied at higher wage rates .Q.1.17 Marginal cost is defined by: (a) total cost increases when one more unit is produced.(b) fixed cost increases when one more unit is produced.(c) Total revenue increases when one more unit is produced.(d) average cost increases when one more unit is produced.To maximize profits, a firm uses a fixed amount of capital and varying amounts of labour inits production processes to produce commodity Y. The output fetches Kshs 3 in the market andthe firm’s production is as summarized.Number of workers Output per hour0 01 92 173 244 305 356 397 428 44 Required;i.Calculate the marginal product of labour for this firm and the value of the marginal productof labour and the Marginal Revenueii.Suppose that the competitive wage for workers who can make Product Y is Ksh16 perhour. How many workers should this firm hire and why?Suppose that labor is the only input used by aperfectly competitive firm. The firm’s productionfunction is as follows:Days of Labor Units of Output0 days 0 units1 72 133 194 255 286 297 29a. Calculate the marginal product of each additionalworker.b. Each unit of output sells for $10. Calculate thevalue of the marginal product of each worker.c. Compute the demand schedule showing thenumber of workers hired for all wages from zeroto $100 a day.d. Graph the firm’s labor-demand curve.e. What happens to this demand curve if the price ofoutput rises from $10 to $12 per unit?
- Consider the market for labor where both firms and workers are price takers. Output is produced using capital and labor.The marginal product of labor can be described by: 200 – 4L, where L is the number of workers hired. The price of the good produced is 5 per unit. a. Illustrate the demand for labor. Be sure to note the specific value of the vertical intercept. b. Suppose that the competitive firm must pay 100 for each worker. Determine the number of workers hired. (Determine the total income to capital. Show your work for both parts. c. Suppose that the price of the good rises but that the wage remains the same. Illustrate how the optimal choice of labor would change. No need to do the explicit calculation; just show the outcome and briefly explain.A household's reservation wage is the ________. Group of answer choices lowest wage rate at which an individual will supply labor highest wage rate at which the individual will supply labor wage rate at which the individual’s income is largest wage at which the individual’s labor supply curve bends backward Quantity of labor (workers) Output (units) Marginal Product of Labor (dollars) 0 0 0 1 10 $100 2 18 $80 3 24 $60 4 28 $40 5 30 $20 Given the production and revenue data in the above table, if the wage rate is $50 per worker, how many workers will be hired? Group of answer choices 5 4 2 3 Please answer to two of these questionsIt deals with the Production Function, Marginal Rate of Technical Subsition . Problem: The Production Function for a Product is given by q=10 K ^1/2 L^1/2 where K is capital and L is Labor and q is output . 1a. Find the Marginal Product of labor and the Marginal Product of Capital 1b. Find the Marginal Rate Of Technical Substitution between Labor and Capital 1c. Denote the wage of Labor by w and the renal of cpaital by r . What is thre cost of the minization condition for a firm . Show it digrammatically.