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- A firm faces a perfectly elastic demand for its output at a price of $6 per unit of output. The firm, however, faces an upward-sloped labor supply curve ofE = 20w - 120where E is the number of workers hired each hour and w is the hourly wage rate. Thus, the firm faces an upward-sloped marginal cost of labor curve ofMCE = 6 + 0.1EEach hour of labor produces five units of output. How many workers should the firm hire each hour to maximize profits? What wage will the firm pay? What are the firm’s hourly profits?Suppose that the govern-ment imposes a producer tax. That is, the firm pays t units of consumption goods to thegovernment for each unit of output it produces. Determine the effect of this tax on the firm’sdemand for labour. (use calculus)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?
- The nation of Ectenia has 20 competitive appleorchards, all of which sell apples at the world priceof $2 per apple. The following equations describethe production function and the marginal product oflabor in each orchard:100100 2 ,2 5 25 2Q L LMPL Lwhere Q is the number of apples produced in a day,L is the number of workers, and MPL is the marginalproduct of labor.a. What is each orchard’s labor demand as a functionof the daily wage W? What is the market’s labordemand?b. Ectenia has 200 workers who supply their laborinelastically. Solve for the wage W. How manyworkers does each orchard hire? How much profitdoes each orchard owner make?c. Calculate what happens to the income of workersand orchard owners if the world price doubles to$4 per apple.d. Now suppose that the price is back at $2 perapple but a hurricane destroys half the orchards.Calculate how the hurricane affects the income ofeach worker and of each remaining orchard owner.What happens to the income of Ectenia as a whole?According to the Wall Street Journal, Mitsubishi Motors recently announced a major restructuringplan in an attempt to reverse declining global sales. Suppose that as part of the restructuring planMitsubishi conducts an analysis of how labour and capital are used in its production process. Priorto restructuring Mitsubishi’s marginal rate of technical substitution is 0.15 ( in absolute value). Tohire workers. Suppose that Mitsubishi must pay the competitive hourly wage of US$ 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…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?
- The marginal and average total cost curves for barbers in an area are cosntant at $12.00/haircut. The daily demand curve for haircuts in the area is given by: P = 22 - 0.001Qd where P is the price in dollars per haircut and Qd is the daily quantity demanded in number of haircuts. Haircuts are provided in a perfectly competitive market and each barber can provide exactly 25 haircuts daily. Suppose that the government decides to limit the number of barbers to 320. Each year, barbers must obtain a government-issued license to cut hair. Based upon the previous information: a. What will be the long-run equilibrium price for a haircut given there are only 320 licensed barbers?b. How much economic profit will each licensed barber earn daily?Table 14.13 shows information from the supply curve for labor for a monopsonist, that is, the wage rate required at each level of employment. What is the monopsonists marginal cost of labor at each level of employment? If each unit of labors marginal revenue product is 13, what is the firms profit maximizing level of employment and wage?Consider a manufacturing firm in a labor market that isperfectly competitive. There are two kinds of workers: productiveworkers whose marginal revenue product is $48,000 per year, andlazy workers whose marginal revenue product is $40,000 per year. Itis difficult for the firm to differentiate between productive andlazy workers. A local college offers a new yearlong astronomy course. Althoughthe cost of tuition is the same for both types of workers, thepsychic cost of having to work hard and get a passing grade islower for productive workers because they are able to learn morequickly than lazy workers. Therefore, the cost of taking the class(including the cost of tuition as well as the psychic cost) is$5,000 per year for a productive worker and $10,000 per year for alazy worker. Because astronomy has little relevance tomanufacturing, taking the class does not increase or decrease aworker's productivity. The firm uses the class as a way to differentiate betweenproductive and lazy…
- The car manufacturing market consists of100 identical factories, each with a marginalcost curve represented by MC =120 + 20where Q represents the amount of carsoffered.a) Derive the industry supply curve for cars.b) If the demand for cars is represented byP=250- 4Q, how many cars are bought atequilibrium?c) Calculate the aggregate consumer andproducer surplus at market equilibrium.Consider a firm that is perfectly competitive in the market for inputs and outputs. Thefirm hires two types of workers: low-skill (high school graduates and high school dropouts) andhigh-skill (undergraduate and postgraduate degree) workers. The firm compensates high-skilledworkers at the rate wH and low-skill workers at the rate wL. It produces the output subject to aCobb-Douglas production technologyF(L,H) = (AH)α(L)β,where H - is the amount of high-skill hours, L - the amount of low-skill hours, and A - thetechnology parameter that augments the productivity of the high-skill labour. 4. In the short run, the firm cannot increase the amount of high-skill labour . Derive the1short-run demand for low-skill labour.5. What is the substitution effect of the wage increase in the short-run?6. Derive the long-run cost-minimizing demands for high- and low-skilled labour. Show thesolution to the cost-minimization problem on the graphTo 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?
