The Whoville Marble Collective (WMC) makes fancy marbles for picky Whos. WMC's output is given by Q = 20K0.75 0.25, where Q is WMC's annual output (measured in 1000s of marbles), K is their annual capital input and L is their annual labor input. WMC's capital input costs PK = $8000 per unit and their labor input costs p₁ = $25000 per unit. Assuming that WMC's annual production budget is B = $800,000, their maximum annual output is ... 412,891 marbles. 726,085 marbles. 578,634 marbles. O...=857,232 marbles.
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- 10)Given the production function f (L K) = L2 / 3. K1 / 3, where L is the working hours and K is the capital. assuming that the capital price is r = 4 euros and the price per hour of work is w = 27 euros and that all the factors of production are variable, what is the minimum cost of producing 10 units of product? Choose one: A) 260e B) 230e C) 240e D) 250e E) 270eQno1.You have been hired by Kia as manager for its Pakistan operations. Assume following is the short-run production function at their assembly plant outside Karachi: Q = 10L2 – 0.5 L3 where L is variable input labor, Q is output of Cars assembled Required. a). Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively at the Karachi plant. What will be your advice if workers’ marginal product is 40 at wage of Rs=5/hour in Karachi and marginal product is 28 at wage of Rs=4/hour in Gawdar?A firm faces the following costs: total cost of capital = $1,000; price paid for labor = $12 per labor unit; and price paid for raw materials = $4 per raw-material unit. a. Suppose the firm can produce 5,000 units of output this year by combining its fixed capital with 100 units of labor and 450 units of raw materials. What are the total cost and average total cost of producing the 5,000 units of output? b. Now assume the firm improves its production process so that it can produce 6,000 units of output this year by combining its fixed capital with 100 units of labor and 450 units of raw materials. What are the total cost and average total cost of producing the 6,000 units of output? c. If units of output can always be sold for $1 each, then by how much does the firm’s profit increase after it improves its production process? d. Suppose that implementing the improved production process would require a one-time-only cost of $1,100. If the firm only considers this year’s profit, would…
- Suppose a Cobb-Douglas Production function is given by the function: P(L,K)=8L^0.7K^0.3Furthemore, the cost function for a facility is given by the function:C(L,K)=300L+500KSuppose the monthly production goal of this facility is to produce 20,000 items. In this problem, we will assume LL represents units of labor invested and KK represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs?Units of Labor LL = (Show your answer is exactly 1 decimal place)Units of Capital KK = Incorrect (Show your answer is exactly 1 decimal place)Also, what is the minimal cost to produce 20,000 units? (Use your rounded values for LL and KK from above to answer this question.)The minimal cost to produce 20,000 units is $ Hint: Your constraint equation involves the Cobb Douglas Production function, not the Cost function. When finding a relationship between LL and KK in your system of…Suppose that a business incurred implicit costs of $200,000 and explicit cost of$1million in a specific year if the firm sold 4,000 units of the output at $300 per unit , the accounting profits were A)$00,000 and it's economic profits were zero B)$200,000 and it's economic profits were zero C)$100,000 and it's economic profits were$100,000 D)zero and it's economic loss was $200,000Why CRS - Constant Returns on Scale would generate (1) No profit-maximizingproduction plan; the only nontrivial production plan involves zero profits. (2) Even when aprofit-maximizing plan exists, it is not unique?
- A small manufacturing plant makes three types of inflatable boats: one person, two-person,and four-person models. Each boat requires the services of three departments, as listed in thetable. The cutting, assembly, and packaging departments have available a maximum of 380,330, and 120 labor-hours per week, respectively.Department One-PersonBoatTwo-PersonBoatFour-PersonBoatCutting 0.5 hr 1.0 hr 1.5 hrAssembly 0.6 hr 0.9 hr 1.2 hrPackaging 0.2 hr 0.3 hr 0.5 hra) Calculate how many boats of each type must be produced each week for the plant tooperate at full capacity.b) Calculate how is the production schedule in part (a) affected if the packagingdepartment is no longer used.c) Calculate how is the production schedule in part (a) affected if the four-person boat isno longer producedGiven that the marginal cost of a ‘backstop’ (e.g. solar energy) is MCb per unit of an exhaustible resource, prove that the cost of the ‘backstop’ sets an upper limit on oil price and also determines the initial price of oil. (Hint:Utilize the expression pt = MC + (p0 − MC)(1 + r)t and consider T as theswitch date.)Suppose that the production function takes the form X = min(10L, 5K) and that a competitive firm faces a wage rate of £60 per week and a weekly capital rental of £32. (a) How much must the firm spend to produce 100 units of output, and what is the average cost of production when X = 100? (b) What is the incremental cost of producing the 101st unit of output? (c) What happens to the cost of producing 100 units of output if the wage rate and the rental cost of capital rise by 25 per cent each? What happens to the average and marginal cost? (d) What happens to the cost of producing 100 units of output if the wage rate increases by £1, or if the cost of capital increases by £1?
- A town is endowed with an oil reserve. The total stock of oil from the reserve is 110 barrels. The townmust sell all 110 barrels within two time periods, so the quantity extracted will be q1 + q2 = 110, whereq1, for example, is the quantity extracted in period 1. The price per barrel that the town can sell theoil for is pt= 150 −10/11 qt in each period. There is a constant cost of extraction c = 50, such that theresource rent earned by each barrel in each period is πt= pt−c. If the interest rate is 20%, how muchoil will the town extract in period 1 and in period 2 (what should q1 and q2 be) if it wanted to extractefficiently (i.e. maximize profits)?Output Y is produced according to Y = F(K, L), where K is the capital stock and Lis the number of workers. The production function F(K, L) has constant returns toscale and diminishing marginal returns to capital and labour individually. The levelof technology is assumed to be constant over time. Capital per worker is denotedby k = K/L and output per worker by y = Y/L, and the two are related according toy = f(k), where f(k) = F(k, 1) is the per-worker production function. Investment is equal to saving, which is a constant fraction s of income Y. Capitaldepreciates at rate δ and the number of workers grows at rate n. The change incapital per worker over time is ∆k = sf(k) − (δ + n)k. Consider a country that has reached its steady-state capital per worker. Then, inone year, the country suffers severe flooding that destroys part of its capital stock.Assume this is treated as a one-off event that is not expected to reoccur. explain what happens to incomeper worker in the short run and the…Logan and Berkeley havea thriving dog grooming business which operates 5 hours a day for 4 days a week. They currently have one dog groomer and are considering hiring a second groomer. They believe that after a 12 week period, the second groomer should be able to groom 3 dogs per hour, but only groom 1 dog per hour inthe frst 12 weeks while they learn the ropes. By adding a second groomer, Logan and Berkeley would need to install an additional sink, costing $20,000, and also incur an additional $27 per hour in labour costs. Apart from labour, their current costs are $15 per dog groom (coveringitems such as dog shampoo) and $30,000 in fixed costs per year (eg. rent). They currently charge $50 per dog groom. How many weeks would it take for the second groomer to pay off and make a profit? A 116 B 23.6 C 37.7 D 49.7