Q4 The output of a production process, Q, is given by the function KL K+ 2L where K and L denote capital and labor. (a) Calculate the output when the capital and labor are 40 and 30 units, respectively. (b) Find the level of labor needed to produce 4 units of output when 10 units of capital are used. (c) Transpose this formula to express K in terms of Q and L. 05
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- 5. An entrepreneur has costs for storing and shipping materials for his manufacturing process given by the function C (k) = 100 (100 + 9k + 144 / k) when 1 ≤ k ≤ 100, where C (k) is the cost total storage and transportation for 100 days of operation. If a load of k tons of material moves every k days, for what values of k does C (k) have a minimum value?Q)solve it correctly The marginal products of capital (MPK) and labor (MPL) are, respectively, MPK = 2000 units; MPL = 1500 units. The input prices are: PK = $10/unit; and PL = $150/unit. To minimize production costs, the firm should A. increase both capital and labor B. decrease both capital and labor C. increase capital; decrease labor D. decrease capital; increase labor E. do nothing; costs are minimizedWhat is the difference between economies of scale andeconomies of scope? How do firms consider these wheninvesting in processes?
- The output (Q) of a production process is a function of two inputs (L and K) and K is given by the following relationship: Q = 0.50LK− 0.10L2− 0.05K2 The per-unit prices of inputs L and K are $20 and $25, respectively. The firm is interested in maximizing output subject to a cost constraint of $500. Use the lagrangian optimization techniques to find the following: How many units of L and K should be used by the firm? What is the total output of this combination? What is the marginal rate of substitution between L and K?How many units of output should each plant produce? Please specify your answer as an integer.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…
- 2-1 Consider the production function Y = X+4x2 – 0.2x3 a. Derive the exact marginal physical product and average physical product equationsA firm uses 3 factors of production. Its production function is f(x, y, z) = min{x3/y, y2, (z4 − x4)/y2}. If the amount of each input is multiplied by 6, its output will be multiplied by A.) 216 B.) 36 C.) 6 D.) 0.16 -the Answer is 36, Please explain in detail why this isYou 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 = 10L^2 – 0.5L^3 where L is variable input labor, Q is output of Cars assembled a. Find the ranges of the three stages of production. b. Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above. c. At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be Q = 60L^.30K^.70 where L is labor and K is capital. Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2, do you observe increasing, decreasing or constant returns to scale? d. Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively at the Karachi plant.…
- Consider the production function: Y=Z*F (K,L,A) where Y is output, z is technology, K is capital, L is labour and A is the area of land.Which 3 of the following statements are correct? a. Diminishing marginal products means that if K,L and A all double, output will less than double.b. The property of a diminishing marginal product of labour means that, if labour is increased while otherinputs to production are held constant, output will increase, but by a decreasing amount.c. If there are constant returns to scale this implies that individual marginal products are not diminishing.d. If marginal products are diminishing, then the marginal product of labour measured in terms of discretechanges is less than the marginal product in terms of calculus.e. If z increases, the average product of all inputs increases but the marginal products do not.f. Holding K and A constant, if z increases the production function in terms of labour input shifts up by aconstant amount at all levels of labour…3. Many production functions have a property called constant returns to scale, about constant returns to scale,which of the following is WRONG? A. This property implies that as all inputs are doubled, output will exactly double. B. This implies that must be true C.This also means that if we want to examine output per worker we could set x = 1/L and we would get D. None of the above is trueProduction function Q=100K^0.5L^0.5 .During the last production of Tyres the following inputs of 100 and 25 for capital and labor were used.What is the marginal product of capital and marginal product of labor based on the stated inputs.