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Explain why a profit function π(K,L) doesn't exist such that:
The marginal benefit with respect to capital is 2KL
Step by step
Solved in 2 steps
- Consider the following production function of DVDS: Q = K0.5L 0.5, where Q represents DVDS (boxes per hour), K denotes capital input (units per hour), and L denotes labour input (units of worker time per hour). The unit cost of capital and labour are $40 and $20, respectively. a) What is the optimal input ratio of labour and capital for the production? b) Determine the appropriate input mix to produce 800 boxes of DVDS. Compute the cost of production. c) Suppose the government decided to offer a subsidy that would make the cost of labour $15. What is the optimal input mix to produce the same level of output, and the new cost of production? Also, compute the substitution effect in the employment of labour.The production function of producing an item is given by 3K Q = 744 VR - where K is the capital required. Calculate the marginal product of capital if the current capital is 512.Suppose the productivity function for I units of labor and k units of capital is P = 21+ 3k2 Find the marginal productivity with respect to capital for 4 units of labor and 3 units of capital.
- If the form of the production function is a Cobb-Douglas function, do diminishing marginal products apply here?If a firm has 5 units of capital, 10 units of labor, and the production function is Q = 4L + 3K what is the average product of capital? 3 4 11 45Consider the production function Q = 2(KL)0.5a) What is the marginal product of labour and capital
- An electronics plant’s production function is Q = 5LK, where Q is its output rate, L is the amount of labor it uses per period of time and K is the amount of capital it uses per period of time. The Price of labor is $1 per unit of labor and the price of capital is $2 per unit of capital. a) What is the optimal combination of inputs the plant should use to produce 1000 units of output per period? b) Suppose that the price of labor increases to $2 per unit. What effect will this have on optimal L and K to produce Q=1000? c) Is this plant subject to decreasing returns to scale? Why or why not?Suppose the production function is given by Q = 5K+2L. What is the marginal product of capital when 5 units of capital and 10 units of labor are employed?If a firm has 5 units of capital, 10 units of labor, and the production function is Q = 4L + 3K what is the Marginal product of capital? 3 4 11 45
- If a firm’s production function is Y = KαL1-α, show that it can earn at most zero profit. Use this production function to express the output–labor ratio as a function of the capital–labor ratio. Discuss the properties of the function derived.Suppose the production function for a product is z = 65x2/5y3/5 where x is the capital expenditures and y is the number of work-hours. (a) Find the marginal productivity of x. (b) Find the marginal productivity of y.The number of souvenir coffee mugs (in hundreds) that Ace Novelty can produce monthly is given by the production function where x denotes the amount of labor utilized (measured in thousands of work-hours per month) and y denotes the expenditure on capital investment (in thousands of dollars per month). Find the marginal productivities if 10,000 work-hours per month are utilized and a capital investment of $5000/month is made. Interpret your results.