Question

1. Consider a firm that has the following CES production function: Q = f(L,K) = [aLP + bK°]!/p where p a. Derive the MRTS for this production function. Does this production function exhibit a diminishing MRTS? Justify using derivatives and in words. What does this imply about the shape of the corresponding isoquants? (10 points) b. What are the returns to scale for this production function? Show and explain. Explain what will happen to cost if the firm doubles its output. (8 points) c. Explain the difference between the concepts of diminishing marginal product and diminishing marginal rate of technical substitution. (5 points) d. Explain the difference between the concepts of diminishing marginal product and diminishing returns to scale. (5 points)

Answer 1

c) Here diminishing marginal product means that while increasing the cost of input weather in the form of money , manpower (labor) , capital and anything else will not make sure the positive results in the production unit, the diminishing marginal product means that the input value increase in the current value of production will initially increase the output of the production while keeping everything (rest variables) same will initially increase the output on the spot or on and only instant basis but will not make it too long positive it provides diminishing marginal product after a particular phase of the production

Here, diminishing marginal rate of technical substitution

It is the basic law in the theory of economics that with the same rate at which the one factor decreased in the factor of production in order to maintain the level of production in the production unit will must have to increase the another factor at same rate at which the another factor decreased the isoquant on the graph of MRTS will be downward sloping which shows us the standard of this theory as it is downward sloping which states that in order to maintain the level of the output same we have to increase another factor with same rate at which the another factor decreased

so, the basic difference between both of them will show that diminishing marginal returns are related to the amount of input and shows the immediate change or increase in the output but on the other hand in MRTS the factor increase and decrease on the basis of the same production level .

d) diminishing marginal product again copying above about the diminishing marginal product

diminishing marginal product means that while increasing the cost of input weather in the form of money , manpower (labor) , capital and anything else will not make sure the positive results in the production unit, the diminishing marginal product means that the input value increase in the current value of production will initially increase the output of the production while keeping everything (rest variables) same will initially increase the output on the spot or on and only instant basis but will not make it too long positive it provides diminishing marginal product after a particular phase of the production

Now here the

diminishing returns to the scale ,

in this law if we increase the input than it will decrease the output value or we can say if doubled the cost of production of the input then the output will decreased by half of the double we can also say it increasing cost, which means if all the factors of the production increase in any given proportion then the output increase in the smaller proportion , which implies if the cost of input is double then value of output will be less than double.

basic difference is of the time period that is the marginal product is related to the short run basis and on the other hand the the diminishing returns to the scale will completely related to the long run.