At some point, if all factors of production are being used, it becomes impossible to generate additional output, so the AS curve becomes (two words, 1 mark). 18
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- Given the following production function Y=X+4X^2-0.2X^3. At what level of X does the Average physical product (APP) reach its maximum?The phrase “returns to scale” is a way of describing the change in output that is produced as a result of a relative change in inputs used. Which of the following statements is true? If inputs are doubled and output doubles, this is called increasing returns to scale. If inputs are doubled and output doubles, this is called constant returns to scale. If inputs are tripled and output doubles, this is called increasing returns to scale. If inputs are doubled and output doubles, this is called decreasing returns to scale. If inputs are tripled and output doubles, this is called constant returns to scaleA farmer has 1 acre of land. If he uses X pounds of fertilizer he can harvest √x tons of wheat. What is his production function if he has A acres of land and can just replicate the same production process on each piece of land? XXX A * A VXA √XA
- Consider the following graph of a production function when capital is constant. (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; three levels of labor are shown as reference; there are L1, L2, and L3; they are related as follows L1<L2<L3; the graph is convex from 0 to L1, that is, its slope is increasing; the graph is concave from L1 on, that is, its slope is decreasing; the line that is tangent to the curve at L2, passes through the origin of the graph.) Denote by APL(L,K)=f(L,K)/L the so-called average product of labor (here f is the production function of the firm). From the graph we know that for the corresponding K: APL(L1,K)=MPL(L1,K) APL(L2,K)>MPL(L2,K)…Suppose the production function for widgets is given by q=kl -0.8k²-0.21² where q represents the annual quantity of widgets produced, k represents annual capital input, and I represents annual labor input. Suppose k = 10; at what level of labor input does this average productivity reach maximum? (please put your answer in numerical values with no comma or decimal place). How many widgets are produced at that point? (please put your answer in numerical values with no comma or decimal place). If k = 10, at what level of labor input does MPL = 0? Suppose capital inputs were increased to k = 20, at what level of labor input does this average productivity reach maximum? widgets are produced at that point? (please put your answer in numerical values with no comma or decimal place). If k = 20, at what level of labor input does MPL = 0? answer in numerical values with no comma or decimal place). Does the widget production function exhibit constant, increasing, or decreasing returns to scale?…Question 3 For each one of the following production function determine whether it has constant, increasing or decreasing return to scale (prove): a. F(K, L) = 5K+ 3L b. F(K,L) K0.7 + 10.3 c. F(K,L)= K0.210.1 = d. F (K, L) = 5 (+1)
- Exercise 3 3.1 Consider the following production function: F(K,L) = K0.3L0.7 State if this function exhibits constant, increasing or decreasing returns to scale. 3.2 Consider the following production funetion: F(K,L) = K0.5L0.8 State if this function exhibits constant, increasing or decreasing returns to scale. 3.3 Consider the following production function: F(K, L) = K°L Find out what relation should exist between a and b in order for this function to exhibit constant returns to scale. 3.4 Constant returns to scale is an assumption that fits the reality most of the times. But it does not always hold. Make an example of a firm or a type of business in the real world that exhibits increasing or decreasing returns to scaleQuestion 19 Consider the following graph of a production function when capital is constant. (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; three levels of labor are shown as reference; there are L1, L2, and L3; they are related as follows L1<L2<L3; the graph is convex from 0 to L1, that is, its slope is increasing; the graph is concave from L1 on, that is, its slope is decreasing; the line that is tangent to the curve at L2, passes through the origin of the graph.) From the graph we know that for the corresponding K: MPL(L2,K)=MPL(L3,K) MPL(L1,K)>MPL(L2,K) MPL(L1,K)=MPL(L2,K) MPL(L1,K)<MPL(L2,K) MPL(L3,K)>MPL(L2,K)For the production function Q = 4LK, returns to scale: O is decreasing O Can be increasing, decreasing, or constant depending on the values of L and K. O is increasing O is constant
- Consider the production function f(x1, X2) = 4x1x2, where x1 and x2 are the quantities of inputs 1 and 2, respectively. One of the following statements is true. %3D Which statement is true? The production function exhibits: А Constant returns to scale. Increasing returns to scale. C Decreasing returns to scale.Prof. Smith and Prof. Jones are going to produce a new textbook. The production function for the book is: ?=?1/2?1/2?= is the number of pages in the finished book?= is the number of working hours spent by Smith?= is the number of working hours spent by JonesSmith's labor is valued at 3 TL per working hour and Jones's labor is valued at 12 TL per working hour. After having spent 900 hours preparing the first draft, Smith cannot contribute any more to the book. Jones will revise the Smith's draft to complete the book.a) How many hours will Jones have to spend to produce a finished book of 300 pages?b) What is the marginal cost of the 300th page of the finished book?Please refer to the table attached. The number of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past data, consider the following production function identifying the relationship between output and labor input. You may assume that capital is fixed at 10 units. Answer all of the question. Calculate APL and MPL. Graph APL and MPL. Do they have the expected shape? On your graph, identify the three stages of production.
