t>0
Thus scaling the inputs t times scales the output greater than t so the production function exhibits increasing returns to scale.
+ cons tant retuens to scate? ren, rn St, scale . Show prove. is or inurlaing...
For the case with spin , prove that U(Rn(a)) = e-inga for arbitrary axis parameterized by ñ = sin cos oi+sin sin oj+cos ek, where Ô = (0,0,0%) are the three Pauli matrices. • Then show that the rotational operator has the following explicit form U(R(Q)) = cos 1 – i sin añoở. You may Taylor expand the exponential operator to find the explicit form.
Given the following production functions, determine if they exhibit increasing, decreasing, or constant returns to scale. Be sure to mathematically prove your answer and show your work. Y = K + L Y = 4(K + L)0.5 Y= 10(KL0.5)
Please prove Problem 11 & 12 carefully (note that m represents Lebesgue measure & m* represents Lebesgue outer measure): 11. Let E c Rn be an arbitrary subset. Show that for all є > 0 there exists an open set G containing E with m(G) m"(E) +e. 12. Let E C Rn be a measurable subset. Show that for all € > 0 there exists an open set G containing Ewith m (G\ E) < є. 11. Let E c...
Briefly show whether the following production functions exhibit increasing, decreasing, or constant returns to scale: Y = K2/3 + L2/3 Y = min {2L+K, 2K+L} Y = 20*L1/5*K4/5
(a) Let R be a commutative ring. Given a finite subset {ai, a2, , an} of R, con- sider the set {rial + r202 + . . . + rnan I ri, r2, . . . , rn є R), which we denote by 〈a1, a2 , . . . , Prove that 〈a1, a2, . . . , an〉 įs an ideal of R. (If an ideal 1 = 〈a1, аг, . . . , an) for some a,...
Do the following production functions exhibit increasing, constant, or decreasing returns to scale? (show your work to illustrate the answer), where Q is quantity of output, K is the amount of capital used, and L is the amount of labor used. a) Q=K^1/3 L^2/3 b) Q=7K^1/5 L^3/5 c) Q=4K+8L d) Q=3k^5 L^4
Does the production function of table 7-1 below show constant, increasing, or decreasing return to scale if the firm increases the quantity of labor and capital used from (a) 2L and 2K to 4L and 4K? (b) 2L and 4K to 3L and 6K? TABLE 7-1 Production Function with Two Inputs 36 40 40 36 30 14 40 42 40 36 30 14 39 40 36 Output (0) 10 12 12 10 24 28 28 23 18 31 36 36...
13) Does the production function of Table 7-1 show constant, increasing or decreasing returns to scale if the firm increases the quantity of labor and capital used from (a) 2L and 2K to 4L and 4K? (b) 2L and 4K to 3L and 6k? TABLE 7-1 Production Functiion with two inputs Capital (K) 6 10 24 31 36 40 39 5 12 28 3640 42 40 4 12 28 36 40 40 36 Output (Q) 3 10 23 33 36...
The city of St Louis in the United States has a monument known as the "Gateway Arch" which is pictured in Figure 1 below. You have been asked to help design a small-scale replica of this arch for Brisbane Figure 1 - Gateway Arch in St Louis, Missouri To simplify the design problem, you can assume that the arch follows a parabolic equation (and that the thickness of the arch is negligible). This equation that the arch follows will be...
Let TRm → Rn be a linear transformation, and let p be a vector and S a set in R Show that the image of p + S under T is the translated set T(p) + T(S) n R What would be the first step in translating p+ S? OA. Rewrite p+ S so that it does not use sets. O B. Rewrite p+S so that it does not use vectors O c. Rewrite p + S as a difference...