2- Answer the following questions:a) Show that Young's Theorem holds for the following function: f(x, y) = 9ye²xy. |b) Let z(x, y, w) = x² + wy +w², where w (r, s) = r² + s²₂ x (r,s) = r² — s² and y (r, s) =r. s. Find the partial derivative 6 =?6sc) The foreign demand for our exports X depends on the foreign income X and our price level P:1X = Y + P-². Find the partial elasticity of foreign demand for our exports with respect to queprice level.d) If production function is Q₁ = A(t) K³L, where A(t) is an increasing function of t, andK₁= Ko + at, and L. Lo + bt. Find the rate of change of output with respect to time?=wwwwwwww.wintim um momw

Young's Theorem states that:Let f(x, y) be a real-valued function defined in a neighbourhood of a…

Answered: 2- Answer the following questions: a)…

Business

Economics

2- Answer the following questions: a) Show that Young's Theorem holds for the following function: f(x, y) = 9ye²xy. |

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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T = - Q² + 17Q – 60 Find Q that maximizes the function:
Suppose that for a company manufacturing calculators, the cost, revenue, and profit equations are given by x² C = 70,000 + 30x, R=200x - A) Costs are increasing at the rate of $ (Simplify your answer.) where the production output in 1 week is x calculators. If production is increasing at a rate of 600 calculators per week when production output is 5,000 calculators. Find the rate of increase (decrease) in cost, revenue, and profit. B) Revenue is decreasing at the rate of $ (Simplify your answer.) C) Profits are (Simplify your answer.) 20 at the rate of $ P=R-C per week at this production level. per week at this production level. per week at this production level.
Given the function f(x) = ln (x+1), x>0 In applying mathematical methods to economics/business problems, we use a broad menu of functions for the purpose of accurately specifying the properties of the economic variables in question. Find an example that you can use the above function to describe certain economic or business activity.
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Which of the following is true? OA. Quantity rises and the effect on price is unknown B. Quantity is unknown and price rises OC. Quantity rises and price falls OD. Quantity and price rise q
Consider the following production function for shirts: q = v6 L3/4K/4, where L is worker-hours, and K is sewing machine-hours. a. Compute the marginal products of labor and capital, the average product of labor, and the marginal rate of technical substitution of labor for capital (i.e. how many units of capital are needed to make up for the loss of one unit of labor)? b. Are there diminishing returns to labor (that is, does the marginal product of labor decrease when labor L increases)? What about to capital? Is there diminishing marginal rate of technical substitution (MRTS)? с.
For a certain company, the cost for producing x items is 60x + 300 and the revenue for selling x items is 100x – 0.5x². - The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratio polynomial.) Part b: Find two values of x that will create a profit of $300. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x – 1). The order of the list does not matter. To enter va, type sqrt(a). x = Part c: Is it possible for the company to make a profit of $15,000?
f(x1,x2) 4 2 0 -2 -4 −1 2 0 1 1 0 2 -1 X1 3-2 x2 Figure 2: Graph of the function f(x1, x2) = 2x1 = x²-x+3 Consider the following function: f(x1, x2) = 2x1 - x-x+3. - For your visual convenience, a portion of the function is depicted in Figure 2. (a) Compute the gradient vector of f. (b) Compute the Hessian matrix of f. (c) Determine all points that yield stationary values of f. (d) Use the second-order conditions to determine whether each of the stationary val- ues of f is a maximum, a minimum, or neither.
A lake has two species of fish: bass and catfish. The number of bass and catfish living in the lake, B and C respectively, depend on the temperature of the lake, T (in degrees Farenheit). The functions modeling this dependency are given below: B(T) = 8T2 + 976T – 28890 С(Т) 3D — 2T?+244T — 6893 What are the two temperatures at which the number of bass in the lake is the same as the number of catfish? Enter exact expressions or round your answers to the nearest thousandth. T : T
Consider the linear spline function f(x) = 1 + x + h1(x, 2) where h1(x,2) = x-2 if x>2 and 0 otherwise. What is the slope of f at the point x=-1?
The production of a certain good in terms of the amount of labour invested L and the amount of capital invested K, is given by the production function Q = 5 L²/3 K ¹/3 At this moment 512 units of labour and 1 000 units of capital are invested daily. This means that at this moment 3200 units are produced daily. a) The company receives an order for 3200 units. Give an implicit equation for the combinations (L, K) resulting in a production of 3200 units. b) Determine K'(L) for L = 100 using implicit differentiation. Interpret your result in a sentence in the context of the word problem. c) Determine the following expression and interpret your result in a sentence in the context of the word problem: 100 K'(100) K d) Set up the graph of K as a function of L using a logarithmic scale on both axes. Interpret the slope in L = 100.