3 Suppose the power,P, from a circuit as a function of current, I s known to obey an equation of the form: P- al+bl+4 w...
Please show all the work nice and neat 3 Suppose the power, P, from a circuit as a function of current, I, is known to obey an equation of the form: P=a12 + bl + 4 where "a" and "b" denote unknown constants. Suppose the actual values of I and P are found to be as shown in Table 1 below. line 2 10 16 22 26 4 a) Formulate a suitable cost function and find the least squares estimates...
a) Formulate a cost function along with constraints, if any, for the following optimization problems. You don't need to solve any of these problems i) Two electric generators are interconnected to provide total power to meet the load. Suppose each generator's cost (C) is a function of its power output P (in terms of units), and costs per unit are given by: C2 = 1 + 0.6P2 + P22 (for Generator 2). -1-P -Pi2 (for Generator 1), If the total...
9. Suppose the firm's production function is given by f(K,L) min (K",L" (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at R = 10,000 and a =. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K, L) = KLi. Let...
9. Suppose the firm's production function is given by f(K,L) = min (Kº,L"} (a) For what values of a will the firm exhibit decreasing returns to scale? Constant returns to scale? Increasing returns to scale? (b) Derive the long-run cost function and the optimal input choices. (c) Suppose the capital is fixed at K = 10,000 and a = 1. Assuming that the firm wants to produce less than 100 units, derive 10. Consider the production function: f(K,L)=KLI. Let w...
Question 4) Suppose that the (univariate) variable y is known to be a quadratic function of the variable x; that is, y = a x2 +bx+c, where the coefficients a, b, c are obtained by conducting an experiment in which values y1, .. , Yn of the variable y are measured for corresponding values 21,.. , Un of the variable x. Find the best least-squares fit of the quadratic polynomial using the data: {(-2,-5),(-1, -1),(0,4), (1,7), (2,6), (3,5), (4, -1)}....
3. (20 pts) Suppose that we have 4 observations for 3 variables y,I, 2 and consider a problem of regressing y on two (qualitative) variables r, 2. Data: 22 obs no. y (Income) 2 (Management Status) I (Gender) 1 None Female 2 None Male Yes Female Yes Male 4 To handle the qualitative variables r, 12, we define dummy variables 1, 22 as for 1, 22= Yes Male for 1, 219 22 -1. for 22= None for 1= Female -1,...
Question 1 (36 points) Suppose that the demand function is given as follows: 5000 3Pr +P, -2I and 2P T - P. where Pr denotes price of good x. P, denotes the price of a related product y, I denotes income, T denotes the tax imposed by the government on firms and P. denotes the price of alternative product that can be produced by firms a-) (8 points) Find equilibrium price and output (Peg and Oe") as a function of...
making sure i did them right. please answer all 4. From theoretical considerations, it is suspected that the rate of flow from a fire hose is proportional to some power of the pressure at the nozzle. Do the following data confirm this observation? Get the least-squares values for the exponent and the proportionality factor Q1. Flow Rate 94 118 147 180 230 Pressure 10 16 25 40 60 These data represent solubility of n-butane in liquid anhydrous hydrofluoric acid. Fit...
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Determine the maximum value of Daf(P), where u is any unit vector at P c) Find the angle between Vfp and PO, where O denotes the origin. d) Find an equation for the tangent plane to S at P rty. I 5. [16...
1. Suppose that a single-price monopolist faces the demand function P 100 Q where I is average weekly household income, and that the firm's marginal cost function is given by MC(Q) 2Q. The firm has no fixed costs. = (a) If the average weekly household income is $600, find the firm's marginal revenue function. (b) What is the firm's profit-maximizing quantity of output? At what price will the firm sell that output? What will the firm's marginal cost be? (c)...