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- Kusho Industries produces and sells computer chips. Its (hourly) production function is Q=4K 0.4L 0.6 while its (hourly) cost function is C=20L+80K. Furthermore, Kusho must produce q0=400 computer chips per hour. a. Which levels of L and K satisfy the first-order conditions for the constrained minimisation of Kusho’s cost? Use the Lagrange Multiplier (LM) method. Also, find and interpret the value of the Lagrangemultiplier b. Show that MRTS=w at the constrained cost minimising levels of L and K obtained aboveDetermine the mode choice (personal vehicle or bus system) for the following regression model: Utility Function: Umode – (8.333 x 10-4)*(Access time in sec) – (6.667 x 10-4)*(Wait Time in sec) – (5.00 x 10-4)*(Riding time in sec) – (1.40)*(Cost, $) PARAMETER PERSONAL VEHICLE CITY BUS SYSTEM MODE CONSTANT -0.01 -0.07 ACCESS TIME (SECS) 300 600 WAITING TIME (SECS) 0 900 RIDING TIME (SECS) 1,500 6,000 COST (DOLLARS) $1.50 $1.00Is it true of false that the classical errors in variables (CEV) assumption is that the measurement error is correlated with the unobserved true value of the explanatory variable.
- Q2B. Which of the following are limitations of using Impulse Response Functions(IRFs) in time series analysis?i. IRFs are only valid for linear time series models.ii. IRFs assume that the underlying time series is stationary.iii. IRFs can provide information about the short-term dynamics of the relationshipbetween variables, but they do not capture longer-term effects or otherimportant aspects of the relationship.iv. IRFs depend on the specification of the model used to estimate the relationshipbetween variables.The demand function for Newton’s Donuts has been estimated as follows:Qx = -14 – 54Px + 45Py + 0.62Ax where Qx represents thousands of donuts; Px is the price per donut; Py is the average price per donut of other brands of donuts; and Ax represents thousands of dollars spent on advertising Newton’s Donuts. The current values of the independent variables are Ax=120, Px=0.95, and Py=0.64.Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary. Calculate the price elasticity of demand for Newton’s Donuts and describe what it means. Describe your answer and show your calculations. Derive an expression for the inverse demand curve for Newton’s Donuts. Describe your answer and show your calculations. If the cost of producing Newton’s Donuts is constant at $0.15 per donut, should they reduce the price and thereafter, sell more donuts (assuming profit maximization is the company’s goal)? Should Newton’s Donuts spend…Q8. Which one of the following is NOT true: Options - We do not need to know the functional form of heteroskedasticity to perform White's test for heteroskedasticity. Lagrange Multiplier test for heteroskedasticity requires us to specify a functional form for heteroskedasticity. Heteroskedasticity makes OLS estimator biased. Jarque-Bera test does not test for heteroskedasticity
- Problem is to max U=u(L,Y) Subject to time constraint Y=w(24-L) Solution Set lagrangian equation (Y-w(24-L) Form the composite function Z=u(L,Y) - (Y-w(24-L) 1st order conditions for maximization requires: dZ/dL = DZ/dY= Dz/dlabda= 2nd order conditions for maximization requiresI cannot figure out how the equation goes from q1 = D1 (p1; p2) = S(1/2 + (p2-p1/2t)) to q1 = S/2 +(p2-p1/2t) why is S not in the numerator of both terms? i.e. q1 = S/2 + S(p2-p1/2t)What conditions must non-linear time series models, such as vector autoregressive models, satisfy in order to use impulse response functions
- The demand function for a product is given by P = 4000/ln (x+10), where P is the price per unit in dollars when x units are demanded.i. Find the rate of change of price with respect to the number of units sold when 40 units are sold ii. Find the rate of change of price with respect to the number of units sold when 90 units are sold.iii. Find the second derivative to see whether the rate at which the price is changing at 40 units is increasing or decreasing.It is projected that in the future, the population of a certain country in millions will be P(t)= 85e^.05t, where t is is time in years since 2022. Round all answers to the nearest whole number a. What is the projected population of the town in 2026 b. Find the simplified derivative function c. At what rate will the population be changing in 2026 d. In what year was the population increasing at a rate of 5 million people per year e. When will the population reach 160 millionWhat are the critical points of CES function with A=100, α= 0.2 ß= -0.5 subject to the constaint 7K+16L=5200? A) K=2,32,L=232,58 B)K=3,23,L=323,58 C)K=4,32,L=432,58 D)K=4,23,L=423,58
