1) By using the Hubbert function for the variation of oil production with time, (t) Qe+eto)2, eva...
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(2 points) An oil company discovered an oil reserve of 130 million barrels. For time t > 0, in years, the company's extraction plan is a linear declining function of time as follows: where q(t) is the rate of extraction of oil in millions of barrels per year at time t and b 0.05 and a -14. (a) How long does it take to exhaust the entire reserve? time years (b) The oil price is a constant 30...
Two countries produce oil. The per unit production cost of Country 1 is C1 = $2 and of country 2 it is C2 = $4. The total demand for oil is Q-40-p where p is the market price of a unit of oil. Each country can only produce either 5 units, 10 units or 15 units. The total production of the two countries in a Nash equilibrium is 10 15 20 25 30
7. The charge Q-Q(t) on a capacitor as a function of time obeys the differential equation Q" + Q = E(t). with the electromotive force E given by E)-cos(ut) here w >0 is a constant. (a) (2 points) Find Q(t) for all 0 t < π if Q(0)-Q'(0) = 0. (b) (8 points) For wメ find Q(t) for all 12 π, assuming that Q and Q, are continuous at t = π. [Remark. Soon, you will be able to solve...
1. (20 points) You are working for Valdez SpillProof Oil Company as a petroleum engineer. Your boss is asking you to estimate the future life of an oil well. The analysis used in the industry is called the decline curve analysis where the barrels of oil produced per unit time are plotted against time, and the curve is extrapolated. One of the standard curves used is harmonic decline model, that is 1 + at Where q is the rate of...
Consider the Solow growth model. Output at time t is given by the production function Yt = AKt3 L3 , where A is total factor productivity, Kt is total capital at time t and L is the labour force. Total factor productivity A and labour force L are constant over time. There is no government or foreign trade and Yt = Ct + It where Ct is consumption and It is investment at time t. Every agent saves s share...
suppose an input voltage is given as V(t) = 240[u(t-5) - u(t-10)]. In a branch of an electronic circuit, the variation of current with time is modeled by the differential equation d^2(i)/dt^2 + 36i = dv/dt. Assuming zero initial conditions, determine I as a function of t. (hint: use laplace transforms)
Calculate the NPV for the following investment with 6 years life time assuming a discount rate of 20% per year: The investor is a Non-integrated petroleum company Total producible oil in the reserve is estimated to be 2,400,000 barrels Production rate will be 400,000 barrels of oil per year from year 1 to year 6 Mineral rights acquisition cost for the property will be $1,600,000 at time zero Intangible drilling cost (IDC) is expected to be $7,000,000 at time zero...
A production function given by: Q = 10K^1/5L^1/2 (a) Find out the equation for an isoquant to produce 20 units. Show your work. (2+4 = 6 points) (b) Write down the equation for the short-run cost function where K is fixed at 243, price of capital is 10 and price of labor is 9 per unit. Show your work. (2+4 = 6 points)
Total Production 1999 2000 Price Hotdogs T-Shirts Factories Total Production 1000 2000 10 Price 2 4 100 Total Production 2000 4000 20 100 26. The chart above shows total production in an economy and the prices of each good produced in 1999 and 2000. Let 1999 be the base year, and let the market basket for the CPI be 1 hotdog and 1 T-shirt. Which of the the following statements is true? a. The inflation rate calculated by using the...
The change of inputs and production function determine the level of output in the long run. Suppose an economy described by the Solow model utilize capital and labour in production process which technology parameter ofa=1/2. Assuming that population has zero growth rate and technology is constant (A=1): a. Write down production function for this country, determine output per worker as function of capital per worker and explain the steady state of capital condition (6 POINTS) b. If 8 and s...