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This is the canonical Arrow-Pratt "portfolio" model. Couple of points on terminology: For a function $u$, we define the risk aversion function by $r_u(x):=-\frac{u''(x)}{u'(x)}$. In your utility function, $r_u(x) = \lambda$; hence, it is a constant absolute risk aversion utility and $\lambda$ is the "coefficient of risk aversion," not the "risk ...

The current jump in price is because one or more suppliers are dropping out. That shifts the supply curve to the left such that for the same demand for oil, the new price is now further up the steeper part of the curve (see the plots below). The demand for oil will react to that new price, but it takes time. Sorry that I don't have a more recent supply ...

This occurs because the price elasticity of demand for oil is near zero, which is to say the demand curve is nearly vertical. This is partly a limited rate of production story (i.e., in the short term the rate of oil production is fixed), but it's mostly a limited substitutes story. Our cars run on gas, as do the trucks that move goods around the nation and ...

This looks like a general equilibrium model in Economics. It should be described in most of microeconomics textbooks (e.g. this). Yes, you need a budget constraint here for$\ a$, otherwise your optimization problem makes no sense. Moreover, the household prefers consumption today to consumption tomorrow and, hence, you may want to enhance your model by ...

That's the problem with China. The official data is nonsense, and the estimates of outsiders can change without warning. Here are some links: China Official Stats 1 China Official Stats 2 China Official Stats 3 More China Stats OECD CIA World Bank 1 World Bank 2 IMF CMF Changing Stats 1 Changing Stats 2 Changing Stats 3 - Copper Changing ...

demand surely decreases? Maybe this is not true because the high demand for oil? Demand for oil, like grains, is very inelastic. People have a very hard time changing their energy consumption habits when price shocks happen. Some of this is unwillingness to change, but a lot is that there are very few alternatives. Most people in the US live too far ...

I basically agree with @John, let me expand: We want to model $y$ using a simple linear model, the most basic setup is $$ y = c + \mathbf{X}\beta $$ with $y$ the $N$ observations, $c$ a constant, $\mathbf{X}$ the $N \times M$ matrix of regressors and $\beta$ a $M$-dimensional vector of coefficients. This model has $M$ parameters, the elements of $\beta$. ...

First, your statement that your utility function goes to infinity is wrong. It's minus exponenta. You can think of it as a minimum of $e^{f(x)}$ which is bounded below by zero whatever $f(x)$ is. In other words, your utility function is bounded above by 0. Second, maximizing expected value, you need to calculate it before deploying maximization techniques. ...