# Tagged Questions

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### How do I express this profit function as a function of prices only?

How do I express this profit function as a function of prices only? The function is $(p-AC)q$, where $p$=price, $AC$=average cost (NOT marginal cost), and $q$=quantity sold. so in numbers ...
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### Show that the least squares estimator of the slope is an unbiased estimator of the true' slope in the model.

Under the assumptions of the classical simple linear regression model, show that the least squares estimator of the slope is an unbiased estimator of the true' slope in the model. Anyone have any ...
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### Deriving Stochastic Euler Equation

If a consumer has utility function \begin{equation*} u(c_t) = ac_t - \cfrac{b}{2}c_t^2 \end{equation*} and present value budget constraint \begin{equation*} \sum_{j=0}^\infty E_t[\beta^jc_{t+j}] = ...
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### Euler Equation and Marginal Rate of Substitution

I was wondering if someone could help me clarify a result from my lecture notes. I have put them as a picture. It concerns the result on the last slide (the other three slides are included as well ...
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### What quantity should the firm produce if it wants to maximize its profit given short run marginal coast and short run total cost function

A bicycle repair shop charges the competitive market price of 10 dollars per bike repair. The firms short run total cost is given by STC(Q)=$\frac{Q^{2}}{2}$ and the associated marginal cost curve is ...
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### utility and uncertainty of economics

United Petroleum is operating a deep water oil rig in the Gulf of Calexico. Management have been informed that the drilling riser may be susceptible to methane build up and hence at risk of an ...
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### Computing the certainty equivalent for the lottery of infinite expected value

How can I compute the certainty equivalent for the lottery for someone whose Bernoulli utility function is $u(x)=\frac{x^{1-\gamma }}{1-\gamma }$ where $0< \gamma < 1$? Also, how much would the ...
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### Show that there exist prices at which agents can engage in mutually beneficial trades.

Consider an exchange economy with $2$ goods and $2m$ identical Households, but in this case each household has utility function $u(x_1,x_2)=x_{1}^2+x_{2}^2$, and endowments $w_1=w_2$. Show that there ...
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### Robinson Crusoe economy problem

Consider the Robinson-Crusoe one-consumer, one-producer economy. Compute the equilibrium prices, profits and consumption when the production function is $f(L)=\sqrt{L}$, the utility function is ...
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### Calculating “deseasonalised sales y” when forecasting 2004Q1-2004Q2

I'm currently having difficulty calculating values for the deseasonalised sales column. How do you go about doing it for 2004Q1-2004Q2? Btw in case you are wondering: $$2004Q1$$ First MA = ...
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### Understanding a Proof in Probability Theory

My question is pretty simple: I have two equations which are supposedly true (from a published paper) but I have no idea how to arrive at the solution myself. So it would be great if someone could a) ...
A consumer has the utility function $u(x_1,x_2)=(x_1^a+x_2^a)^{1/a}$ where $0\neq a<1$. Her expenditure must satisfy $p_1x_1+p_2x_2=I$, where $p_i$ is the price of a good i, and I is her income. ...
### Using the definition of a concave function prove that $f(x)=4-x^2$ is concave (do not use derivative).
Let $D=[-2,2]$ and $f:D\rightarrow \mathbb{R}$ be $f(x)=4-x^2$. Sketch this function.Using the definition of a concave function prove that it is concave (do not use derivative). Attempt: ...