Tagged Questions
0
votes
1answer
23 views
L'hopital's rule in deriving Cobb-Douglas function from CES production function
$$ \ln(Y) = \ln(A) + \frac{\ln[\alpha K^\gamma + (1-\alpha) L^\gamma]}{\gamma}$$
can be taken to the limit by applying l'Hôpital's rule:
$$\lim_{\gamma\rightarrow 0} \ln(Y) = \ln(A) + ...
4
votes
0answers
95 views
Open Problem in Fixed Point Theory [Prize]
This open problem appeared on the bulletins of Evans Hall at Berkeley this week.
I hope this doesn't violate StackExchange policy (the solution carries a $500 prize), but I thought why not re-post ...
0
votes
1answer
53 views
Quasilinear utility functions
Is the utility function below quasilinear?
$U(X,Y)=XY+10Y$
I know that an equation of the form $U(X,Y)=f(X)+Y$ is quasilinear but I'm not sure about functions of the form $U(X,Y)=f(X,Y)+Y$.
0
votes
0answers
212 views
Deriving demand functions given utility
A consumer purchases food $X$ and clothing $Y$. Her utility function is given by: $U(X,Y) = XY +10Y$, income is $\$100$ the price of food is $\$1$ and the price of clothing is $P_y$.
Derive the ...
0
votes
1answer
66 views
Deriving a demand curve intermediate microeconomics
The exercise says as follows: Zac consumes only pizza and Chianti in fixed proportions. 2slices of pizza per 1 glass of chianti. income is $100. Derive demand functions for pizza and Chianti.
How do ...
1
vote
0answers
56 views
Differentiation help
I recently got some lecture slides, but needed a little help understanding the maths behind them.
(equations)
(Working and Answer)
Basically, I don't understand how to get from step (4) to (5). ...
4
votes
2answers
117 views
Slope of a nonlinear curve at a single point
This part of my microeconomics lesson plan has me baffled.
Consider for example the nonlinear continuous and differentiable function Y = f(X) = X 2 + 4. Suppose we want to know its slope at the ...
2
votes
1answer
67 views
Applied Math for economics question: mostly algebra help
I am teaching myself the calulus component necessary to get thorugh an econ based stats and applied math class. My algebra is killing me please help - the practive problem is given
$y = –x^3 + 7x – ...
0
votes
1answer
36 views
Either find an example of a differentiable downward-sloping function $p$ such that $\frac{d}{dx}[p(x)+xp'(x)]<0$
In economic models we assume that firms which face a decreasing demand curve also face a decreasing marginal revenue curve. I just realized that I wasn't sure that this is true, so I tried to prove ...
0
votes
1answer
95 views
Economic Analysis / Minimization Problem
I am studying and going through some old exams for a microeconomic analysis class. I am just looking for some clarification regarding one of the answers given. The question is as follows
Suppose ...
0
votes
0answers
70 views
Unique utility, but variable Walrasian Equilibrium Consumption set
Basically, I am not sure why the utilities in this economy is unique even though Walrasian Equilibrium consumption is not unique.
Here's the setup:
Consider an exchange economy with one money good ...
0
votes
1answer
216 views
Finding Nash Equilibria with Calculus
The problem is summarized as:
There are two players. Player 1's strategy is h. Player 2's strategy is w. Both of their ...
0
votes
0answers
37 views
proving existence of an equilibrium in an equation involving PDF and CDF
I have an equation for which I want to show existence of at least one equilibrium. The equation, call it $h(x)$, is:
$$h(x)=[a-q'(y)]f(x-y) - q''(y)[1-F(x-y)],$$
where $a$ is a positive constant, ...
1
vote
1answer
94 views
Optimization price per unit
I have no idea how to do this, I tried a lot of things but they don't make sense and I have too many variables.
A manufacturer has been selling lamps at the price of \$6/lamp, and at this price ...
1
vote
0answers
267 views
Maximizing two codependant profit equations for Bertrand Model Oligopolies
For this problem I was given the Fixed Cost, Marginal cost, and demand curves for two firms (x and y). So far, from this information I derived the profit (π) function for each firm.
...
