# Tagged Questions

138 views

### How to derive demand function from a utility function without any knowledge of Lagrange Multipliers?

How do I derive the demand function for a utility function of, say, $U(x,y)=\sqrt{11x+11y}$ for goods X and Y in terms of $P_x$, $P_y$, and income $I$, with basic mathematics (basic calculus, but no ...
47 views

### Cost per item. Diminishing marginal discount, if you will. (Bigger discount for first few items) Optimal number of units to buy?

The graph above shows price per unit. Say they are cupcakes. When you buy a higher quantity, you get a lower price per unit. Say it levels off like this graph. Obviously, buying 2 nets a nice ...
15 views

### Profit Maximization without an explicit functional form for f(x1, x2) - Need to infer the signs of derivatives

Consider the following 2 input, 1 output profit maximization problem: $$\max_{y,x1,x2} \{py-w_1x_1-w_2x_2 : y=f(x_1,x_2)\}$$ where f is the producers production function, w_i>0 is the price of ...
41 views

### Maximizing a derivative of a two-variable function in an economic application [closed]

What is the solution to this problem: Thank You
48 views

### Need help explaining how the elasticity was derived [closed]

We had a lecture on calculating elasticity in microeconomics and I need help understanding how the answer was derived. I didn't quite get how we came up with the answer. My classmate said to just ...
39 views

### Problem understanding an implicit differentiation

Here is a general budget constraint: $p{_1}x{_1}+p_{2}x_{2}=M\Leftrightarrow \frac{p_1}{p_2}x_1+x_2=\frac{M}{p_2}\Leftrightarrow {p_{1}}'x_1+x_2=M{}'$. The main idea is that since prices are given, ...
51 views

### Finding criteria for a household financial budget falsification

I’m working on a financial problem about budget of households. Households in a state fill a form about their net budget in every year and our insurance company investigate their financial status and ...
66 views

### Help to solve this problem, the result doesn't seem right :/ silly mistake somewhere probably

Suppose that Coke and Pepsi are the only firms producing cola. Their products are not identical, but are very close substitutes. Let $P_c$ denote the price of Coke and $P_p$ the price of Pepsi. Demand ...
38 views

### Utility optimization question

Having trouble with how to put this together. I have an answer key, but the individual steps I am struggling with. Two period economy with a representative consumer that maximizes the utility ...
56 views

### How to differentiate this expression with respect to t

I don't understand how to differentiate $f(tx_1,\cdots, tx_n)$ with respect to t.
129 views

### Sequence of learning mathematics from basic algebra to calculus.

What would be a step by step sequence of learning mathematics from basic algebra to basic calculus? I pose this question because I am in the process of self-learning mathematics as a preparation for a ...
27 views

### 2 competitive or cooperative products?

I found this question in a calculus book and I'm not sure how to go about solving it: What exactly am I supposed to do to answer this? Do I need to find the first and second derivatives of each ...
119 views

### Cobb Douglas production function problem

My question is related to the Cobb-Douglas production function: $Y= A \cdot L^\alpha \cdot K^\beta$ Assumptions: constant-returns to scale, meaning that when $L$ and $K$ increase with a factor ...
51 views

### Differentiate the utility function.

I've never differentiated utility functions. I'm struggling to understand how the differentiation of this problem results in the answer that it does. Could someone please show me (step by step) how ...
181 views

### Elasticity of demand given a quantity and a price function

I have a price function: $$\frac{8,100,000}{q^2+8,100}$$ Where $q$ is quantity demanded. How can I find the price elasticity when $q = 30$? I know how to differentiate, but I'm just not sure what ...
59 views

### Using data points and a best-fit to find a function for quantity with respect to price

So I'm taking an entrepreneurship class, and we're doing a simulation where we run a donut shop. My math is pretty strong (integral and differential calculus level), so I'm trying to use my math ...
50 views

### differentiating a cost function using chain rule

How to differentiate the function (cost function) $$C(x)=V\left(\frac{px-W}{q}\right)$$ where $W,p,q$ are constants,and $W$ representing the consumer's budget or wealth. $V$ is a function of $x$. ...
215 views

### Consumer optimization problem

A customer has to decide how many of products $x$ and $y$ to buy. The price of $x$ is $2x^{1/2}$ and the price of $y$ is $4y^{1/2}$. The cost of $x$ is 10 dollars and the cost of $y$ is 5 dollars. ...
100 views

### For a price and cost function, at what rate do the weekly sales change per week?

For a price function of $p=4000-25x$ and a cost function of $C=1800x+4500$, if the profit is increasing at a rate of $3000$ per week and the weekly sales are $x=32$ units, at what rate do the weekly ...
893 views

### Profit Maximization Question of a Leontief (Perfect Complements) Production Function?

This is a question from my intermediate micro economics text book. Any help is very appreciated! Given Info: Company ST (a company which offers custom travel-planning services) is a ...
512 views

### derivative with respect to $\log(x)$

I have a dynamic equation, $$\frac{\dot{k}}{k} = s k^{\alpha - 1} + \delta + n$$ Where $\dot{k}/k$ is the capital growth rate as a function of savings $s$, capital $k$, capital depreciation rate ...
62 views

### what is a connection between two simple yet important economics and math formula: elasticity

what makes it interesing to define them in mathematics? what is a connection between two simple yet important economics and math formula: elasticity? Something interesting to read: ...
2k 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) + ...
233 views

62 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). ...
863 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 ...
174 views

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 $y = –x^3 + 7x – ... 1answer 50 views ### Either find an example of a differentiable downward-sloping function$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 ... 1answer 150 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 ... 1answer 761 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 ... 1answer 226 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 ...
Homework problem: We have a graph of value: x coordinate number of widgets made. y coordinate value in $. For the first 5 widgets the value greatly increases to$100 and then after 5 ...