Intereting Posts

No group of order $400$ is simple – clarification
Is the standard definition of vector wrong?
Intersection of kernels and linear dependence of functionals
Calclute the probability?
solve$\frac{xdx+ydy}{xdy-ydx}=\sqrt{\frac{a^2-x^2-y^2}{x^2+y^2}}$
A finite abelian group $A$ is cyclic iff for each $n \in \Bbb{N}$, $\#\{a \in A : na = 0\}\le n$
Tightness condition in the case of normally distributed random variables
Calculating the probability of seeing a shooting star within half an hour if we know it for one hour
inflexion points of a composition of functions
What is the use of the Dot Product of two vectors?
finding a minorant to $(\sqrt{k+1} – \sqrt{k})$
To show that $S^\perp + T^\perp$ is a subset of $(S \cap T)^\perp$
High school math definition of a variable: the first step from the concrete into the abstract…
Naive set theory question on “=”
evaluate $\int_{0}^{\infty}\cos(t) t^{z-1}dt=\Gamma(z)\cos(\frac{\pi z}{2})$

A. The demand function is given by p=20-q where p is price and q is quantity. Your cost function is c(q)=q^2.

- How many units should you produce and what price should charge to maximize profits? What would profits be?
- Calculate the dead weight loss

For #1 I calculated 20- q = 2q. Q = 6.67 p = 13.33 Profit = 44.42. Does anyone know if this correct? I find it weird that q could be a decimal.

#2, I am not sure how to caluclate dead weight loss…do you need a p2 and q2? Any and all help would be greatly appreciated. Thanks in advance

- Evaluate the partial derivatives of the following function:
- By using d'Alembert's formula, substitute $P(z)$ and $Q(z)$ into the general solution to obtain an expression for $u(x, t)$
- Are the any non-trivial functions where $f(x)=f'(x)$ not of the form $Ae^x$
- Meaning of different Orders of Derivative
- Example of a function differentiable in a point, but not continuous in a neighborhood of the point?
- Continuity of the inverse matrix function

- Holomorphic function $f$ such that $f'(z_0) \neq 0$
- Prove that if $f$ is differentiable on $$ and $f$ is Lipschitz, then $f$ has a bounded derivative.
- For a differentiable function $f:\mathbb{R} \rightarrow \mathbb{R}$ what does $\lim_{x\rightarrow +\infty} f'(x)=1$ imply? (TIFR GS $2014$)
- Derivation of Euler-Lagrange equation
- Why can you mix Partial Derivatives with Ordinary Derivatives in the Chain Rule?
- Finding the derivative of $2^{x}$ from first terms?
- Why is the derivative of a circle's area its perimeter (and similarly for spheres)?
- Only once differentiable
- Derivative under a double integral
- If $f$ continuous differentiable and $f'(r) < 1,$ then $x'=f(x/t)$ has no other solution tangent at zero to $\phi(t)=rt$

The demand is $q=20-p$.

Your revenue is $r=qp=20p-p^2$

Your net profit is $n=r-c=r-q^2=60p-2p^2-400$

which is maximised when $\frac{\partial n}{\partial p}=0$

Accordingly, the solution of $p_*=60-4p_*$ gives the optimum price of $p=15$

I found this definition of “Deadweight Loss” from Wikipedia:

“In economics, a deadweight loss (also known as excess burden or allocative inefficiency) is a loss of economic efficiency that can occur when equilibrium for a good or service is not achieved or is not achievable. “

This requires knowledge of a supply function though, which I did not notice in the problem specs. I may be missing something.

$$\begin{align}

p(q)&=20-q\\

c (q)&=q^2\\

r (q)&=p (q) \times q=20q-q^2\\

\pi (q)&=r (q)- c(q)=20q-2q^2\\

\\

\pi'(q)&=20-4q=0\quad \Longrightarrow \quad q_m=5,\; p_m=20-q_m=15,\;\pi (q_m)=\pi_m=20q_m-2q_m^2=50

\end{align}

$$

The marginal cost is $c'(q)=2q $. The equilibrium is $c'(q)=p (q) $ that is $q_e=\frac{20}{3},\,p_e=\frac{40}{3}$. So the dead weight loss is

$$

D=\frac{1}{2}(p_m-p_e)(q_e-q_m)=1.39

$$

- Show that $(1+\frac{x}{n})^n \rightarrow e^x$ uniformly on any bounded interval of the real line.
- Using the Mean Value Theorem, show that if $f'(x) > 0$ $\forall x \in (a, b)$ then $f$ is increasing on $(a, b)$
- Is there a closed form expression for this sum involving Stirling number of second kind
- Prove this inequality $\frac{1}{xy+z}+\frac{1}{yz+x}+\frac{1}{zx+y}\le\frac{1}{2}$
- Entropy of a binomial distribution
- Countable/uncountable basis of vector space
- Proving $\lim\limits_{x\to0}\left(\frac{1}{\log(x+\sqrt{1+x^2})}-\frac{1}{\log(1+x)}\right) =-\frac12$
- Find all $n$ for the coins
- Prove this inequality: $\frac n2 \le \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+…+\frac1{2^n – 1} \le n$
- A bound for the product of two functions in BMO
- Is $1+2+3+4+\cdots=-\frac{1}{12}$ the unique ''value'' of this series?
- Calculating an Angle from $2$ points in space
- Write $-\Delta u = f(x,u,Du)$ as fixed point problem
- Can a countable group have uncountably many subgroups?
- What is CDF – Cumulative distribution function?