0
$\begingroup$

I was given a word problem. No formulas. So I set up the following equations:

Demand Function \begin{equation} D(p) = a - p \end{equation} Cost Function: \begin{equation} c(q) = 9 + 10q \end{equation} Marginal Cost \begin{equation} MC = 10 \end{equation}

I am supposed to find how much the man in the problem would produce for any value of $a$. But, without a production function, I am unsure how to determine how much he will produce.

Specifically, suppose I write

\begin{equation} R = pD(p) \end{equation}

I can't then differentiate R by q to find marginal revenue.

So how do I know how much he would produce?

$\endgroup$
2
$\begingroup$

Here are some hints. Either solve the profit function in terms of $p$, substituting out all references to $q$ (recall that $D(p) = q$), or solve the profit function in terms of $q$, substituting out all references to $p$. Then you'll find that the profit function is concave and the differentiated with respect to $p$ in the first case or $q$ in the second case will give you the profit maximizing solution.

EDIT: Yeah, $a = 2q + 10$ looks correct. Just solve the equation for $q$ and the interpretation is clear. That is, the quantity produced is $q = (a - 10)/2$. If you want to know the price, then just substitute $q$ in for $D(p)$ like so: $a - p = D(p) = q = (a - 10)/2$.

$\endgroup$
  • $\begingroup$ I calculated the value of $a$: $a = 2q + 10$. But how am I supposed to interpret this? In this case, $a$ is just the $b$ in a standard 7th grade $y = mx + b$ formula, so it corresponds to the y intercept in Cartesian coordinates. But $q$ can't take negative values and presumably must be integers. Therefore, for $a < 30$ he wouldn't produce, but for $a \geq 30$ he would. Does that make any sense? Economics confuses me sometimes to the point where I forget how to add and subtract because I can't tell what I should be performing the operations on. $\endgroup$ – Stan Shunpike Jan 19 '15 at 23:26
  • $\begingroup$ You don't need to give me the correct answer. Simply telling me if my deductions are true based on the premises I gave would be enough. That would leave it to me to decide if my premises are correct. $\endgroup$ – Stan Shunpike Jan 19 '15 at 23:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.