-2
$\begingroup$

a)Determine marginal revenue curve if firm can only charge 1 price,List demand curve,marginal revenue curve,,marginal cost,average total cost equations.

b)What is optimal price and quantity?

c)If firm fixed cost are 16 dollars, what are the profits?

P=20-q

MC=12

Attempt:

I tried

mc=c/p

12*20-q=x

to find P*X=MR

b)

12=240-12q

q=-228/12

c)

MC=6

6=240-12q/20-q

q=24

The numerical answer is wrong so what mistake did I make? What's the correct equation to solve for test equation?

$\endgroup$
2
$\begingroup$

I assume that the firm is a monopolist.

We know the inverse demand function, the fixed costs and the marginal costs:

  • $P(q) = 20 - q$
  • $MC(q) = 12$
  • $F = 16$

As the marginal costs are constant, we can compute the total costs function as:

  • $TC(q) = MC\cdot q + F = 12 q + 16$

The average total costs is obtained by dividing by $q$:

  • $AC(q) = \frac{TC(q)}{q} = 12 + \frac{16}{q}$

The demand curve is obtained by inverting the inverse demand function:

  • $q(P) = 20 - P$

Total revenue is obtained by multiplying together price and quantity:

  • $R(q) = P(q)\cdot q = (20-q)\cdot q = 20 q - q^2$

Marginal revenue is obtained by taking the derivative of revenue with respect to $q$

  • $MR(q) = \frac{\partial R(q)}{\partial q} = 20 - 2q$.

If the firm maximizes profits, then the marginal revenue equals the marginal costs so:

  • $12 = 20 - 2q \to q = 4$

The optimal price can be found by substituting $q = 4$ into the inverse demand function:

  • $P = 20 - 4 = 16$

Profits are determined as total revenue minus total costs:

  • $\pi = R - TC = P\cdot q - TC = 16 \cdot 4 - (12 \cdot 4 + 16) = 0$
$\endgroup$

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.