got this from my teacher,

A monopolist faces a demand curve given by the following equation: P = $500 − 10Q, where Q equals quantity sold per day. Its marginal cost curve is MC = $100 per day. Assume that the firm faces no fixed cost.

and have the answers for most, but can someone give me a bump in the right direction for the follow up -

Now suppose a tax of $100 per unit is imposed. How will this affect the firm’s price?

Government adds taxes; prices go up.

sorry, i understood that, but as the prices go up the output goes down.

but how can you recalculate the price. output drops to 15 in an earlier question, but i cant get my head around working out the price

I don't know how you can predict or calculate such a thing. Some manufacturers will pass along most/all of the tax, while others will try to absorb as much as possible; still others may decide to shift their focus to other manufacturing areas; and some may decide to reduce their workforce.

Example: the new tax on manufacture of medical devices.

ah ok, i see your point.

i had worked out that P = $500 - 2xQ(10x20) as MC = MR (100=100), so price was 300 and output 20.

the tax would mean a reduction in output to 15 units, by my calcs but how can i work out the corresponding price.

if amonopolist competing firm has ademaned function and cost function under the following

P=100-30+4a½
Tc=4q²+10q+a
a refers adevertising price and q quantity and p price calculate the maximizing out put and advertising price and also price of the demaned function please with great pardon help;.

To determine how the tax of $100 per unit will affect the firm's price, we need to consider the impact on both the demand curve and the cost curve.

First, let's find the firm's initial equilibrium price and quantity without the tax. The firm's profit-maximizing condition is to set its marginal cost (MC) equal to the marginal revenue (MR) generated from each unit sold. Since the monopolist faces a linear demand curve, we can find MR by taking the derivative of the demand curve equation with respect to Q.

Given that P = $500 - 10Q, the MR can be calculated as follows:
MR = d(P)/d(Q) = 500 - 20Q

Setting MR equal to MC, we get:
500 - 20Q = 100

Solving this equation, we find the monopolist's initial equilibrium quantity (Q) as:
Q = (500 - 100) / 20 = 20

Plugging this value back into the demand curve equation, we can find the initial equilibrium price (P):
P = $500 - 10Q = $500 - 10(20) = $500 - $200 = $300

So initially, without the tax, the equilibrium price is $300.

Now, let's consider the effect of the tax. With a tax of $100 per unit imposed, the firm will have to adjust its pricing strategy to account for this extra cost.

Let's assume that the firm bears the entire burden of the tax, meaning they are responsible for paying the full $100 per unit. This additional cost will impact the firm's cost curve.

Since the firm faces no fixed cost, the only cost we need to consider is the marginal cost, which remains unchanged at MC = $100 per day. However, with the tax, the firm's new marginal cost will be MC = $100 + $100 = $200 per day. This is because for each unit sold, the firm needs to pay the $100 tax in addition to the $100 marginal cost.

To determine the new equilibrium price, we can repeat the profit-maximizing calculation using the new marginal cost. Setting the new MR equal to the new MC, we have:
500 - 20Q = 200

Solving this equation, we find the new equilibrium quantity (Q) as:
Q = (500 - 200) / 20 = 15

Plugging this value back into the demand curve equation, we can find the new equilibrium price (P):
P = $500 - 10Q = $500 - 10(15) = $500 - $150 = $350

Therefore, with the tax of $100 per unit imposed, the firm's new equilibrium price will be $350. The tax has caused an increase in the equilibrium price by $50 from the initial price of $300.