Skip to main content

Exercise: monopoly

You have the following information about a monopoly:

  • Derive the MR, find the profit maximizing price and quantity.
    • Find profit, consumer surplus, and dead-weight loss using the price and quantity from the previous question.

Now that we have derived the MR function, set MR=MC and solve for Q.


Choose Q1 (it does not make sense to have a negative quantity in our model),then plug this number into the demand function to obtain its price.


Consumer surplus:

Dead-Weight Loss:


Profit:


  • The government wants to intervene in order to increase consumer surplus, while keeping the monopoly from making a loss.At what price should the firm be forced to sell its goods?
Although the DWL is completely eliminated when the the price is equal to the intersection between the MC and demand curve, the consumer surplus can be further expended by setting the firm's price equal to the intersection between the ATC and demand curve. This is due to the fact that the point at which the ATC intersects the demand is smaller than at the intersection between the MC and demand curve.


Choose Q3 and plug it into either the ATC or demand function in order to find the price.


Let's graph this:


Note that the MC used for this problem isn't really the actual MC. However, this function used for this problem mimics the actual MC's behavior. In order to derive the "real" MC, multiply ATC by Q to obtain the cost function. Then, take its derivative. 






Location: New York, NY, USA

Comments

Post a Comment

Popular posts from this blog

Macroeconomics: multiplier and crowding out effects

Multiplier effect: whenever   any of the components of AD increases, the increase in GDP will be greater than the initial increase in expenditures. The impact on GDP of a particular increase in spending depends on the proportion of the new income that is taken out of the system to the proportion that continues to circulate in the economy. The multiplier effect tells us the impact a particular change in one the components of AD will have on the total income (GDP).  Let k denote the spending multiplier, which is a function of MPC and MPS. The larger the marginal propensity to consume, the larger the spending multiplier. Notice that the larger the MPC, the greater the impact a particular change in the spending variables will have on the nation's GDP. The crowding out effect: If government spending increases without an increase in taxes, the government must borrow funds from the private sector to finance its deficit, thereby increasing the interest rate. This increase in interest ...
Post a Comment
Read more

Exercise: short and long run effects of a fiscal policy

  You are in charge of the government budget for the year 2021. You are told that schools and public roads need to be updated, and you estimate an appropriate budget in order to carry out the task. Describe what will happen in the short run to the economy, and what type of inflation do we see? Describe the supply side effect from this policy, explain what happens in the long run. Assume that there is no crowding out effect. First, note that updating public infractures, assuming taxes stay the same, will require an increase in government spending, which will also have an impact on the investment and consumption level in the economy (remember the spending multiplier?). Therefore, the aggregate demand curve will shift to the right. This will cause inflation (i.e positive change in the price level) and a higher output in the short-run.  Note that if we were to assume a large crowding out effect, the short run aggregate supply curve would shift to the left (increase in production c...
Post a Comment
Read more

Exercise: maximizing profit

Assume that you are the owner of a small business that produces T-shirts. Your the total revenue for your business can be modeled by the following equation: and your total cost corresponds to this function: Find the point at which your firm maximizes its profit. Then, find how much profit the firm if able to earn at that point. Using the total cost and total revenue functions we can set up the profit function: Then, realize that if you want to find the maximum profit, take the derivative of the function and set it up equal to zero, and solve for Q. This is equivalent of taking the derivative of the total cost and total revenue functions and setting them equal to each other. In this problem, I chose the latter option as it was explained in the previous lessons. Notice that profit is often denoted by a capital pi.  We are assuming that the TR>TC for some positive value, you can check for yourself. However, if we did not know that, we would first take the first ...
Post a Comment
Read more