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

Macroeconomics: Fiscal Policy and short run effects of fiscal and monetary policies

  Fiscal Policy: government spending and taxation, aimed at expending or contracting the level of macroeconomic activity in a nation. A tax increase (decrease) will raise (lower) households' disposable income, leading to more (less) consumption. Furthermore, firms will increase (decrease) the number of investment as they get to keep a larger (smaller) share of their profits. An increase (decrease) in government spending affects the variable G that defines the aggregate demand. Government spending also leads to a change in household income, affecting the level of consumption. Tax multiplier: just like any multiplier so far, it is just the sum of a converging geometric series: Say the MPC is equal to 70%, then it must be the case that the MPS is 30%. Thus, the tax multiplier, t, is equal to about -2.32. In other words, for every dollar that goes to tax revenue, total spending decreases by about 2.32 dollars. Note that a tax decrease would be negative, and thus have a positi...
Post a Comment
Read more

Microeconomics: Factor Markets

Definition: Factor markets: markets for the factors of production (example: labor and capital). Markets are formed whenever consumers and producers meet to exchange goods or services. Deriving factor demand: the demand for goods or services in the product markets creates demand for the factors of production.  An increase (decrease) in demand for good X leads the suppliers to increase their production thereby increasing (decreasing) the demand for the factors of production.   Marginal revenue product: The demand for the factor of production is formed by multiplying a firm's marginal revenue by its marginal product.  Remember that by taking the derivative of the TR function with respect to Q we are able to find the MR. Marginal product on the other hand is found by taking the derivative of the production function with respect to a factor of production (L or K for example). Marginal revenue product (MRP): the change in total revenue when one more input is employed. It decrea...
Post a Comment
Read more