Monopolist Profit Maximization with Elasticity Calculation

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In summary, the conversation discusses a monopolist's demand and total cost functions and how to derive the marginal cost and marginal revenue functions. It also asks for the profit-maximizing output and price for the monopolist and the elasticity when given specific values. The conversation ends with a question about the definitions of marginal cost and marginal revenue and the attempts made to find them mathematically.
  • #1
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Homework Statement



A monopolist faces demand y=96-4p and has total costs c=10y.
a) derive the marginal cost and marginal revenue functions.
b) what is the profit-maximizing output and price for this monopolist?
c) Suppose p=10 and MR=5, calculate the elasticit.

Any feedback would be greatly appreciated.

Homework Equations





The Attempt at a Solution

 
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  • #2


Do you know the definition of marginal cost and marginal revenue?
 
  • #3


I have an idea of what they mean, but I am having a hard time finding them for this problem.
 
  • #4


So what do they mean? Show us what attempts have you made to figure them out.
 
  • #5


What i did to find the marginal revenue was divide the derivative of the total revenue by the derivative of the quantity function. d(96p-4p^2)/d(96-4p)=96-4p/-4=-24+p. Thats what i got for the marginal revenue.

For the marginal cost, i divided the derivative of the cost function by the derivative of the quantity function. 10/-4 was the result i got for the marginal cost function.
 
  • #6


Can you state in words what marginal cost is and what marginal revenue is? I can't tell if you don't have a clear concept of what those quantities are or if you just don't know how to represent them mathematically.
 

What is elasticity and why is it important?

Elasticity is a measure of the responsiveness of a variable to a change in another variable. It is an important concept in economics and business, as it helps us understand how changes in price, income, or other factors impact the quantity demanded or supplied of a good or service.

What is the formula for calculating elasticity?

The general formula for calculating elasticity is (% change in quantity / % change in price). This gives us the percentage change in quantity demanded or supplied for a one percent change in price.

How is elasticity used to classify goods?

Goods can be classified as elastic or inelastic based on their elasticity. If a good has an elasticity greater than 1, it is considered elastic, meaning that a change in price will have a relatively large impact on the quantity demanded or supplied. If a good has an elasticity less than 1, it is considered inelastic, meaning that a change in price will have a relatively small impact on the quantity demanded or supplied.

What is the difference between price elasticity and income elasticity?

Price elasticity measures the responsiveness of quantity demanded or supplied to a change in price, while income elasticity measures the responsiveness of quantity demanded to a change in income. Both are important in understanding consumer behavior and market trends.

How can I use elasticity to make business decisions?

Elasticity can be used to make informed business decisions, such as setting prices, determining the impact of taxes or subsidies, and predicting changes in demand for a product. By understanding the elasticity of a good or service, businesses can adjust their strategies to maximize profits and stay competitive in the market.

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