How to Solve for Equations of Demand and Supply with Given Price Elasticity?

• MHB
• abigmole
In summary, the market for bananas in Small-town, Malaysia has a current price of $0.10 per pound and sells 1 million pounds per year. The price elasticity of demand is -5 and the short run price elasticity of supply is 0.05. Assuming linear demand and supply curves, the equations for demand and supply can be represented by P=aQ_d+b and P=cQ_s+d, where a, b, c, and d are constants. With the given elasticities and equilibrium point, the values of a, b, c, and d can be solved for to determine the specific equations for demand and supply in this market. abigmole The current price in the market for bananas is$0.10 per pound. At
this price, 1 million pounds are sold per year in Small-town, Malaysia.
Suppose that the price elasticity of demand is -5 and the short run
price elasticity of supply is 0.05. Solve for the equations of demand
and supply, assuming that demand and supply are linear.Hi, was given this question to do and I'm lost! Anyone knows how to solve this?

Would greatly appreciate any form of help! Thanks!

abigmole said:
The current price in the market for bananas is \$0.10 per pound. At
this price, 1 million pounds are sold per year in Small-town, Malaysia.
Suppose that the price elasticity of demand is -5 and the short run
price elasticity of supply is 0.05. Solve for the equations of demand
and supply, assuming that demand and supply are linear.Hi, was given this question to do and I'm lost! Anyone knows how to solve this?

Would greatly appreciate any form of help! Thanks!

Hi abigmole, :)

Let $$P$$ be the price, $$Q_{d}$$ be the quantity demanded and $$Q_{s}$$ be the quantity supplied. Since the demand and supply curves are linear those curves could be represented by,

$P=aQ_{d}+b\mbox{ and }P=cQ_{s}+d$

The elasticity of demand and supply are defined by,

$E_{d}=\frac{P}{Q_{d}}\frac{dQ_{d}}{dP}\mbox{ and }E_{s}=\frac{P}{Q_{s}}\frac{dQ_{s}}{dP}$

$\therefore E_{d}=\frac{1}{a}\frac{P}{Q_{d}}\mbox{ and }E_{s}=\frac{1}{c}\frac{P}{Q_{s}}$

It is given that $$E_{d}=-5\mbox{ and }E_{s}=0.05$$. Since this market is in a economic equilibrium situation, $\frac{P}{Q_{d}}=\frac{P}{Q_{s}}=\frac{0.1\times 10^{6}}{10^{6}}=0.1$

I hope you can do the rest yourself. You have to find the values of $$a$$ and $$b$$. Then consider the equilibrium point so that you can solve for $$c$$ and $$d$$ in the supply and demand curves.

Kind Regards,
Sudharaka.

1. What is managerial economics?

Managerial economics is the application of economic theory and methodology to managerial decision-making. It involves the use of economic principles and tools to analyze and solve business problems and make informed decisions about production, pricing, resource allocation, and other managerial issues.

2. What are some key topics in managerial economics?

Some key topics in managerial economics include demand analysis, production and cost analysis, pricing strategies, market structure and competition, risk and uncertainty, and decision-making under different market conditions.

3. What is the role of quantitative methods in managerial economics?

Quantitative methods, such as statistical analysis, mathematical models, and optimization techniques, are used in managerial economics to analyze data, make predictions, and support decision-making. These methods help managers to evaluate the potential outcomes of different courses of action and choose the most optimal solution.

4. How does managerial economics differ from traditional economics?

Managerial economics focuses on applying economic principles and tools to practical business problems, while traditional economics is concerned with studying the behavior of markets and economies as a whole. Managerial economics also places more emphasis on decision-making and uses more quantitative methods than traditional economics.

5. What are the benefits of studying managerial economics?

Studying managerial economics can provide insights into the economic factors that affect business decision-making, help managers to make more informed and strategic decisions, and enable businesses to improve their performance and profitability. It also allows individuals to develop critical thinking and problem-solving skills that are valuable in many industries and careers.

• General Math
Replies
1
Views
3K
• General Math
Replies
1
Views
2K
• Biology and Chemistry Homework Help
Replies
1
Views
3K
• Precalculus Mathematics Homework Help
Replies
6
Views
3K
• Linear and Abstract Algebra
Replies
1
Views
1K
• General Discussion
Replies
2
Views
6K
• General Discussion
Replies
7
Views
7K
• General Math
Replies
1
Views
6K
• Precalculus Mathematics Homework Help
Replies
17
Views
21K
• General Discussion
Replies
22
Views
30K