1. Suppose you own a lemonade stand and sell delicious lemonade in your neighborhood. Ittakes 3 lemons, L2 0, to make a glass of lemonade, Q2 0. Each lemon costs c> 0 and you sell your lemonade for pi > 0. Furthermore, assume that you must pay your neighbor Karen a bribe of F > 0, as you do not have a license to operate the lemonade stand and she will call the police otherwise. a. What is the production function of the lemonade stand? b. What is the profit function of the lemonade stand? c. What is profit maximizing amount of lemonade to sell?
1. Suppose you own a lemonade stand and sell delicious lemonade in your neighborhood. Ittakes 3 lemons, L2 0, to make a glass of lemonade, Q2 0. Each lemon costs c> 0 and you sell your lemonade for pi > 0. Furthermore, assume that you must pay your neighbor Karen a bribe of F > 0, as you do not have a license to operate the lemonade stand and she will call the police otherwise. a. What is the production function of the lemonade stand? b. What is the profit function of the lemonade stand? c. What is profit maximizing amount of lemonade to sell?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:### Lemonade Stand Economics
1. **Scenario**: You operate a lemonade stand in your neighborhood, requiring 3 lemons (denoted as \(L \geq 0\)) to produce one glass of lemonade, with a production quantity \(Q \geq 0\). Each lemon costs \(c_L > 0\) and you sell your lemonade for a price \(p_L > 0\). Additionally, due to lack of a permit, you must pay your neighbor Karen a bribe of \(F > 0\) to avoid being reported to the authorities.
a. **Production Function**: What is the function that describes the relationship between the inputs (lemons) and the output (lemonade)?
b. **Profit Function**: What is the equation that determines the profit of the lemonade stand considering costs and revenues?
c. **Profit Maximization**: How much lemonade should be sold to achieve maximum profit?
### Explanation
In this scenario, students will explore elements of production and profit optimization. The exercise is designed to help understand concepts such as production functions, cost analysis, and profit maximization within a small business context.
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