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As is true for all of us, Lisa has many weekly expenses. What might be less common is the fact that Lisa likes to buy broccoli (qB) and carrots (qc) for all the money left after her required expenses. Lisa's utility function is standard Cobb-Douglas, U(qB, qc) = 98³9c7. ,0.3 1. Before we specify what Lisa's "disposable" income is and what the price of a head of broccoli and a small bag of carrots are, please derive expressions for the demand for broccoli and carrots (that is, derive demand for the two goods as functions of Y, PB, and pc). In other words, find the following demand functions: qB = f(Y, PB, Pc) and qc = f(Y,PB, PC). Use the substitution method for one good and the short-cut for the other good. 2. Using the demand functions that you derived in question 1, please find Lisa's optimal consumption of broccoli and carrots (the quantity demanded, if you will) if Y = 10, 0.60 and 1.00

As is true for all of us, Lisa has many weekly expenses. What might be less common is the fact that Lisa likes to buy broccoli (qB) and carrots (qc) for all the money left after her required expenses. Lisa's utility function is standard Cobb-Douglas, U(qB, qc) = 98³9c7. ,0.3 1. Before we specify what Lisa's "disposable" income is and what the price of a head of broccoli and a small bag of carrots are, please derive expressions for the demand for broccoli and carrots (that is, derive demand for the two goods as functions of Y, PB, and pc). In other words, find the following demand functions: qB = f(Y, PB, Pc) and qc = f(Y,PB, PC). Use the substitution method for one good and the short-cut for the other good. 2. Using the demand functions that you derived in question 1, please find Lisa's optimal consumption of broccoli and carrots (the quantity demanded, if you will) if Y = 10, 0.60 and 1.00

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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As is true for all of us, Lisa has many weekly expenses. What might be less common is the fact that Lisa likes to buy broccoli (\(q_B\)) and carrots (\(q_C\)) for all the money left after her required expenses. Lisa’s utility function is standard Cobb-Douglas, \(U(q_B, q_C) = q_B^{0.3} q_C^{0.7}\). 1. **Before we specify what Lisa’s “disposable” income is and what the price of a head of broccoli and a small bag of carrots are**, please derive expressions for the demand for broccoli and carrots (that is, derive demand for the two goods as functions of \(Y, p_B,\) and \(p_C\)). In other words, find the following demand functions: \(q_B = f(Y, p_B, p_C)\) and \(q_C = f(Y, p_B, p_C)\). - *Use the substitution method for one good and the short-cut for the other good.* 2. **Using the demand functions that you derived in question 1**, please find Lisa’s optimal consumption of broccoli and carrots (the quantity demanded, if you will) if \(Y = 10, p_B = 0.60,\) and \(p_C = 1.00\). 3. **Draw the (inverse) demand curve for broccoli and indicate Lisa’s consumption of broccoli.** To do this, you need to pick at least one other price of broccoli, I suggest choosing \(p_B = 0.30\). - Next assume that Lisa’s weekly required expenses are reduced so that she now is able to spend 20 (\(Y = 20\)) on broccoli and carrots. 4. **In your previous demand diagram, please draw a new demand curve and describe what happened.** That is, find the new demand curve for the two prices of broccoli, \(p_B = 0.60\) and \(p_B = 0.30\), but with a new income (budget) level. - *Use the short-cut for this question.* 5. **Finally, derive Lisa’s Engel curve for broccoli.** For this question, suppose that the price of broccoli is \(p_B = 0.60\). - *NOTE: The Engel curve shows a relationship between quantity demanded of a single good and income, holding prices constant. To draw the
Transcribed Image Text:As is true for all of us, Lisa has many weekly expenses. What might be less common is the fact that Lisa likes to buy broccoli (\(q_B\)) and carrots (\(q_C\)) for all the money left after her required expenses. Lisa’s utility function is standard Cobb-Douglas, \(U(q_B, q_C) = q_B^{0.3} q_C^{0.7}\). 1. **Before we specify what Lisa’s “disposable” income is and what the price of a head of broccoli and a small bag of carrots are**, please derive expressions for the demand for broccoli and carrots (that is, derive demand for the two goods as functions of \(Y, p_B,\) and \(p_C\)). In other words, find the following demand functions: \(q_B = f(Y, p_B, p_C)\) and \(q_C = f(Y, p_B, p_C)\). - *Use the substitution method for one good and the short-cut for the other good.* 2. **Using the demand functions that you derived in question 1**, please find Lisa’s optimal consumption of broccoli and carrots (the quantity demanded, if you will) if \(Y = 10, p_B = 0.60,\) and \(p_C = 1.00\). 3. **Draw the (inverse) demand curve for broccoli and indicate Lisa’s consumption of broccoli.** To do this, you need to pick at least one other price of broccoli, I suggest choosing \(p_B = 0.30\). - Next assume that Lisa’s weekly required expenses are reduced so that she now is able to spend 20 (\(Y = 20\)) on broccoli and carrots. 4. **In your previous demand diagram, please draw a new demand curve and describe what happened.** That is, find the new demand curve for the two prices of broccoli, \(p_B = 0.60\) and \(p_B = 0.30\), but with a new income (budget) level. - *Use the short-cut for this question.* 5. **Finally, derive Lisa’s Engel curve for broccoli.** For this question, suppose that the price of broccoli is \(p_B = 0.60\). - *NOTE: The Engel curve shows a relationship between quantity demanded of a single good and income, holding prices constant. To draw the
Expert Solution
Step 1: Describe the problem

Lisa has two goods available to consume : Broccoli (qb) & Carrots (qc ).

Utility function : U(qb , qc ) = qb0.3qc0.7

Price of Broccoli : Pb

Price of Carrots : Pc 

Income = I 




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