Given a utility function: U(q1, q2) = q1 + q 2^2 where q1 and q2 is...

Given a utility function: U(q1, q2) = q1 + q 2^2 where q1 and q2 is the consumption of good 1 and good 2 respectively. and the budget constraint: p1q1 + p2q2 = Y where p1 and p2 are prices of good 1 and good 2 respectively, Y is the consumer’s income a. Holding p2 and Y fixed, find the demand function for good 2. b. Holding p1 and p2 fixed, find the functional form of the Engel curve for good 2

Expert Solution

Rahul Sunny answered 2 years ago

Given a utility function: U(q1,q2)=q1 +βlnq2 where q1 and q2 is the consumption of good 1...

Given a utility function: U(q1,q2)=q1 +βlnq2 where q1 and q2 is the consumption of good 1 and good 2 respectively, β is a positive constant, and the budget constraint: p1q1 + p2q2 = Y where p1 and p2 are prices of good 1 and good 2 respectively, Y is the consumer’s income a. Holding p2 and Y fixed, find the demand function for good 2. b. Holding p1 and p2 fixed, find the functional form of the Engel curve for...

Suppose the utility function for goods q1 and q2 is given by U(q1, q2) = q1q2...

Suppose the utility function for goods q1 and q2 is given by U(q1, q2) = q1q2 + q2 6 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. 3 (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1, p2, U) 4 (d) Use the expenditure function...

1. Suppose the utility function for goods q1 and q2 is given by U(q1, q2) =...

1. Suppose the utility function for goods q1 and q2 is given by U(q1, q2) = q1q2 + q2 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1, p2, U) (d) Use the expenditure function calculated in part...

Suppose the utility function for goods q1 and q2 is given by U(q1,q2)=q1q2 +q2 (a) Calculate...

Suppose the utility function for goods q1 and q2 is given by U(q1,q2)=q1q2 +q2 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1, p2, U) (d) Use the expenditure function calculated in part (c) to compute the compensated...

1. Suppose the utility function for goods q1 and q2 is given by U(q1,q2) = q1q2...

1. Suppose the utility function for goods q1 and q2 is given by U(q1,q2) = q1q2 + q2 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1,p2, U) (d) Use the expenditure function calculated in part (c) to...

Carl enjoys Coffee (q1) and smoothie (q2) and the utility function is: U=q1^2 + q2^2 Suppose...

Carl enjoys Coffee (q1) and smoothie (q2) and the utility function is: U=q1^2 + q2^2 Suppose that Carl has $100 spend on coffee and smoothies and the price of a pitcher of smoothie is $10 and the price of a coffee jar is $4. e) Derive Carl’s optimal bundle. Draw the graph of the budget constraint and show the optimal bundle on the graph. Draw a free hand indifference curve. It is not necessary to use the given utility function...

Assume a consumer’s utility function is U = √q1 + 2√q2 and her total income is...

Assume a consumer’s utility function is U = √q1 + 2√q2 and her total income is $90. The price of both good 1 and good 2 is $1. (a) (5 points) What is the bundle that maximizes this consumer’s utility? What is the consumer’s utility level at that point? (b) (5 points) Suppose that the price of good 1 drops to $0.50. What is the new bundle that maximizes this consumer’s utility? What is the consumer’s utility at this point?...

Suppose the utility function for goods q1 and q2 is given byU(q1,q2)=q1q2 +q2 (a) Calculate the...

Suppose the utility function for goods q1 and q2 is given byU(q1,q2)=q1q2 +q2 (a) Calculate the uncompensated (Marshallian) demand functions for q1 and q2 (b) Describe how the uncompensated demand curves for q1 and q2 are shifted by changes in income (Y) or the price of the other good. (c) Calculate the expenditure function for q1 and q2 such that minimum expenditure = E(p1, p2, U) (d) Use the expenditure function calculated in part (c) to compute the compensated demand...

Utility function is U = 0.5 ln q1 + 0.5 ln q2 a) What is the...

Utility function is U = 0.5 ln q1 + 0.5 ln q2 a) What is the compensated demand function for q1? b) What is the uncompensated demand function for q1? c) What is the difference between uncompensated demand functions and compensated demand functions?

Given Barbara's estimated Cobb-Douglas utility function, U(q 1, q 2) = q 1^0.2 q 2^0.8, for...

Given Barbara's estimated Cobb-Douglas utility function, U(q 1, q 2) = q 1^0.2 q 2^0.8, for CDs, q 1, and DVDs, q 2, derive her Engel curve for movie DVDs. Illustrate in a figure. Let p be the price of DVDs, $1.00 be the price of CDs, and Y be income. Barbara's Engel curve for movie DVDs is Y= ? (Please provide answer) (Properly format your expression using the tools in the palette. Hover over tools to see keyboard...

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