Question

In: Economics

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 good 2.

Solutions

Expert Solution


Related Solutions

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...
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...
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...
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...
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...
Amy’s utility function is U = √ C, where C is consumption and is given by...
Amy’s utility function is U = √ C, where C is consumption and is given by C = Income − Expenses. Amy’s income is $10,000 and there is a 5% chance that she will get sick, which would cost $3,600 in medical expenses. (a) (5 points) What is Amy’s expected utility if she doesn’t have insurance? (b) (5 points) What is the actuarially fair premium for a full-coverage insurance plan? What is the actuarially fair premium for an insurance plan...
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...
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...
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?
If the Utility function for the consumption of milk and bananas is given by U =qm0.6qb0.4...
If the Utility function for the consumption of milk and bananas is given by U =qm0.6qb0.4 and the price of milk is $12 and price of banana is $8, find Marginal Utility from consuming milk Marginal Utility from consuming banana Will the consumer be maximizing satisfaction when he/she consumes one unit each of milk and bananas? If not, what should he/she consume next to increase satisfaction? Will the consumer be maximizing satisfaction when he/she consumes two units of milk and...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT