Question

In: Economics

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 shortcuts.​E.g., a subscript can be created with the​ _ character.)

Solutions

Expert Solution

The utility function is given to be , and the budget constraint would be or . The marginal utility would be or or and or or . The optimal combination of goods would be where or or or or or .

Putting this in budget constraint, we have or or or . This is the Marshallian demand for q2, ie DVDs. Now, the Engel curve is the combination of income and quantity demanded for different incomes with a constant price. Hence, the Engel curve would be or .

The graph is as below.

Engel curve with different prices is shown in the graph.

Rahul Sunny answered 1 year ago
Next > < Previous

Related Solutions

Assume a Cobb-douglas utility function of 2 goods x and y given by U = x...
Assume a Cobb-douglas utility function of 2 goods x and y given by U = x 0.5y 0.5 and an initial income I of 100. Let initial price be px = 4 and py = 1. Now vary the price of x from 1 to 7 in steps of 1. So you have 7 prices for x. px = {1, 2, 3, 4, 5, 6, 7} For each of these px, py REMAINS the SAME at 1. In the excel...
Katherine has an estimated Cobb-Douglas utility function of U = q1^0.25q2^0.75 for food, q1, and housing,...
Katherine has an estimated Cobb-Douglas utility function of U = q1^0.25q2^0.75 for food, q1, and housing, q2. The price for food is arbitrarily set at $1 per unit and the average monthly rent near the University of Chicago , p2, is a dollar fifty per square foot. Caroline, like the average University of Chicago student spend $750 on food and housing per month.      (a) Using calculus, solve for Katherine's optimal quantities of housing and food. Provide the marginal utility...
III. A common utility function used to illustrate economic examples is the Cobb-Douglas function where U(X,...
III. A common utility function used to illustrate economic examples is the Cobb-Douglas function where U(X, Y)= XαYβ, where α and β are decimal exponents that sum to 1.0 (for example, 0.3 and 0.7). a. For this utility function, the MRS is given by MRS = MUX=MUY = αY/βX. Use this fact together with the utility-maximizing condition (and that α+ β =1) to show that this person will spend the fraction of his other income on good X and the...
Solve the optimization problem for a Cobb-Douglas utility function with three goods: U(x1, x2, x3) =...
Solve the optimization problem for a Cobb-Douglas utility function with three goods: U(x1, x2, x3) = x c 1x d 2x f 3 , where c, d, f > 0.
Substitution and Income Effect (Calculation) Suppose that the consumer's utility function is Cobb-Douglas U(x; y) =...
Substitution and Income Effect (Calculation) Suppose that the consumer's utility function is Cobb-Douglas U(x; y) = xy. She initially has $100 income and the prices that she faces are px = py = $2: a. Compute her demands for x and y. b. Now suppose that px decreases to $1 while py remains unchanged. Compute her new demands for x and y. c. What is the total (price) effect on the consumption of x? d. What is the substitution effect...
Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l...
Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l 1−α (a) Determine the relation between α and the marginal product of k and l. For what values of α is the marginal product for each input: (i) increasing, (ii) constant, and, (iii) decreasing. (b) Show that the marginal rate of technical substitution (MRTS) is equal to α 1 − α l k . For what values of α is MRTS decreasing in k?...
Consider the following Cobb-Douglas utility function: U(x,y) = 10 + 22xy, where x denotes the quantity...
Consider the following Cobb-Douglas utility function: U(x,y) = 10 + 22xy, where x denotes the quantity of apples and y denotes the quantity of pears. Income is m; the price for one apple is px and the price for one pear is py. b) By applying the Lagrangian method, derive the optimal demands for apples and pears. c) What is the impact of an increase in the price of apples on the optimal demand for pears? What is the impact...
A consumer has the following utility function ?(?, ?) = ?^0.2 ?^0.8 and Income=$800, Px =2,...
A consumer has the following utility function ?(?, ?) = ?^0.2 ?^0.8 and Income=$800, Px =2, Py =4 Note that ??? = 0.20 (y/x)^0.80 and ??? = 0.8 (x/y)^0.20 a) Find the initial equilibrium (x, y, U) b) Assume that Px increases by 20% and Py decreases by the same percentage. Find the new equilibrium (x, y, U). c) Find the income and substitution effects of the above price changes.
Marvin has a​ Cobb-Douglas utility​ function, U=q10.5q20.5 his income is Y=​$900​, and initially he faces prices...
Marvin has a​ Cobb-Douglas utility​ function, U=q10.5q20.5 his income is Y=​$900​, and initially he faces prices of p1=​$44 and p2=​$2. If p1 increases from $4 to $5​, what are his compensating variation​ (CV), change in consumer surplus (Δ​CS), and equivalent variation​ (EV)? ​Marvin's compensating variation​ (CV) is ​$nothing. ​(Enter your response rounded to two decimal places and include a minus sign if​ necessary.) ​Marvin's change in consumer surplus ​(Upper DeltaΔ​CS) is ​$nothing. ​(Enter your response rounded to two decimal places...
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...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT