Julia likes to consume two brands of jeans: jeans from the Gap (G) and jeans from...

Julia likes to consume two brands of jeans: jeans from the Gap (G) and jeans from J. Crew (J). She considers these goods to be substitutes and her utility function is:?(?,?)=?+4?. Julia’s birthday is this weekend and her (very generous) parents have given her $3000 to spend on jeans at the mall. In addition, Julia’s (very generous) Aunt Sally has sent her a birthday card with a gift certificate to the Gap worth $600.The price of jeans at the Gap is $30 and the price of jeans at J. Crew is $60.What is Julia’s optimal bundle? Show this solution graphically, putting G on the horizontal axis. As before, label the optimal consumption levels ?∗and ?∗, draw the indifference curve at the optimum (does not need to be exact but please make sure that you get the correct shape and the correct tangency), the budget line, and all axes and other relevant points).

Solutions

Expert Solution

The two goods are perfect substitutes

Max U(G,J)= G+4J subject to 30G+60J = 3600

60J= 3600-30G

or J= (3600/60) - (30/60)G

J= 60- 0.5J

Similarly, 30G= 3600-60J

G= 120-2J

Now, U= G+4J

4J= U-G

or J= U/4 - G/4

Therefore, Slope of the budget line is negative 1/4

Rahul Sunny answered 2 years ago

Next > < Previous

Related Solutions

A shop sells two competing brands of socks, Levis and Gap. Each pair of socks is...

A shop sells two competing brands of socks, Levis and Gap. Each pair of socks is obtained at a cost of 33 dollars per pair. The manager estimates that if he sells the Levis socks for xx dollars per pair and the Gap socks for yy dollars per pair, then consumers will buy 10−3x+y10−3x+y pairs of Levis socks and 1+3x−2y1+3x−2y pairs of Gap socks. How should the manager set the prices so that the profit will be maximized? Round your...

An individual likes to consume 2 goods X and Y . The utility function for this...

An individual likes to consume 2 goods X and Y . The utility function for this individual is U = X+0.5Y . What is the marginal utility of X and Y ? The individual has an income of $90. The price of X is $10 and the price of Y is $5. What is the optimal consumption bundle of this individual? Graph the individuals optimal bundle with the budget line and indierence curve. (answer: Infinitely many solutions). Do the same...

Utility Problem Set #5H Moe likes to visit a local establishment to consume pizza and beer....

Utility Problem Set #5H Moe likes to visit a local establishment to consume pizza and beer. He has $16 in his pocket and plans to spend it all tonight. When he arrives at this establishment tonight he see the regular price for a draft beer is $4 and a slice of pizza is also $2 per slice. On a napkin he sketches out the following information: Qty of Beer TU MU MUb/Pb Pizza slices TU MU MUs/Ps 1 100 1...

Marginal Propensity to consume is .68 when a recessionary gap of 200 Billion exist. Calculate the...

Marginal Propensity to consume is .68 when a recessionary gap of 200 Billion exist. Calculate the amount of government spending, ceteris paribus, necessary to remove the gap. Calculate the amount of a tax cut, ceteris paribus, necessary to remove the recessionary gap. Contrast the approach a supply side economist would use to remove the recessionary gap in question 3.

The Ruff Jeans Company produces two different types of jeans, Simple Life, and Fancy Life. The...

The Ruff Jeans Company produces two different types of jeans, Simple Life, and Fancy Life. The company sales budget estimates that 350,000 of the Simple Life jeans and 200,000 of the Fancy Life jeans will be sold during the current year. The production budget requires 353,500 units of Simple Life and 196,000 Fancy Life be manufactured. The Simple Life jeans require 3 yards of denim material, a zipper, and 25 yards of thread. The Fancy Life jeans require 4.5 yards...

The Ruff Jeans Company produces two different types of jeans, Simple Life, and Fancy Life. The...

1. Suppose Betty likes to consume cheese and biscuits, consuming 3 ounces of cheese(C) per every...

1. Suppose Betty likes to consume cheese and biscuits, consuming 3 ounces of cheese(C) per every 2 biscuits(B). What is the utility function that best illustrates Betty’s preferences? a) U(C, B) = min{ C 2 , B 3 } b) U(C, B) = min{ 2C 3 , B} c) U(C, B) = min{C, B 2 } d) U(C, B) = min{ C 2 , B} 2. A consumer buys food (F) and shelter (S). If the consumer’s income doubles and...

A consumer has budgeted a total of K100 to spend on two goods, X and Y. She likes to consume a unit of good X in combination with a unit of good Y.

A consumer has budgeted a total of K100 to spend on two goods, X and Y. She likes to consume a unit of good X in combination with a unit of good Y. Any unit of good X that she cannot consume in combination with a unit of good Y is useless. Similarly, any unit of good Y that she cannot consume in combination with good X is useless. If the price of a unit of good X is K5...

A person named Leslie lives in Urbana and likes to raise goats (G) for milk, grass...

A person named Leslie lives in Urbana and likes to raise goats (G) for milk, grass mowing, and company. Unfortunately, her neighbor named Lee finds the noise of the goats very annoying. The total welfare of each neighbor as a function of the number of goats that Leslie keeps is: Number of Goats 0 1 2 3 4 5 Welfare of Lee 140 100 60 40 20 0 Welfare of Leslie 5 20 30 40 50 60 a) At first,...

For Levi’s, there are two types of consumers: Spouses who buy jeans for themselves and their...

For Levi’s, there are two types of consumers: Spouses who buy jeans for themselves and their spouse, and single people. Spouses are willing to pay $100 for the first pair of jeans, $80 for the second pair, and $0 for any further pairs of jeans. Single people are willing to pay $120 for the first pair of jeans, and $0 for any further pairs of jeans. Assume that there 10 single people and 1 spouse who shop at Levi’s. Which...

Subjects