Question

In: Economics

u(x1, x2) = min {x1/2, x2/3} if the price of good 1 is $7/unit, the price...

u(x1, x2) = min {x1/2, x2/3}

if the price of good 1 is $7/unit, the price of good 2 is $4/unit and income is 114..

What is this person's optimal consumption level for good 2?

Solutions

Expert Solution

u(x1, x2) = min{x1/2, x2/3}

At optimal consumption bundle, the condition is:

x1/2 = x2/3

3x1 = 2x2

x1 = (2/3)x2

The additional information provided is:

Px1 = 7

Px2 = 4

M = 114

The budget line is:

x1*Px1 + x2*Px2 = M

7x1 + 4x2 = 114

7(2/3)x2 + 4x2 = 114

(14/3)x2 + 4x2 = 114

(26/3)x2 = 114

x2 = 114*3/26

x2 = 13.15385

Hence, the person's optimal consumption level for good 2 is 13.15385

Hence, the correct answer is 13.15385


Related Solutions

Burt’s utility function is U(x1, x2)= min{x1,x2}. Suppose the price of good 1 is p1, the...
Burt’s utility function is U(x1, x2)= min{x1,x2}. Suppose the price of good 1 is p1, the price of good p2, the income is y. a. Derive ordinary demand functions. b. Draw indifference curves and budget line for the case when the price of good 1 is 10, the price of good 2 is 20, the income is 1200. c. Find the optimal consumption bundle.
Question 1) Charlie's utility is U(x1, x2) = 4x^1/2+x2. If the price of nuts (good 1)...
Question 1) Charlie's utility is U(x1, x2) = 4x^1/2+x2. If the price of nuts (good 1) is $1, the price of berries (good 2) is $4, and his income is $132, how many units of nuts will Charlie choose? A. 128 B. 32 C. 67 D. 64 E. 17 Question 2) Kyle's utility function is U(A, B) = AB, where A and B are the numbers of apples and bananas, respectively, that he consumes. If Kyle is consuming 15 apples...
Amy has utility function u (x1, x2) = min { 2*(x1)^2*x2, x1*(x2)^2 }. Derive Amy's demand...
Amy has utility function u (x1, x2) = min { 2*(x1)^2*x2, x1*(x2)^2 }. Derive Amy's demand function for x1 and x2. For what values (if any) of m, p1, and p2 are the goods gross complements or gross substitutes of each other?
A consumer has a utility function of U = min{4x1, x2}. The price of good 1...
A consumer has a utility function of U = min{4x1, x2}. The price of good 1 is $8 and the price of good 2 is $5. The consumer has $112 in income. How many units of each good does she consume? x1 = 8, x2 = 8 x1 = 16, x2 = 4 x1 = 12, x2 = 8 x1 = 4, x2 = 16 None of the above Consider the inter-temporal model of consumption studied in class, with two...
Pat’s preference is given by u(x1, x2) = min {x1, x2}. Currently, prices are p =...
Pat’s preference is given by u(x1, x2) = min {x1, x2}. Currently, prices are p = (p1, p2) and Pat’s income is I. Is he better off if the price of good one is halved so that p = (p1/2 ,p2), or if his income is doubled to 2I?
1/Laura's preferences over commodities x1 and x2 can be represented by U(x1,x2)=min{3x1, x2}. She maximizes her...
1/Laura's preferences over commodities x1 and x2 can be represented by U(x1,x2)=min{3x1, x2}. She maximizes her utility subject to her budget constraint. Suppose there is an increase in p1.   There is an income effect but not a substitution effect of this price change. There are both income and substitution effects of this price change. There is a substitution effect but not an income effect of this price change. It is unclear whether the consumer will buy more or less x1...
Sara’s utility function is u(x1, x2) = (x1 + 2)(x2 + 1). a. Write an equation...
Sara’s utility function is u(x1, x2) = (x1 + 2)(x2 + 1). a. Write an equation for Sara’s indifference curve that goes through the point (2,8). b. Suppose that the price of each good is 1 and that Clara has an income of 11. Draw her budget line. Can Sara achieve a utility of 36 with this budget? Why or why not? c. Evaluate the marginal rate of substitution MRS at (x1, x2) = (1, 5). Provide an economic interpretation...
Nigella has the following utility function over two goods (x1, x2): U(x1, x2) = min {0.5x1,...
Nigella has the following utility function over two goods (x1, x2): U(x1, x2) = min {0.5x1, 3x2} a.What is the Nigella’s utility level if x1= 20 andx2= 3? b.Suppose P1= 1 andP2= 3(where P1is the price x1andP2is theprice of x2) and Nigella has an income of 18. What is Nigella’s budget constraint? Illustrate it in a graph c.Solve for the Nigella’s utility maximizing bundle of x1andx2.
Let U=min(X1, X2), the minimum of two independent exponentials. What is the distribution of U?
Let U=min(X1, X2), the minimum of two independent exponentials. What is the distribution of U?
Sophie's utility function is given as U = 2(x1)^(1/2) + 8(x2) where x1 and x2 represent...
Sophie's utility function is given as U = 2(x1)^(1/2) + 8(x2) where x1 and x2 represent the two goods Sophie consumes. Sophie's income is $3400 and the prices are given as x1 = $2 and x2 = $160 a) derive & represent in two separate diagrams the demand for x1 and x2 ( for any income and prices) b) If Sophie's income is increased to $6600, what is the income effect on x1? Is x2 a normal good? Justify your...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT