Verify/Prove whether X,Y are gross or net substitutes or complements. U(x,y)=min{ax,by}
Homework Answers
X,Y are complements when utility function is U(x,y)=min{ax,by}.
Complements are the goods which are consumed together in fixed proportion to satisfy the demand of the individual. However, the fixed proportion must not be necessarily 1:1. General form of expressing it is min{ax,by} where a and b are constants and indicate the proportion in which goods are consumed .
The above pictures show the derivation of demand of Complements and the graphical representation of it. (L shaped curve )
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Verify/Prove whether X,Y are gross or net substitutes or
complements.
U(x,y)=min{ax,by}
and X...,X, U[0,1], Given X...., X, are iid Y, is defined as Yn = min(x1,x2,...,x,). a.s. Prove that in Y, probabilit →...
and X...,X, U[0,1], Given X...., X, are iid Y, is defined as Yn = min(x1,x2,...,x,). a.s. Prove that in Y, probabilit → = 0 and Y. →=0
1) u(x,y)= 2min(x, 2y),after finding the demand function for x and y, are x and y...
1) u(x,y)= 2min(x, 2y),after finding the demand function for x and y, are x and y normal good? Are they substitutes and complements?
1 Substitutes and complements Consider the quasilinear utility function U(x) log (minfxi, ^2]) + over R....
1 Substitutes and complements Consider the quasilinear utility function U(x) log (minfxi, ^2]) + over R. Suppose the agent's wealth w is large enough that good 3 is demanded in non-zero quantities. Do not normalize the price of good 3 for this problem 1. Find the agent's Hicksian demand for each good. (Hint: first use the fact that goods 1 and 2 are optimally demanded in the same quantity. Then use the fact that bang for the buck for the...
2. Consider a consumer with the utility function ility function U(x, y)= min{3x, 5 y} that...
2. Consider a consumer with the utility function ility function U(x, y)= min{3x, 5 y} that is ,J)= min (3x, that is, the two goods are perfect complements in ratio 3:5. The prices of the two goods are andy , and the consumer's income is $220. Determine the optimum consumption basket.
Prove the following statements • corr(ax,y) = corr(x,y) • show that if x,y and z are...
Prove the following statements
• corr(ax,y) = corr(x,y)
• show that if x,y and z are independent. Show what happened
to:
cov(x+y,x+z)= ?
• assume x and y are not independent:
cov(ax + b, y)= ?
70 tre la Car
How to prove that: Cov(aX, aY) = a^2Cov(X,Y)
How to prove that: Cov(aX, aY) = a^2Cov(X,Y)
(20 points) Amy has utility function u(x1, x2) = min{2x12x2, x1x22}. De- rive Amy’s demand function...
(20 points) Amy has utility function u(x1, x2) = min{2x12x2, x1x22}. De- rive 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?
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)=...
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)= min[3x,2y]. Furthermore, suppose that she faces a standard linear budget constraint, with income denoted by m and prices denoted by px and p,, respectively. a) Derive the demand functions for x and y. b) How does demand for the two goods depend on the prices, p, and p, ? Explain.
For constants a and b, X and Y are random variables. Please prove that, var(aX +...
For constants a and b, X and Y are random variables. Please prove that, var(aX + bY ) = a 2 var(X) + b 2 var(Y ) + 2abcov(X, Y ) If X and Y are uncorrelated, what will be the results?
how do i solve these questions? andich aenet bs 6. If we have two goods X and Y which are net substitutes, a rise i...
how do i solve these questions?
andich aenet bs 6. If we have two goods X and Y which are net substitutes, a rise in Pr must necessarily a. reduce spending on X b. increase spending in Y. c. reduce spending in Y. d. uncertain from information given. With only two goods, X and Y, İEX and Y are gross substitutes, a rise in Pr must necessarily a. increase spending in X. b. reduce spending in X increase spending in...
and X...,X, U[0,1], Given X...., X, are iid Y, is defined as Yn = min(x1,x2,...,x,). a.s. Prove that in Y, probabilit → = 0 and Y. →=0
1 Substitutes and complements Consider the quasilinear utility function U(x) log (minfxi, ^2]) + over R. Suppose the agent's wealth w is large enough that good 3 is demanded in non-zero quantities. Do not normalize the price of good 3 for this problem 1. Find the agent's Hicksian demand for each good. (Hint: first use the fact that goods 1 and 2 are optimally demanded in the same quantity. Then use the fact that bang for the buck for the...
2. Consider a consumer with the utility function ility function U(x, y)= min{3x, 5 y} that is ,J)= min (3x, that is, the two goods are perfect complements in ratio 3:5. The prices of the two goods are andy , and the consumer's income is $220. Determine the optimum consumption basket.
Prove the following statements
• corr(ax,y) = corr(x,y)
• show that if x,y and z are independent. Show what happened
to:
cov(x+y,x+z)= ?
• assume x and y are not independent:
cov(ax + b, y)= ?
70 tre la Car
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)= min[3x,2y]. Furthermore, suppose that she faces a standard linear budget constraint, with income denoted by m and prices denoted by px and p,, respectively. a) Derive the demand functions for x and y. b) How does demand for the two goods depend on the prices, p, and p, ? Explain.
how do i solve these questions?
andich aenet bs 6. If we have two goods X and Y which are net substitutes, a rise in Pr must necessarily a. reduce spending on X b. increase spending in Y. c. reduce spending in Y. d. uncertain from information given. With only two goods, X and Y, İEX and Y are gross substitutes, a rise in Pr must necessarily a. increase spending in X. b. reduce spending in X increase spending in...
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