Question

Consider the utility function U(x1,x2) = ln(x1) +x2. Demand for good 1 is: •x∗1=p2p1 if m≥p2...

Consider the utility function U(x1,x2) = ln(x1) +x2. Demand for good 1 is: •x∗1=p2p1 if m≥p2 •x∗1=mp1 if m < p2 Demand for good 2 is: •x∗2=mp2−1 if m≥p2 •x∗2= 0 if m < p2 (a) Is good 1 Ordinary or Giffen? Draw the demand curve and solve for the inverse demand curve. (b) Is good 2 Ordinary or Giffen? Draw the demand curve and solve for the inverse demand curve. (c) Is good 1 Normal or Inferior? Derive and draw the Engel curve. (d) Is good 2 Normal or Inferior? Derive and draw the Engel curve. (e) Draw the income offer curve. (f) Is good 1 a gross substitute/complement for good 2? (g) Is good 2 a gross substitute/complement for good 1?

Homework Answers

Answer #1

f)

Two goods are gross substitutes if an increase in the price of one good increases demand for other. That is for two goods x and y

Two goods are gross complements if an increase in the price of one good decreases the demand for other. That is for two goods x and y

The demand for good 1

Therefore,

Then good 1 and 2 are gross substitutes.

g)

The demand for good 2 does not depend on the price of good 1. Then good 2 is neither substitutes nor compliment of good 1.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider a consumer who consumes two goods and has utility function u(x1,x2)=x2 +√x1. The price of...
Consider a consumer who consumes two goods and has utility function u(x1,x2)=x2 +√x1. The price of good 2 is 1, the price of good 1 is p, and income is m. (1) Show that a) both goods are normal, b) good 1 is an ordinary good, c) good 2 is a gross substitute for good 1.
The utility function is given by u (x1,x2) = x1^0.5 + x2^0.5 1) Find the marginal...
The utility function is given by u (x1,x2) = x1^0.5 + x2^0.5 1) Find the marginal rate of substitution (MRSx1,x2 ) 2) Derive the demand functions x1(p1,p2,m) and x2(p1, p2,m) by using the method of Lagrange.
The utility function is given by u (x1, x2) = x1^0.5+x2^0.5 1) Find the marginal rate...
The utility function is given by u (x1, x2) = x1^0.5+x2^0.5 1) Find the marginal rate of substitution (MRSx1,x2 ) 2) Derive the demand functions x1(p1, p2, m) and x2(p1,p2, m) by using the method of Lagrange.
A consumer’s preferences over two goods (x1,x2) are represented by the utility function ux1,x2=5x1+2x2. The income...
A consumer’s preferences over two goods (x1,x2) are represented by the utility function ux1,x2=5x1+2x2. The income he allocates for the consumption of these two goods is m. The prices of the two goods are p1 and p2, respectively. Determine the monotonicity and convexity of these preferences and briefly define what they mean. Interpret the marginal rate of substitution (MRS(x1,x2)) between the two goods for this consumer.   For any p1, p2, and m, calculate the Marshallian demand functions of x1 and...
Consider utility function u(x1,x2) =1/4x12 +1/9x22. Suppose the prices of good 1 and good 2 are...
Consider utility function u(x1,x2) =1/4x12 +1/9x22. Suppose the prices of good 1 and good 2 are p1 andp2, and income is m. Do bundles (2, 9) and (4, radical54) lie on the same indifference curve? Evaluate the marginal rate of substitution at (x1,x2) = (8, 9). Does this utility function represent convexpreferences? Would bundle (x1,x2) satisfying (1) MU1/MU2 =p1/p2 and (2) p1x1 + p2x2 =m be an optimal choice? (hint: what does an indifference curve look like?)
Consider a two good economy. A consumer has a utility function u(x1, x2) = exp (x1x2)....
Consider a two good economy. A consumer has a utility function u(x1, x2) = exp (x1x2). Let p = p1 and x = x1. (1) Compute the consumer's individual demand function of good 1 d(p). (2) Compute the price elasticity of d(p). Compute the income elasticity of d(p). Is good 1 an inferior good, a normal good or neither? Explain. (3) Suppose that we do not know the consumer's utility function but we know that the income elasticity of his...
Qin has the utility function U(x1, x2) = x1 + x1x2, where x1 is her consumption...
Qin has the utility function U(x1, x2) = x1 + x1x2, where x1 is her consumption of good 1 and x2 is her consumption of good 2. The price of good 1 is p1, the price of good 2 is p2, and her income is M. Setting the marginal rate of substitution equal to the price ratio yields this equation: p1/p2 = (1+x2)/(A+x1) where A is a number. What is A? Suppose p1 = 11, p2 = 3 and M...
Consider the following Constant Elasticity of Substitution utility function U(x1,x2) = x1^p+x2^p)^1/p                         &nbs
Consider the following Constant Elasticity of Substitution utility function U(x1,x2) = x1^p+x2^p)^1/p                                                                                                                                           a. Show that the above utility function corresponds to (hint:use the MRS between good 1 and good 2. The ->refers to the concept of limits.                  1. The perfect substitute utility function at p=1 2. The Cobb-Douglas utility function as p -->0 3. The Leontiff (of min(x1,x2) as p--> -infinity b. For infinity<p<1, a given level of income I and prices p1 and p2. 1. Find the marshallian...
How do you solve a utility problem that yields demand function for good x and good...
How do you solve a utility problem that yields demand function for good x and good y we have three goods,x1,X2,x3 income ,M and prices ,P1,p2,p3 and utility function U=U(X1,X2,x3)=3logX2+3logX2+2logx3
1. Using the following utility function, U(x1,x2) = x1x2+x1+2x2+2 Find the demand functions for both x1...
1. Using the following utility function, U(x1,x2) = x1x2+x1+2x2+2 Find the demand functions for both x1 and x2 (as functions of p1, p2, and m). Thank you!
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT