Q1. Suppose consumer consumes two goods, X and Y. The price of X
is P x , price of Y is P Y
and the consumer income is m.
a. Derive and interpret the budget constraint and its slope.
b. If slope is -3, how will you interpret it?
c. Suppose a government wants to discourage the excessive
consumption of X and
decides to impose a tax t 1 if someone consume more than X 1 but
less than X 2 and
imposes a higher tax t 2 if consumption exceeds X 2 . However
consumption of X is not
allowed to exceed the level of X 3 . Derive budget constraint and
explain with logic.
(Note: X 1 < X 2 < X 3 and t 1 < t 2 )
Q2: a. Derive indifference curve in case if both the commodities are “bad”. Explain your
answer logically?
b. What happens to the shapes of indifference curve if (i) a
consumer’s preferences
are not “Transitive”? (ii) If an assumption of “No-satiation” is
violated?
c. Explain the meaning of MRS. What is the meaning of MRS of good 1
for 2 is -
2.5?
Q3: Consider a Cobb-Douglas Utility Function
a. Find marginal utility of Y. Does marginal utility of depend on
the level of
consumption of X? how do you know? Explain
b. Find slope of the indifference curve.
c. Find MRS and draw the indifference curve for above function.
Q1. Suppose consumer consumes two goods, X and Y. The price of X is P x...
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4) Denote the price of good X by Px, price of good Y by Py and the income of the consumer by I. a) (2 points) Write down the budget constraint for the individual. b) (4 points) Derive the marginal utilities of X and Y. c) (3 points) Derive the expression for the marginal rate of substitution of X for Y. Write down the tangency...
1. Price of x is 12 and price of y is 8. Answer the following questions for a consumer who earns $600 and whose preference can be represented with the utility functions U(x,y) x0.4y0.6 = a) Write down the utility maximization problem. (2 points) b) Does the utility function represent convex preference? Explain. (2 points) c) Write down the budget constraint. What is the slope of the budget line? (2 points) d) What is the slope of the indifference curve...
A consumer buys only two goods, X and Y. a. If the MRS between X and Y is 4 and the marginal utility of X is 20, what is the marginal utility of Y? b. If the MRS between X and Y is 3 and the marginal utility of Y is 6, what is the marginal utility of X? c. If a consumer moves downward along an indifference curve, what happens to the marginal utilities of X and Y? What...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first...
4. A consumer has income I = 120. She consumes the goods V (Veggies) and M (Meat), which have prices Py = 6 and PM = 4 respectively. (a) Use the above information and plug it into the budget re- striction: PV V + PMM = I. Illustrate it in a figure, with V on the horizontal axis. How does the budget line change if the price of M falls so that PM = 2? Show in the figure. (b)...
Q2: a. Derive indifference curve in case if both the commodities are “bad”. Explain your b. answer logically? What happens to the shapes of indifference curve if (i) a consumer's preferences are not “Transitive”? (ii) If an assumption of "No-satiation” is violated? c. Explain the meaning of MRS. What is the meaning of MRS of good 1 for 2 is - 2.5?
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) = xłyż. a. Graph the indifference curve for U = 10. b. If x = 5, what must y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. Derive a general expression for the MRS for this utility function. Show how it can be interpreted as the ratio of the marginal utilities. d. Does this individual...
Suppose that there two goods, X and Y , available in arbitrary nonnegative quantities (so the the consumption set is R 2 +). The consumer has preferences over consumption bundles that are monotone, strictly convex, and represented by the following (differentiable) utility function: u(x, y) = α √ x + (1 − α) √ y, where x is the quantity of good X, y is the quantity of good Y , and α ≥ 0 is a utility parameter. The...
Question 2 A consumer purchases two goods, food (x) and clothing (y). He has the utility function U(X,Y) = XY, where X and Y denote amounts of X and Y consumed. Marginal utilities of X and Y are MUx = y and MUy = x. The consumer’s income is $72 per week and that the price of y is Py = $1 per unit and price of x is Px1 = $9 per unit. What are his initial quantities of X and...