Homework Answers
Please see the attached.
We have the following budget equation
W= 24= p1q1 + p2q2+ p3q3 = 4q1 + 3q2 + 3q3
We maximise the utility function, U subject to W using the
Langrajian Multiplier, Lambda
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4. Suppose an agent has utility function ulgr4ra) min (qz4), where these goods have respective prices...
4. Suppose an agent has utility function u(1q2.q3)1 min {q2q3), where these goods have respective prices...
4. Suppose an agent has utility function u(1q2.q3)1 min {q2q3), where these goods have respective prices p1 4 and p2 p3 3. Supposing the agent has wealth of W 24, how much of each good will the agent consume?
4. Suppose an agent has utility function u(12.93)min1q243), where these goods have respective prices pi-4 and...
4. Suppose an agent has utility function u(12.93)min1q243), where these goods have respective prices pi-4 and p2-p,-3. Supposing the agent has wealth of W-24, how much of each good will the agent consume?
3. What is the marginal rate of substitution of u-VIn (qa) + In (q2)? 4. Suppose...
3. What is the marginal rate of substitution of u-VIn (qa) + In (q2)? 4. Suppose an agent has utility function u(1.q2,q3)q min {q2,433, where these goods have respective prices p1-4 and p2 p3 3. Supposing the agent has wealth of W- 24, how much of each good will the agent consume?
Utility maximization with more than two goods Suppose that there four goods Q, R, X and Y , avail...
Utility maximization with more than two goods Suppose that there four goods Q, R, X and Y , available in arbitrary non-negative quantities (so the the consumption set is R 4 +). A typical consumption bundle is therefore a vector (q, r, x, y), where q ≥ 0 is the quantity of good Q, r ≥ 0 is the quantity of good R, x ≥ 0 is the quantity of good X, and y ≥ 0 is the quantity of...
2 Perfect substitutes Consider an agent with perfectly substitutable utility over R The agent has total...
2 Perfect substitutes Consider an agent with perfectly substitutable utility over R The agent has total wealth w>0 1. Suppose the agent faces linear prices and that P1くPi for every i > 1, what is the agent's optimal consumption bundle? What fraction of her wealth does she spend on each good? Show that the tangency conditions for optimality are satisfed for the bundle you've found. 2. Suppose instead she faces the same linear price for every good. Describe the set...
i) Suppose that Mary’s utility function is where W is wealth. Is she risk averse? Suppose...
i) Suppose that Mary’s utility function is where W is wealth. Is she risk averse? Suppose that Mary has initial wealth of $125,000. How much of a risk premium would she require to participate in a gamble that has a 50% probability of raising her wealth to $160,000 and a 50% probability of lowering her wealth to $90,000? ii) Suppose that Irma’s utility function with respect to wealth is U(W) = 100 + 80W − W2. Find her Arrow-Pratt risk...
13. Consider an individual with a utility function U = min{3x,, x} where x1 and x2...
13. Consider an individual with a utility function U = min{3x,, x} where x1 and x2 are the quantities of goods 1 and 2 consumed, respectively. If the prices of good 1 is $5 and the price of good 2 is $5 and the consumer's income is $60, how much of goods 1 and 2 does she buy? a. x, = 4, x, = 4 b. x, = 6,X, = 3 c. x, = 8, x, = 2 d. x,...
6. Modou has a utility function U(X1,X2) = 2X1 + X2 The prices of X1 &...
6. Modou has a utility function U(X1,X2) = 2X1 + X2 The prices of X1 & X2 are $1 each and Modou has an income of $20 budgeted for this two goods. a. Draw the demand curve for X1 as a function of p1.: b. At a price of p1 = $1, how much X1 and X2 does Modou consume?: c. A per unit tax of $0.60 is placed on X1. How much of good X1 will he consume now?:...
3 Clara consumes two goods x and y. Suppose her utility function is given as U(x,y)=min{3x,4y}...
3 Clara consumes two goods x and y. Suppose her utility function is given as U(x,y)=min{3x,4y} The prices of the two goods are Px for good x and Py for good y. If her monthly income is $M, Derive her uncompensated demand function for good x Derive her uncompensated demand function for good y Derive the cross-price effects and show that the two goods are complementary goods.
Ex. 1: Imagine there are two goods, X and Y. The utility function is: U =...
Ex. 1: Imagine there are two goods, X and Y. The utility function is: U = XY. The price of X is $2 and the price of Y is $4. The budget is $20. What is the optimal quantity of X and Y to consume? Ex. 2: Imagine there are two goods: books and coffees. Your utility function is U = BC, where B is the number of books you consume and C is the number of coffees you consume....
4. Suppose an agent has utility function u(1q2.q3)1 min {q2q3), where these goods have respective prices p1 4 and p2 p3 3. Supposing the agent has wealth of W 24, how much of each good will the agent consume?
4. Suppose an agent has utility function u(12.93)min1q243), where these goods have respective prices pi-4 and p2-p,-3. Supposing the agent has wealth of W-24, how much of each good will the agent consume?
3. What is the marginal rate of substitution of u-VIn (qa) + In (q2)? 4. Suppose an agent has utility function u(1.q2,q3)q min {q2,433, where these goods have respective prices p1-4 and p2 p3 3. Supposing the agent has wealth of W- 24, how much of each good will the agent consume?
2 Perfect substitutes Consider an agent with perfectly substitutable utility over R The agent has total wealth w>0 1. Suppose the agent faces linear prices and that P1くPi for every i > 1, what is the agent's optimal consumption bundle? What fraction of her wealth does she spend on each good? Show that the tangency conditions for optimality are satisfed for the bundle you've found. 2. Suppose instead she faces the same linear price for every good. Describe the set...
13. Consider an individual with a utility function U = min{3x,, x} where x1 and x2 are the quantities of goods 1 and 2 consumed, respectively. If the prices of good 1 is $5 and the price of good 2 is $5 and the consumer's income is $60, how much of goods 1 and 2 does she buy? a. x, = 4, x, = 4 b. x, = 6,X, = 3 c. x, = 8, x, = 2 d. x,...
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