A consumer of two goods (X and Y) has the following utility function: U(x,y)=xy-ay^2, whre x>=0...
A consumer of two goods (X and Y) has the following utility function: U(x,y)=xy-ay^2, whre x>=0 and y>=0 and a>0 is a parameter.
(a) Are there bundles for which one of the goods is actually a "bad" (in the sense that consuming more of it reduces utility)?
(b) Find the MRS.
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A consumer of two goods (X and Y) has the following utility
function: U(x,y)=xy-ay^2, whre x>=0...
For U(x,y) -xy, MRS ▼ , while Uxx_ and Uyy This means that this utility function...
For U(x,y) -xy, MRS ▼ , while Uxx_ and Uyy This means that this utility function has MRS, while exhibiting marginal utility in x andy For U(x,y)-x2y2, MRS ▼ , while Uxx_ and Uyy This means that this utility function has MRS, while exhibiting marginal utility in x and y For U(x,y) = In x + In y, MRS- ,while Ux- and Uyy ▼ . This means that this utility function has MRS, while exhibiting marginal utility in x and...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) =...
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...
A) Let utility over 2 goods be defined as U(x,y)=x+xy+y. Find the MRS by implicitly solving...
A) Let utility over 2 goods be defined as U(x,y)=x+xy+y. Find the MRS by implicitly solving for y (hint: set U=k) and calculate -dy/dx. B) Now find the MRS by using MRS =Ux/Uy.
24. Consider a consumer with a utility function of u(x,y)=xy. (10 total) a) Draw to scale...
24. Consider a consumer with a utility function of u(x,y)=xy. (10 total) a) Draw to scale the consumer's indifference curves for u(x,y)=100 and u(xy)=400. (2) b) Verify the both x and y are "goods" rather than "bads." (3) c) Verify that the law of diminishing marginal rate of substitution holds. (3) d) Suppose that the utility numbers assigned to bundles are determined by the formula (xy) Vxy, instead of u(x,y)= xy. How does the change in the formula change the...
) A consumer's utility function is given by: U(x,y) = 10xy Currently, the prices of goods x and y...
) A consumer's utility function is given by: U(x,y) = 10xy Currently, the prices of goods x and y are $3 and $5, respectively, and the consumer's income is $150 . a. Find the MRS for this consumer for any given bundle (x,y) . b. Find the optimal consumption bundle for this consumer. c. Suppose the price of good x doubles. How much income is required so that the Econ 201 Beomsoo Kim Spring 2018 consumer is able to purchase...
Consider a utility function u(x,y) = Xayb, where 0くaく1 and 0 < b 〈 1. Also...
Consider a utility function u(x,y) = Xayb, where 0くaく1 and 0 < b 〈 1. Also assume that x,y>0 7.1. Derive the marginal utility of x and the marginal utility of y and state whether or not the assumption that more is better is satisfied for both goods. 7.2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x?What does it mean in words? 7.3. What is MRS.y? 7.4. Suppose a, b- Wht...
Consider the following utility function of 2 goods, x and y: U(x,y)= - [(x-10)2 + (y-10)2];...
Consider the following utility function of 2 goods, x and y: U(x,y)= - [(x-10)2 + (y-10)2]; x,y≥0 The prices of good x and y is 10 and 20 respectively. The income is denoted by m. a. Draw the indifference curves for the utility function and use arrows to explain in which direction utility increases or decreases. b. Find the consumption bundle that maximizes utility for the consumer. c. Find the Engel curve.
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...
(f) A representative consumer has a utility function U (x, y) = xy. A representative firm...
(f) A representative consumer has a utility function U (x, y) = xy. A representative firm makes good x and has a production function x = f(k, l) = (kl)0.25and an unavoidable fixed cost equal to A. There are 100 consumers and, initially, 100 firms. Prices are w = v = Py = 1 and Px is determined in a competitive market. Representative consumer income is I = 2. In the long run,the number of firms is M (determined endogenously),...
For U(x,y) -xy, MRS ▼ , while Uxx_ and Uyy This means that this utility function has MRS, while exhibiting marginal utility in x andy For U(x,y)-x2y2, MRS ▼ , while Uxx_ and Uyy This means that this utility function has MRS, while exhibiting marginal utility in x and y For U(x,y) = In x + In y, MRS- ,while Ux- and Uyy ▼ . This means that this utility function has MRS, while exhibiting marginal utility in x and...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
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...
24. Consider a consumer with a utility function of u(x,y)=xy. (10 total) a) Draw to scale the consumer's indifference curves for u(x,y)=100 and u(xy)=400. (2) b) Verify the both x and y are "goods" rather than "bads." (3) c) Verify that the law of diminishing marginal rate of substitution holds. (3) d) Suppose that the utility numbers assigned to bundles are determined by the formula (xy) Vxy, instead of u(x,y)= xy. How does the change in the formula change the...
Consider a utility function u(x,y) = Xayb, where 0くaく1 and 0 < b 〈 1. Also assume that x,y>0 7.1. Derive the marginal utility of x and the marginal utility of y and state whether or not the assumption that more is better is satisfied for both goods. 7.2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x?What does it mean in words? 7.3. What is MRS.y? 7.4. Suppose a, b- Wht...
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