Explain why preferences ≽ that are induced by a utility function are always complete, reflexive, and...

Explain why preferences ≽ that are induced by a utility function are always complete, reflexive, and transitive.

Expert Solution

Rahul Sunny answered 1 year ago

Find each of the Definitions a. Transitive preferences b. Reflexive preference c. Marginal utility

1. Erika has preferences that are complete, transitive, continuous, monotonic, and convex. Her utility function is...

1. Erika has preferences that are complete, transitive, continuous, monotonic, and convex. Her utility function is U(x1, x2), where goods 1 and 2 are the only goods she values. Her income is M, and the prices of the goods are p1 and p2; assume M, p1 and p2 are positive numbers. a. Suppose M decreases, good 1 is normal, and good 2 is inferior. Using a graph, show what happens to the demand for each good. b. Is it possible...

I What does it mean that preferences are reflexive, complete andtransitive?ii What characterises convex...

I What does it mean that preferences are reflexive, complete and transitive?ii What characterises convex preferences?iii Explain what the assumption of monotonicity of preferences imply.vi If the five properties above (reflexive, complete transitive, convexity and monotonicity) are satisfied, preferences are said to be “well-behaved”. Explain, which of these properties that make sure that:i.indifference curves cannot slope upwards, ii.indifference curves (for an individual) cannot cross each other, iii.indifference curves are bowed into the origin.

For two goods x and y, the individual’s preferences are measured by the utility function ?(?,?)=...

For two goods x and y, the individual’s preferences are measured by the utility function ?(?,?)= ?0.5?0.5, the price of good y is $10, income equals $100, and the price of good x increase from $5 to $10. Draw the price consumption curve for x and y and compute the slop of the price consumption curve. Show your calculation step by step.

This is considering the Phi function (The Euler Phi Function) (a) Explain why φ(m) is always...

This is considering the Phi function (The Euler Phi Function) (a) Explain why φ(m) is always even when m ≥3. (b) φ(m) is rarely a prime number. Find all numbers m so that φ(m) is prime. I'm solving for part b. From part a, it looks like there is no prime number for phi of m when it's greater than or equal to 3. Now, I notice that Phi of 4 is 2, Phi of 3 is 2, and Phi...

4. Provide an example of utility function that describes the preferences of a consumer who consumes...

4. Provide an example of utility function that describes the preferences of a consumer who consumes only two goods and considers these two goods to be non-perfect substitutes. Explain also the meaning of variables and coefficients in the utility function. 5. Provide an example of utility function that describes the preferences of a consumer who consumes only two goods and considers these two goods to be perfect complements. Explain also the meaning of variables and coefficients in the utility function....

Consider a consumer's preferences over consuming two goods that are represented by the following utility function:...

Consider a consumer's preferences over consuming two goods that are represented by the following utility function: U（x1，x2）= x1^a x2^1-α 0 < α < 1 x1，x2 ≥ 0 (a) Do her preferences satisfy monotonicity? (4 mark) (b) Do her preferences exhibit diminishing marginal utility? (c) Are her preferences convex? In other words, do her preferences exhibit diminishing marginal rate of substitution? (Hint: Find MRS and its rate of changes with respect to the good on the horizontal axis.) (d) Use a...

For each of the following utility functions, explain whether the preferences that they represent are strictly...

For each of the following utility functions, explain whether the preferences that they represent are strictly convex. Use indifference curve diagrams to help explain your answers. 1. Preferences represented by u (x1, x2) = x1 + x2. 2. Preferences, represented by u (x1, x2) = min {x1, x2}.

1) Explain why chemically induced changes in renal function may not be detected immediately after toxic...

1) Explain why chemically induced changes in renal function may not be detected immediately after toxic exposure. 2) Explain the reasons for the susceptibility of kidney to toxicity. 3) Give two examples of nephrontoxicants and their mechanism of action.

Judy's preferences over x and y can be represented by the utility function: U=xy3 The price...

Judy's preferences over x and y can be represented by the utility function: U=xy3 The price of x is Px = 8, the price of y is Py = 4, and her income is I = 480. At Judy's optimal consumption bundle, What is her demand for x? What is her demand for y?

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