Question

In: Economics

Furiosa has individual preferences for gasoline (G) and water (W), which can be represented by the...

Furiosa has individual preferences for gasoline (G) and water (W), which can be represented by the following utility function: U(G,W) = 7G4W5 + 31.9

if the price of gas is $20, the price of water is $45, and furiosas income is $900, what is the optimal amount of gasoline?

Solutions

Expert Solution

The utility function is

Determine the Marginal utility of Gasoline by differentiating the utility function wrt G

Similarly calculate the Marginal utility of water by differentiating U wrt W, we get

At equilibrium the following relationship must hold true (Law of equimarginal criterion)

Plug in the values in the above expression

Given, Income =.$ 900

The budget constraint can be expressed as

Plug in the value of W in the above expression

Amount of Gasoline = 20

Amount of water = 11.11

Please contact if having any query will be obliged to you for your generous support. Your help mean a lot to me, please help. Thank you.

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Suppose that the preferences a typical American has for quantities of electricity (E) and gasoline (G)...

Suppose that the preferences a typical American has for quantities of electricity (E) and gasoline (G) is given by U(E, G) = αln(E) + (1 − α)ln(G) where 0 < α < 1. Suppose the prices of gasoline and electricity in the units provided are both $1/unit and the consumer has an income of $100. Suppose in addition, the government has chosen to ration electricity by allowing 2 a maximum consumption of 50 units of electricity (E ≤ 50). a....

Consumer Theory. A consumer has preferences over goods x and y that can be represented by...

Consumer Theory. A consumer has preferences over goods x and y that can be represented by the utility function ?(?,?) = ?+??(?) where ln is the (natural) log function. The consumer has income I (all to be spent on x and y) and the price of x and y are px and py respectively. (You may assume the “at least as good as x” set B(x) is a convex set, so the solution to the consumer’s problem will be a...

Consider an individual with preferences defined over two goods, X1 and X2. This individual has preferences...

Consider an individual with preferences defined over two goods, X1 and X2. This individual has preferences that can be represented by the following utility function: u(X1, X2) = X1 + X 0.5 2 Let P1 = 4 and P2 = 2. In addition, suppose this individual has an income of $120. (a) Write down the expression for this consumer’s marginal rate of substitution of X1 for X2 (MRS12). Identify the distinguishing feature of this particular MRS12. (b) Calculate the optimal...

George has preferences over two goods (G1and G2) that can be represented by the utility function...

George has preferences over two goods (G1and G2) that can be represented by the utility function U(G1, G2) = ???{ 10G1,2G2}. Assume that both goods can only be purchased in integer (whole number) amount! First, if George has $120 to spend and the first good costs $20 per unit, while the second good costs $4 per unit, how many units of both goods will George purchase when he is maximizing his utility subject to his budget? Second, calculate his utility...

1. Consider a consumer who has income of m = 30 and preferences represented by the...

1. Consider a consumer who has income of m = 30 and preferences represented by the utility function u(x, y) = 2x + 3 ln y. Note that this is quasilinear utility. (a) Initially, suppose that prices are given by px = 12 and py = 1. Find the optimal bundle. This is point “A.” (b) Suppose that the price of y increases to 4. In the notation we have used, this means p 0 y = 2. Find the...

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?

Jacinto consumer two goods: A and B, his preferences can be represented by the Cobb-Douglas function:...

Jacinto consumer two goods: A and B, his preferences can be represented by the Cobb-Douglas function: U (XA, XB) = 2XA * XB2, where XA represents the units consumed of good A and XB the units consumed of good B. Consider generic prices for the goods PA, PB and an income of m A) Find Jacinto's demand functions for good A and B B) if PA = 60, PB = 90 and m = 540: i. What are the optimal...

The market demand for gasoline can be represented by the equation Q=120-2P, where quantity Q is...

The market demand for gasoline can be represented by the equation Q=120-2P, where quantity Q is measured in gallons/week and price P is measured in dollars per gallon. The supply curve for gasoline, however, depends on whether the time frame is the short run or the long run. A per-gallon tax of $6 is imposed on the gasoline market. a. In the short run, the supply function for gasoline is represented by 80 if P>5 Q = anything between 0...

Suppose that an individual has wealth of $20,000 and utility function U(W) = ln(W), where ln(W)...

Suppose that an individual has wealth of $20,000 and utility function U(W) = ln(W), where ln(W) indicates the natural logarithm of wealth. What is the maximum amount this individual would pay for full insurance to cover a loss of $5,000 with probability 0.10?

Dr Pepper’s preferences can be represented by the utility function u(x,y) = x + y where...

Dr Pepper’s preferences can be represented by the utility function u(x,y) = x + y where x is his consumption of Coca Cola (hereafter, referred to as Coke) and y is his consumption of orange juice (hereafter, referred to as OJ). Initially, both types of drinks are not taxed and with an income of $12 he faces prices ($1, $2). On the advice of nutritionists, the government decides to impose a specific tax of $2 on Coke which leads to...

Subjects