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. Suppose we discard the assumption that 0 < α < 1 and assume α > 1 instead, determine whether the given utility function U(E, G) = αln(E) + (1 − α)ln(G) is still a valid utility function.

b. Find a utility function with a different functional form that represents the same ordering of bundles as the given utility function U(E, G) does

c. If α = .25, find the optimal consumption bundle of gasoline and electricity.

d. If α = .75, find the optimal consumption bundle of gasoline and electricity.

e. Find the minimum value of α such that the rationing is binding

Solutions

Expert Solution

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

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?

A typical American household uses 26.5 kW-hour of electricity per day, and that electricity is mostly...

A typical American household uses 26.5 kW-hour of electricity per day, and that electricity is mostly supplied by fossil fuels. If we wanted to instead power a house by solar panels, which receive on average 370 W/m2 from the Sun each day and are 15.7% efficient (fraction of solar energy converted into useable electrical energy), what area of solar panels is needed to power an average American home?

A typical American family uses 1000 kWh of electricity pro 30 days.

A typical American family uses 1000 kWh of electricity pro 30 days. What is the average RMS current in the 160 V power line to the house?

Kindly show how to do in Excel: Suppose that the weight of a typical American female...

Kindly show how to do in Excel: Suppose that the weight of a typical American female follows a normal distribution with μ = 140 lb. and σ = 20 lb. Also, suppose 80.15% of all American females weigh more than I weigh. What fractions of American females weigh more than 165 pounds? How much do I weigh? If I weighed 20 pounds more than I do, what percentile would I be in? A production process manufactures items with weights that...

Lexicographic Preferences: Suppose that a consumer has lexicographic preferences over bundles of non-negative amounts of each...

Lexicographic Preferences: Suppose that a consumer has lexicographic preferences over bundles of non-negative amounts of each of two commodities. The consumer’s consumption set is R2+. The consumer weakly prefers bundle a = (a1,a2) over bundle b = (b1,b2) if either (i) a1 > b1, or (ii) both a1 = b1 and a2 ? b2. In any other circumstance, the consumer does not weakly prefer bundle a to bundle b. (Note that these preferences are not continuous. Furthermore, they cannot be...

Juan has an income of $ 500 and consumes gasoline (G) for his car and tacos...

Juan has an income of $ 500 and consumes gasoline (G) for his car and tacos (T). The respective prices per liter of gasoline and tacos are (PG, PT) = (10,10). Its utility function is a Cobb Douglas function with alpha = beta = 1. a. What is the Marshallian demand for both goods? (Algebraically) G * = T * = b. What is the indirect utility? (Algebraically) V (I, pg, Pt) = c. Calculate the optimal amount Juan consumes...

Roughly what proportion of the American population has no health insurance? What is the typical income...

Roughly what proportion of the American population has no health insurance? What is the typical income level of this population?

ii. Let G = (V, E) be a tree. Prove G has |V | − 1...

ii. Let G = (V, E) be a tree. Prove G has |V | − 1 edges using strong induction. Hint: In the inductive step, choose an edge (u, v) and partition the set vertices into two subtrees, those that are reachable from u without traversing (u, v) and those that are reachable from v without traversing (u, v). You will have to reason why these subtrees are distinct subgraphs of G. iii. What is the total degree of a...

Suppose G is a connected cubic graph (regular of degree 3) and e is an edge...

Suppose G is a connected cubic graph (regular of degree 3) and e is an edge such that G − e has two connected components G1 and G2 (a) Explain what connected means. (b) We say that e is a____________ of G (c) show that G1 has an odd number of vertices. (d) draw a connected cubic graph G with an edge e as above.

Part A A particular brand of gasoline has a density of 0.737 g/mL at 25 ∘C....

Part A A particular brand of gasoline has a density of 0.737 g/mL at 25 ∘C. How many grams of this gasoline would fill a 15.8 gal tank (1US gal=3.78L)? Part B A block of metal has a width of 3.2 cm, a length of 17.1 cm, and height of 5.0 cm . Its mass is 1.1 kg . Calculate the density of the metal. Express your answer to two significant figures and include the appropriate units.

Subjects