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?

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

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Rahul Sunny answered 1 year ago

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