# What type of function is the utility function expressed as u(x,y)=30lnx + y? Also, how would you go about deriving the demand for x and y in this function?

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What type of function is the utility function expressed as u(x,y)=30lnx + y? Also, how would you go about deriving the demand for x and y in this function?

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Step 1

A utility function u (x, y) represents a consumer’s preferences. That is, a utility function provides a representative number for utility derived from every combination of x and y. This helps in ranking the available bundles of x and y and thus helps in representing consumer's preferences.

Step 2

The given utility function u (x, y) = 30lnx + y represents quasi-linear preferences. That is, the preference is linear in y and non-linear in x, hence, quasi-linear.

Step 3

The consumer equilibrium is given by the tangency of the indifference curve (u (x, y)) and the budget line. Assuming the total income of the consumer represented by the preference u (x, y) = 30lnx + y to be M. Also, assuming the prices for x and y to be P1 and P2 respectively.

The budget line is given in equation (1).

The slope of budget line is given by the ratio of prices i.e. P1 /P2.

Marginal Rate of Substitution (MRS): MRS i...

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