# Answer to Question #12816 in Microeconomics for Nat

Question #12816

Finn has the following utility function:

U=√C*L

where C represents real consumption spending and L hours of leisure time consumed daily (i.e., T = 24). As a result, his first-order condition for utility maximization can be written as a simple ratio of the arguments in his utility function:

MRS=C/L

a) Show that Finn’s indifference curves will be convex to the origin (e.g., choose U = 10 and show that the resulting indifference curve is convex). Under what conditions will this result in a unique equilibrium? (HINT: a graph will definitely help here.)

b) Suppose Finn has $96 of nonlabour income each day (he comes from a wealthy family) and faces the minimum wage of $12 per hour. Set the price of consumption (P) equal to one, and do the following:

(i) Write down Finn’s budget constraint. Show his first-order condition for utility maximization.

(ii) Compute Finn’s optimal daily consumption of leisure (L*), hours of work (H*) and consumption of goods and services (C*).

U=√C*L

where C represents real consumption spending and L hours of leisure time consumed daily (i.e., T = 24). As a result, his first-order condition for utility maximization can be written as a simple ratio of the arguments in his utility function:

MRS=C/L

a) Show that Finn’s indifference curves will be convex to the origin (e.g., choose U = 10 and show that the resulting indifference curve is convex). Under what conditions will this result in a unique equilibrium? (HINT: a graph will definitely help here.)

b) Suppose Finn has $96 of nonlabour income each day (he comes from a wealthy family) and faces the minimum wage of $12 per hour. Set the price of consumption (P) equal to one, and do the following:

(i) Write down Finn’s budget constraint. Show his first-order condition for utility maximization.

(ii) Compute Finn’s optimal daily consumption of leisure (L*), hours of work (H*) and consumption of goods and services (C*).

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