Angela's Choice of Working Hours

5.4.2 of The Economy 1.0 & The Economy #3

Given this utility function and the production function: c = g(t), solve the constrained optimisation problem.

-The FOC can be found via MRS = MRT.

MRS = v’(t) and MRT = g’(t)

-Because v’’(t) is negative (indifference curve slopes downward) and g’’(t) is negative too (feasible frontier slopes downward), only one value of t exists. Therefore:

v’(t) + g’(t) = 0

-Thus, t* exists such that we get c* = g(t*) which is the optimal consumption of grain

Given this utility function and the production function: c = g(t), solve the constrained optimisation problem.

v(t) = 4√(t)

g(t) =2√(48-2t)

-Using the FOC:

MRS = 2/√(t)

MRT = 2/√(48-2t)

-This nicely simplifies down to:

48-2t = t

-Thus leading to optimal values of:

t = 16

c = 8

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