Question

Consider a model with no savings, a production function with positive, but diminishing marginal product and a household with a utility function utility = u(c, l), where c is consumption and l is work effort. The marginal utility from consumption is positive, MU(c)>0, but the marginal utility from work effort is negative, MU(l)<0. Both marginal utilities diminish. In this model argue that the utility household will adjust its consumption and work effort until the marginal utility benefit for an additional unit of work effort equals the marginal utility cost of an additional unit of work effort. Be sure to explain how you arrived at the expressions for your marginal effects

Answer 1

Marginal utility derived from the additional consumption is positive while marginal utility derived from additional work effort is negative. This means adding one more unit of consumption will increase our utility while later will decrease our utility. But note that reducing one unit of work effort will reduce whatever we have to consume.i.e, what we produce.

You can easily understand this problem by considering a hypothetical world where there is only one person Robinson Crusoe. where he's the only producer and consumer of only good coconuts. Either he will gather coconuts or he will enjoy lesiure. Working will reduce his utility directly but he will be consuming more coconuts and hence will increase his utility. As you can see there is a one to one trade off between time he takes leisure and time he devotes gathering coconuts.

If working one more hour increases his utility more than the taking lesiure than he will definitely work more as he is a utility maximizer. But there is a cost of working one more hour the leisure he forgets. So in order to maximize his utility he should equate the marginal cost of working with marginal utility of consumption. Otherwise whichever will be higher he will devote his time there more. Hence, he should equate the marginal utility of consumption to marginal cost ( in terms of utility) of working.Hope you have got the answer to your problem.