4. (15 points) Suppose that the consumer's preferences are given by U(c, I) = sci + 21% where c is the level of consumption and l is leisure. The consumer has to allocate 24 hours between leisure and labour. The real wage rate is $10 per hour and the real non-wage income is $1521]. Assume that there is no government. (a) Write the budget constraint of the household. (b) Solve for the tangency condition using the marginal rate of substitu- tion MRSIPC, and the wage [c] Solve for optimal consumption, leisure1 and hours worked