Part I:

Fact I: Suppose in Econland there are N identical consumers and one government. The representative consumer derives utility from consumption goods, denoted by C (numeraire), and leisure, denoted by l, according to the utility function U(C,l). They earn hourly wage $w = $12 and pay a lump-sum tax amounting to $fl each day. They have no non-wage income. Each day the consumer hash hours to divide between work and leisure.

If preference of the representative consumer is given by: U(C,l) = ln C + ln l find out what is the ratio of l vs

C consumed by the consumer at the optimum level (that is find out !*IC*=?).

Part II:

Fact II: Assume an economy in the context of the simple one period model where the representative consumer is choosing between consumption good C (numeraire) and leisure l according their preference: U(C, l), earning wage income $w/hour and non-wage income: n - T. Representative firms are having two-factor production function, using labour as the variable factor (denote by Nd) and capital (denoted by K), which is fixed in the short run and both factors are subject to diminishing marginal productivity. Government is having non-productive government expenditure, G, following the constraint that government expenditure must equal tax. Based on Fact II, assume that the economy reached a competitive equilibrium.

What are the four conditions that a competitive equilibrium must satisfy for this economy?