For all questions, if necessary, make appropriate assumptions. 1. Each consumer's preferences are given by u (c, l; g) = log (c + 7g) + Bl where c and I are the individual's consumption and leisure, respectively, and g denotes the goods purchased by the government from the goods market and provided to each consumer (e.g., school lunch). The parameter B > 0 reflects the value of leisure relative to the utility from consumption. y E (0, 1) denotes the substitutability of goods provided by the government: a one unit of government spending is equivalent to y units of private consumption. This government spending is financed by the lump-sum tax 7. The production technology is given by y = n where y is output and n is the labor input. (a) Define a competitive equilibrium. (b) Solve for all prices and quantities in a competitive equilibrium. (c) Determine the effects of an increase in government spending g on consumption, output, employ- ment, and the real wage. Explain your results. (d) Determine the effect of increasing government spending on the welfare of the consumers in equi- librium, and find the optimal level of g that maximizes the welfare