Suppose that following represents the utility function of the individual U(c,l)=log⁡(l)+c c, represents the consumption level of the individual and l, represents the leisure, while the market wage is w

, non-wage income is v, and available time is T. Find algebraically and draw the Labor Supply function? b) Prove the validity of Slutsky equation for the individual with labor supply preferences as implicitly described above? (Please emphasize the income and substitution effects in your solution) Suppose that following represents the utility function of the individual U(c,l)=log⁡(c)+log⁡(l) c, represents the consumption level of the individual and l, represents the leisure, while the market wage is 10 and available time is 20. The followings are short run production functions for two firms operating in different industries with different capital structures. 〖F(L)〗_1=K ̅_1 √AL 〖 F(L)〗_2=Min{αG,〖AK ̅〗_2}+θ√L K ̅_1, represents the sector-specific capital employed by the firm 1, K ̅_2,represents the sector-specific capital, employed by the firm 2, while L represents the labor employed by the firm. Use r_1 〖,r〗_(2 )to represent the rental price of capital structures. w to represent the wage of labor, P_1 is the price of the good produced in the first industry and P_2 is the price of the good produced in the second industry. Assume that all markets (commodities and factor markets) are competitive, and labor are mobile across industries. G represents public infrastructure investment by the government and A represents the technology level. (Hint: G is fixed in the short run). Find and draw the the Value of Marginal Product for Labor for two firms? (5 Marks) b) Write down the profit maximization problem and derive labor demand curves for each firm? What is the employment (for labor) level for firm 1 and firm 2 ? c) Find the profit level for each firm? (5 Marks) d) Discuss the impact of public infrastructure investment ,and technological advancement on labor productivity and employment levels for each firm ? 5- “In partial equilibrium we analyze the single market, while in general equilibrium we analyze all markets together including factor markets. Labor market as one of the factor market will be affected and will be affecting all other markets.” i) Given the statement above, discuss the occurence of inflation followed by the taste shock on the labor supply (i.e. labor prefers more laziness)? ii) Discuss the consequences you referred above by emphasizing the short-run consequences versus long-run consequences ? iii) Given the fact that the globalization level of the country affects its adaptation to shocks on the labor market, how your answer to a) and b) would change if the country is globalized versus closed-economy ?