Consider a 2-period production economy with money and government. Assume that firms should borrow to financ...

 

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Consider a 2-period production economy with money and government. Assume that firms should borrow to financ their investment spending. They borrow with a rate of r = re +ft, where fi is an exogenous spread that the firm need to pay when they are borrowing from the financial intermediary. Government, levies lump-sum taxes and borrows Be to finance their government spending G₁. Moreover, the government prints money M₁. Average price level in this economy is denoted by P. Households carn a hourly real wage w₁, and earn net interest r, for their savings. Time t utility function of the household is given by: U(C₁ N₁) = ln Cr + In +In(1-N₂) Me P₁ Me P Firms use a Cobb-Douglas production function for production: YA,KON (a) Write down the flow budget constraints for the household and derive the IBC. (b) Derive the IBC for the government. (c) Derive the optimality conditions for the household, and interpret them economically. (d) Now assume that households pay a proportional tax on their savings. That is households have to pay a proportional tax from their investment income. Solve the household's problem and interpret optimality conditions. Discuss whether Ricardian equivalence holds or not. (e) Derive the consumption function for the household under lump sum taxes and interest on savings. (f) Derive the optimality conditions for the firm, and interpret them economically. Describe the effects of an increase in f, on optimality conditions. Now assume that f by, where b is a po ive constant. How would your answers change? (g) Now assume that the firm finance & fraction of its investment by issuing equities and the rest with borrowing with the interest rate r. Does investment financing method matter for the firm? Explain. (h) Now assume that the firms have to pay proportional taxes from their profits and finance investment through borrowing. Write the firm's problem and derive optimality conditions. Describe the effects of higher profit tax on investment decisions. (i) Define competitive equilibrium for this economy. Clearly derive market clearing conditions. Is money important for equilibrium conditions? Make sure you define classical dichotomy and how it relates to this model. Can you offer a change in the model such that money has real effects? (i) Discuss the effects of higher technology at time t. How would these effects change if technology increases at time t+1 but not in t? (k) Discuss the effects of higher money supply at time t. (1) Solve the social planner's problem. Are decentralized allocations (under every extension given above) Pareto optimal? Define Pareto optimality in your answer. Consider a 2-period production economy with money and government. Assume that firms should borrow to financ their investment spending. They borrow with a rate of r = re +ft, where fi is an exogenous spread that the firm need to pay when they are borrowing from the financial intermediary. Government, levies lump-sum taxes and borrows Be to finance their government spending G₁. Moreover, the government prints money M₁. Average price level in this economy is denoted by P. Households carn a hourly real wage w₁, and earn net interest r, for their savings. Time t utility function of the household is given by: U(C₁ N₁) = ln Cr + In +In(1-N₂) Me P₁ Me P Firms use a Cobb-Douglas production function for production: YA,KON (a) Write down the flow budget constraints for the household and derive the IBC. (b) Derive the IBC for the government. (c) Derive the optimality conditions for the household, and interpret them economically. (d) Now assume that households pay a proportional tax on their savings. That is households have to pay a proportional tax from their investment income. Solve the household's problem and interpret optimality conditions. Discuss whether Ricardian equivalence holds or not. (e) Derive the consumption function for the household under lump sum taxes and interest on savings. (f) Derive the optimality conditions for the firm, and interpret them economically. Describe the effects of an increase in f, on optimality conditions. Now assume that f by, where b is a po ive constant. How would your answers change? (g) Now assume that the firm finance & fraction of its investment by issuing equities and the rest with borrowing with the interest rate r. Does investment financing method matter for the firm? Explain. (h) Now assume that the firms have to pay proportional taxes from their profits and finance investment through borrowing. Write the firm's problem and derive optimality conditions. Describe the effects of higher profit tax on investment decisions. (i) Define competitive equilibrium for this economy. Clearly derive market clearing conditions. Is money important for equilibrium conditions? Make sure you define classical dichotomy and how it relates to this model. Can you offer a change in the model such that money has real effects? (i) Discuss the effects of higher technology at time t. How would these effects change if technology increases at time t+1 but not in t? (k) Discuss the effects of higher money supply at time t. (1) Solve the social planner's problem. Are decentralized allocations (under every extension given above) Pareto optimal? Define Pareto optimality in your answer.

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a The flow budget constraint for the household can be derived as follows Y B T C S T Where Y represents the households income real wage hours worked B represents the transfer payments received from th... View the full answer