Exercise 5 (Borrowing Constraints and Consumption Taxes). Consider a two-period economy in which households face the borrowing constraint S p 1 ≥ 0. Suppose that the constraint is binding. In period 1, the household receives an exogenous endowment of goods Y1 = 50, and the government levies a proportional tax on consumption at the rate τ1 = 0.25 and has expenditures in goods and services in the amount G1 = 2. Firms borrow in period 1 at the interest rate r and use the funds to invest in physical capital, denoted I1. Investment becomes productive in period 2. The investment schedule is I1 = 12.5 (1 + r) ^2 1. Calculate private consumption in period 1 (C1), government saving in period 1 (S g 1 ), and national saving in period 1 (S1). 2. Calculate the equilibrium real interest rate (r).
Exercise 5 (Borrowing Constraints and Consumption Taxes). Consider a two-period economy in which households face the borrowing constraint S p 1 ≥ 0. Suppose that the constraint is binding. In period 1, the household receives an exogenous endowment of goods Y1 = 50, and the government levies a proportional tax on consumption at the rate τ1 = 0.25 and has expenditures in goods and services in the amount G1 = 2. Firms borrow in period 1 at the interest rate r and use the funds to invest in physical capital, denoted I1. Investment becomes productive in period 2. The investment schedule is I1 = 12.5 (1 + r) ^2
1. Calculate private consumption in period 1 (C1), government saving in period 1 (S g 1 ), and national saving in period 1 (S1).
2. Calculate the equilibrium real interest rate (r).
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