# 2. Consider a two-period ecornomy. Households preferences are described bythe utility functionIn C1n C2, where C1 denotes consumption in period 1 and C2 denotes consumption inperiod 2. In period 1, households receive an endowment Yhouseholds receive profits from firms that they own. Households pay lump-= 10. In period 2,sum taxes Ti and T2 in periods 1 and 2, respectively, and can save at theinterest rate r. Firms borrow funds in period 1 to invest I1 units of goodsin physical capital. In period 2, firms produce output, denoted Y2, using thetechnologyf(I1) 10Iandback their loans. The government levies lump-sum taxes to house-рayholds in the amounts Ti and T2 in periods 1 and 2, respectively, and consumesG2 units of goods in period 1. Government consumption in period 2 iszero. T1 equals 1. (a) State the household's budget constraints in period 1 and period 2 andderive the intertemporal budget constraint of the household.(b) Find the optimal consumption, Ci, and private saving, S, as a functionof r,Y1 Ti, and Y2 T2.(c) State the government's budget constraint in period 1 and in period 2 andderive the intertemporal budget constraint of the government. Find Siand T2

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I need help with a-c

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Step 1

(a) Household’s budget constraint in period 1 is:

C1 + S1p = Y1 – T1

Household’s budget constraint in period 2 and the intertemporal budget constraint of the household is:

Step 2

(b) Now to find the optimal consumption level we will equate the slope of budget constraint (BC) with the marginal rate of substitution (MRS).

Slope of BC = (1+r)

MRS = U’C1 / U’C2

= (1/C1) / (1/C2)

= C2 / C1

Equating the ...

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