Consider an economy where n = 1.25 and y_t =1.1y_t-1 (an economy where both population and endowment are growing. Assume old people do not receive any endowments. Assume that a young person's preferences are such that they want to consume two-thirds of their endowment such that

C_1.t = 0.66y_t.

Additional Information if needed

Competitive Equilibrium

• Mutually beneficial trades : utility maximization
• Price taking : no collusion
• supply equal demand(markets clear)
• No frictions ( perfect record keeping)

Budget Constraints :

Facing the person in the first period of life: c1,t + t y.

Facing the person in the second period of life: c2,t+1 ^Rt+1

(Where t is the consumption given to old person at time t)

(Where ^Rt+1 is the goods received as transfer when old)

Budget constraint after conversion: Let xt+1 > 0 denote the conversion rate of consumption good at period t for t+1 good

c1,t + c2,t + 1 /xt+1 y

Assume stationary equilibria, c1,t = c1 and c2,t+1 = c2 for all t

• Rational expectations in nonrandom environment : perfect foresight.

Total transfer supply : Nt ( y- c1,t)

Total demand for transfer: Nt-1 ( xt t-1)

Thus : Nt-1(xt t-1 ) = Nt ( y-c1,t)

Constant population implies : xt = 1

a)Show the equation for supply of transfers by a young individual at time t.

b)Show the equation for demand of transfers by an old individual at time t (Note and old person in t is young at time t-1).

c)Using the equilibrium for transfers find the rate of transfer between young and the old.

d)Now suppose population growth rate is 1.2. Calculate and find the new rate of transfer. Given the answer what is the impact of population growth on rate of transfer.

e)In the current Covid-19 scenario, there is a decline in older generation combined with economic slowdown. In a few sentences, what impact would these have on the rate of transfer.