Suppose utility equals In (c 1,t ) + In (c 2 , t +1 )where In

Suppose utility equals In (c_1,t) + β In (c₂, _t+1)where In (c)represents the natural logarithm of c, whose derivative equals 1/c. The parameter β is a positive number.
a. Prove that real money balances are q^* = βy/1 + β.
b. Derive expressions for the lifetime consumption pattern c^*₁,_t and c^*₂, _t+1.
c. What effect does an increase in β have on real money balances and the lifetime consumption pattern? Give an intuitive interpretation of the parameter β.