Please help Using the Fisher model explain how impatience ca

Please help!

Using the Fisher model explain how impatience can interfere with consumption smoothing. Give an example of a utility function that incorporates impatience.

Solution

Let us assume that there are two periods, 1 and 2 respectively. Consumption in both period=c1 and c2. Hence utility received from that is U=U(c1,c2). Say, income of first period is y1 and savings and rate of interest is s, r respectively.

Income of period 2 is assumed to be y2. It is also assumed that total income is consumed at the end of period 2.

Hence, c1(1+r)+c2=y1(1+r)+y2

or, c1+c2/(1+r)=y1+y2/(1+r)

The above is the budget constraint.

Hence, the problem is:

max: U=U(c1, c2)

Subject to: c1+c2/(1+r)=y1+y2/(1+r)

By setting up lagrange we get MUc1/MUc2=1/(1+r)

Cobb-Douglas production function exhibits the desired functional form as it is neo-classical production function that exhibits-CRS, DMU and innada condition.