Consider the problem of modeling national income. At time n, let y[n] = national income, c[n] = consumer expenditure, p[n] = induced private investment (capital equipment to increase production), and...

y[n] = national income,

c[n] = consumer expenditure,

p[n] = induced private investment

(capital equipment to

increase production),

and g[n] = government expenditure.

In this model, the consumer expenditure during any period is directly proportional to the national income during the previous period. On the other hand, the induced private investment is directly proportional to c[n]−c[n−1], the increase in the consumer spending over the previous period. Finally, the national income is the sum of the consumer spending, the induced private investment, and the government expenditure.

(a) Construct the model (equation) for the prevailing price during the nth period.

(b) Determine a block realization of this system.