# 查看完整版本 : 高手求救,MACROECONOMICS

Stockgg 2017-4-11 01:41 PM

## 高手求救,MACROECONOMICS

Government Investment

Consider a closed economy in which both capital ¯ K and labor ¯ L are fully employed. Let F(·,·) be the production function of this economy, then the economy’s output is
Y = ¯ Y = F( ¯ K, ¯ L) (1)

The economy allocates the output to consumption C, investment I and government purchases G. We assume that

i) consumption is a function of the level of disposable income, and the marginal propensity to consume is less than one;
ii) investment is a function of the real interest rate;
iii) government purchases and taxation are equal and exogenous.

Then the national income accounts identity becomes

¯ Y = C(¯ Y − ¯ T) + I(r) + ¯ G (2)
where r is the real interest rate.

Suppose the government invests in the production technology so that the production function becomes ˜ F(·,·) = aF(·,·), where a > 1 (this is diﬀerent from the investment I). Then the output becomes
Y = ˜ Y = ˜ F( ¯ K, ¯ L) = aF( ¯ K, ¯ L) (3)

The government ﬁnances this investment by increasing the government purchases to ˜G > ¯ G. Deﬁne the gross return of government investment as
φ =˜ Y − ¯ Y ˜ G− ¯ G (4)

Question A: Suppose there is no change in the taxation. How does the government investment aﬀect investment and real interest rate? (Hint: Your answer should depend on the marginal propensity to consume and the return of government investment.)

Question B: Suppose the government adopts a balanced budget policy. How does the government investment aﬀect investment and real interest rate? (Hint: Your answer should depend on the marginal propensity to consume and the return of government investment.)

Question C: Compare your results in the ﬁrst two questions, which one is more likely to have greater eﬀects on investment and real interest rate? Explain in economics.