1   Multiple Choice Questions (3pts each)

Q1. Determine the returns to scale of the following production function:

Y = K3 + N3

A. constant

B. increasing

C. decreasing

D. indeterminate

Q2. Assume an economy has the Cobb–Douglas production function

Y = 10KN 

If the economy’s stock of capital doubles, the share of total income paid to the owners of capital will

A. increase by 10 percent.

B. increase by one-third.

C. increase by two-thirds.

D. stay the same.

Q3. In the two-period consumption model, which of the following will surely occur for a bor- rower when the interest rate increases?

A. Future consumption increases.

B. Current consumption increases.

C. Future consumption falls.

D. Current consumption falls.

Q4. Assume a general saving rate s, depreciation rate 6 and a production per worker y = k α , where 0 < α < 1. Suppose the depreciation rate decreases. What happens to the steady state output per worker?

A. cannot be determined.

B. remains the same.

C. decreases.

D. increases.

Q5. Many demographers predict that the US will have zero population growth in the 21st cen-

tury, in contrast to a population growth of about 1% in the 20th century. Using the growth

model and assuming that there is no technological progress, how will this change affect the long-run level of output per worker ?

A. remains the same.

B. increases.

C. decreases.

D. cannot be determined.

Q6. Consider an economy that is described by the production function Y  = Kα N1−α . The depreciation rate is 6 and the savings rate is s. The government decides to increase the savings rate to the golden rule level saving rate.  What is the immediate impact of the policy on consumption per worker?

A. cannot be determined.

B. increases.

C. decreases.

D. remains the same.

Q7. Assume a general savings rate s, depreciation rate 6 and a population per worker y = k α , where 0 < α < 1. Suppose the savings rate increases. What happens to the golden rule level of capital?

A. increases.

B. decreases.

C. cannot be determined.

D. remains the same.

Q8. In the Solow growth model, the steady-state occurs when:

A. capital per worker is constant.

B. the saving rate equals the depreciation rate.

C. output per worker equals consumption per worker.

D. consumption per worker is maximized.

Q9. In the Solow growth model, if investment exceeds depreciation, the capital stock will          and output will          until the steady state is attained.

A. increase; increase

B. increase; decrease

C. decrease; decrease

D. decrease; increase

Q10. If a war destroys a large portion of a country’s capital stock but the saving rate is un-

changed, the Solow model predicts output will grow and that the new steady state will approach:

A. a higher output level than before.

B. the same output level as before.

C. a lower output level than before.

D. the Golden Rule output level.

Q11. If the national saving rate increases, the:

A. economy will grow at a faster rate forever.

B. capital per worker will increase forever.

C. economy will grow at a faster rate until a new, higher, steady-state capital per worker is reached.

D. capital per worker will eventually decline.

Q12. If an economy is in a steady state with no population growth or technological change and

the capital stock is above the Golden Rule level and the saving rate falls:

A. output, consumption, investment, and depreciation will all decrease.

B. output and investment will decrease, and consumption and depreciation will increase.

C. output and investment will decrease, and consumption and depreciation will increase and then decrease but finally approach levels above their initial state.

D. output, investment, and depreciation will decrease, and consumption will increase and then decrease but finally approach a level above its initial state.

Q13. In an economy with population growth at rate n, the change in capital stock per worker is given by the equation:

A. ∆k = sf(k) + 6k.

B. ∆k = sf(k) − 6k.

C. ∆k = sf(k) + (6 + n)k.

D. ∆k = sf(k) − (6 + n)k.

Q14. In the Solow growth model of an economy with population growth but no technological change, if the population grows at rate n, then capital grows at rate         and output grows

at rate         

A. n; n.

B. n; 0.

C. 0; 0.

D. 0; n.

Q15. In the Solow growth model, the steady-state level of output per worker would be higher if the          increased or the          decreased.

A. saving rate; depreciation rate

B. population growth rate; depreciation rate

C. depreciation rate; population growth rate

D. population growth rate; saving rate

2   Short Answer Questions

Q1.  (6pts) Suppose that 80% of output is consumed every period, and capital depreciates at 10%

every period. The production function is Cobb-Douglas with the share of capital income in the total income equal to  .

Suppose the capital per worker k1  equals 1, 000 initially. Assume there is no population growth.

(a) (3pts) In the initial period, how much are consumption per worker, investment per worker, output per worker, and depreciation per worker?

(b) (3pts) How much will be the capital stock per worker in the next period?

Q2. (18pts) Consider an economy with a Cobb-Douglas production function, with the share of capital income in total income equal to  . Let the depreciation rate be 6 = 0.016, and the savings rate is s = 0.4. Assume there is no population growth.

(a) (4pts) What are capital stock per worker, output per worker, consumption per worker, and investment per worker in the steady state?

(b) (6pts) Use calculus to derive an expression for the saving rate (s), which maximizes steady-state consumption per worker. Denote this saving rate as sgr .

(c) (8pts) Suppose the economy reaches the steady state level (with α = ,6 = 0.016,s = 0.4). Consider the effect dynamic response of capital per worker, output per worker, consumption per worker, and investment per worker to the following changes. Draw graphs with clear illustrations. [Hint: using time as the horizontal axis]

(i) (4pts) depreciation rate 6 temporarily increases at time T∗ .

(ii) (4pts) saving rate s temporarily increases at time T∗ .

Q3. (6pts) Consider an economy with a Cobb-Douglas production function, with the share of capital income in total income equal to  (α = ). Let the depreciation rate be 6 = 0.1, the population growth rate be n = 0.025 and the savings rate be s = 0.5. What are the capital stock per worker, output per worker, consumption per worker, and the growth rate of output per worker in the steady state?

Q4. (15pts) A consumer’s income in the current period is y = 250, and her income in the future period is y\  = 300. The real interest rate r is 0.05, or 5%, per period. Assume there are no taxes. Suppose that the utility function is

U(c,c\ ) =^c + β ^c\

and let β = 0.9

(a) (2pts) Determine the consumer’s lifetime wealth we (present discounted value of life-

time income). Write down the lifetime budget constraint.

(b) (2pts) Derive the Marginal Rate of Substitution between c and c\ .

(c) (4pts) Write down the consumer maximization problem. What is the objective func- tion? What are exogenous variables? What are endogenous (choice) variables?

(d) (2pts) Solve for c\  as a function of c using the lifetime budget constraint. Replace it into the objective function so the problem only depends on c.

(e) (3pts) Take the first order condition with respect to c and use it to and c* and c*\ .