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Consider an economy described by the equations of the
Solow-model (without technological or population growth), except that all labor income
is consumed and all other income is saved. The production function is Cobb-Douglas,
so f(k(t)) = k(t)α.
1. Write down the equation that governs capital accumulation!
2. Does this economy converge to a steady-state? If so, what is the steady state level
of k. How does that compare to the level derived in the lecture notes?
3. Is the saving rate in the economy constant? Increasing? Decreasing? What is the
intuition for that?
Solow-model (without technological or population growth), except that all labor income
is consumed and all other income is saved. The production function is Cobb-Douglas,
so f(k(t)) = k(t)α.
1. Write down the equation that governs capital accumulation!
2. Does this economy converge to a steady-state? If so, what is the steady state level
of k. How does that compare to the level derived in the lecture notes?
3. Is the saving rate in the economy constant? Increasing? Decreasing? What is the
intuition for that?
You work as a tutor for Econ. You sell your services at $12/hr., and you can only tutor one person at a time. Suppose you currently have 5 clients. If it cost you on average $14/hr to tutor the first student, in order to increase profits you should.
A. Get rid of some clients
B. Find more clients
C. Continue to see the same number of clients
D. we need more information to answer
E. raise the price
A. Get rid of some clients
B. Find more clients
C. Continue to see the same number of clients
D. we need more information to answer
E. raise the price
If an industry’s long run average total cost curve has an extended range of constant returns to scale:
A. Both relatively small and relatively large firms can be viable in the industry. B. Only relatively small firms can be viable in the industry. C. Short run production costs will increase. D. Production will be dominated by large firms.
Economics
the oppurtunity cost of an hour she spends commuting is 50$ initially, what is the total net benefit?
The Cobb–Douglas production function is
y=Z1^aZ2^b a>0, b>0
show that the MP1 = ay/z1, MP2 = by/z2
What is the MRTS21? How does it vary with: (a) y; (b) z2 /z1?
y=Z1^aZ2^b a>0, b>0
show that the MP1 = ay/z1, MP2 = by/z2
What is the MRTS21? How does it vary with: (a) y; (b) z2 /z1?
The Cobb–Douglas production function is
y=Z1^aZ2^b a>0, b>0
show that the MP1 = ay/z1, MP2 = by/z2
What is the MRTS21? How does it vary with: (a) y; (b) z2 /z1?
y=Z1^aZ2^b a>0, b>0
show that the MP1 = ay/z1, MP2 = by/z2
What is the MRTS21? How does it vary with: (a) y; (b) z2 /z1?
Fixed Proportions Technology (Leontief)
(a) Process 1 uses at least b11 units of z1 and b12 units of z2 to produce one unit of output.
Draw the isoquant for y = 1, and distinguish between the technical and output-efficient
(z1, z2) points. Suppose that at least yb11 units of z1 and yb12 units of z2 are required to
produce y units of output, so that the production function for process 1 is
y = min [ z1 / b11, z2/b12]
Draw the isoquant map for the process. What does the economic region look like?
(a) Process 1 uses at least b11 units of z1 and b12 units of z2 to produce one unit of output.
Draw the isoquant for y = 1, and distinguish between the technical and output-efficient
(z1, z2) points. Suppose that at least yb11 units of z1 and yb12 units of z2 are required to
produce y units of output, so that the production function for process 1 is
y = min [ z1 / b11, z2/b12]
Draw the isoquant map for the process. What does the economic region look like?
Consider an economy with technological progress but
without population growth that is in steady-state. Now suppose there is a one-time
jump in the number of workers.
(a) At the time of the jump, does output per unit of effective labor rise, fall or stay
constant.
(b) After the initial change (if any) in output per unit of effective labor when the new
workers appear, is there any further change in output per unit of effective labor? If
so, does it rise or fall? Why?
(c) Once the economy reaches its new steady-state, is output per unit of effective labor
higher, lower or the same as it was before the new workers appeared? Why?
without population growth that is in steady-state. Now suppose there is a one-time
jump in the number of workers.
(a) At the time of the jump, does output per unit of effective labor rise, fall or stay
constant.
(b) After the initial change (if any) in output per unit of effective labor when the new
workers appear, is there any further change in output per unit of effective labor? If
so, does it rise or fall? Why?
(c) Once the economy reaches its new steady-state, is output per unit of effective labor
higher, lower or the same as it was before the new workers appeared? Why?
An efficient outcome maximizes?
Suppose the level of output that creates full employment in the economy is 1800, using the multiplier, datermine the level of investment spending that will create full employment in this economy
