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Problemset
Title
Introductory
Text
Graphing and Quantitative Exercises
Question 1
Provide an example of a business situation that portrays both constant
and increasing returns to scale.
Hint:
Type:
Essay
Question 2
Type:
Essay
Feedback: Answer: Students may provide a case in which when
multiplying the amount of factors of production by a factor
z, output multiplies by z, in the case of constant returns to
scale. In the case of increasing returns to scale, production
would multiply by a factor greater than z, such as z+ 𝛼,
even if α is very small.
Get MPL and MPK based on the production function (Equation 3)
specified in the chapter. Based on your partial derivatives, explain from
your equations the diminishing aspect of the marginal productivity of L
and K respectively. (Hint: your equation will look like Equations 4 and
5 in this chapter.
Hint:
Feedback: Answer: Once students mathematically understand
Equations 4 and 5 on their own, they will be able to see that
both MPL and MPK decreases when both L and K increase,
respectively.
Question 3
Type:
Essay
Calculate the factor shares using the Cobb-Douglas production function
so
(MPK ● Kt)/Yt = α and (MPL ● Lt)/Yt = (1- α). Interpret your results.
Hint:
Feedback: Answer: When students calculate the two ratios, terms will
cancel and the end results will be α and (1-α), respectively.
The share of capital in the economy is given by the total
payments to K as given by MPK times its quantity, and it
will be equal to parameter α. Likewise, the share of labor in
the economy is the equivalent of the total payments to labor
times its quantity, and it is equal to 1 minus parameter α.
These outcomes reveal that factor shares are stable
regardless of the fluctuation in both price and quantity of
labor and capital. Empirical evidence supports these
findings.
Question 4
Type:
Essay
Explain with words and a graph the steady state, k*, in the Solow
Growth model. How does a decrease in population growth, n, affect k*?
Show the changes in your graph and explain.
Hint:
Feedback: Answer: Students need to replicate Figure 4.2 to explain the
original steady state. With the decrease in population, the
steady state k* increases since lower population increases
capital intensity. The graph with the change in k* must look
like Figure 4.3.
Question 5
Type:
Essay
In the context of the Solow model, assume two countries 1 and 2 with
the same A, n and δ and an α equal to 0.2845, have, respectively,
savings rates of 4% and 12%. Determine the role of savings in the
relative rate of economic growth for countries 1 and 2. Provide a realworld application of your numerical outcome.
Hint:
Feedback: Answer: If you get the ratio of income per capita for
countries 1 and 2, y1/y2, you get y1/y2 = (s1/s2) (α/1-α). That is,
y1/y2 =(s1/s2) (α/1-α) = (4/12)0.3976 = 0.6461. So, country 1’s
steady state is 64.61% of country 2’s due to country 1’s
lower savings rate. The Asian economies are a good
example of the role of savings in a country’s relative
economic growth.