Question

In: Economics

Unit_production.xls: Output and Inputs in the agricultural sector YEAR Q K L 1958 16607.7 17803.7 275.5...

Unit_production.xls:

Output and Inputs in the

agricultural sector

YEAR Q K L

1958 16607.7 17803.7 275.5

1959 17511.3 18096.8 274.4

1960 20171.2 18271.8 269.7

1961 20932.9 19167.3 267

1962 20406 19647.6 267.8

1963 20831.6 20803.5 275

1964 24806.3 22076.6 283

1965 26465.8 23445.2 300.7

1966 27403 24939 307.5

1967 28628.7 26713.7 303.7

1968 29904.5 29957.8 304.7

1969 27508.2 31585.9 298.6

1970 29035.5 33474.5 295.5

1971 29281.5 34821.8 299

1972 31535.8 41794.3

288.1

Consider the data provided in Unit_production.xls provided in this email. This worksheet contains information on Output (Q), Labor employed (L) and capital hired (K) in the US agriculture sector. Answer the following questions based on this data.

1. Consider the Cobb-Douglas production function that expresses Output (Q) as a function of capital (K) and labor (L):

Q = A K a L b

Economic theory tells us that both K and L should have positive marginal products, and independently exhibit diminishing returns. For what values of the parameters will these conditions be satisfied ?

2. For what values of the parameters will the function exhibit different returns to scale ?

3. Rewrite the above function as a log-linear equation. Use this to calculate output-elasticities with respect to K and L. What do these output-elasticities tell us ?

Statistics:

4. Estimate the Cobb-Douglas function for the data given in unit-Production.xls. Write the estimated equation explicitly in both the log-linear and in the multiplicative forms.

Log-Linear form:

Multiplicative form (remember to find the exponential of the intercept for A):

5. Interpret R-squared.

Expert Solution

The results of the log-linear regression is

variable	coefficient
logK	0.489858
logL	1.49877
logA	-3.33847

Therefore, a = 0.5 and b = 1.5 and logA = -3.3.

The log-linear form can be written as, logQ = -3.338 + 0.5logK + 1.5logL

The multiplicative form: Q = 0.036K^0.5L^1.5

5. The R-squared of the regression result is 0.8890

It means that the variation in the log of Quantity is 88.9% explained by the variation in the log of the input variables.

Rahul Sunny answered 2 years ago

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