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.

Solutions

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 1 year ago

Next > < Previous

Related Solutions

Suppose that output Q is produced with the production function Q = f(K;L), where K is...

Suppose that output Q is produced with the production function Q = f(K;L), where K is the number of machines used, and L the number of workers used. Assuming that the price of output p and the wage w and rental rate of capital r are all constant, what would the prot maximizing rules be for the hiring of L and K? (b) What is theMRTSK;L for the following production function: Q = 10K4L2? Is this technology CRS, IRS or...

Suppose that output Q is produced with the production function Q = f(K,L), where K is...

Suppose that output Q is produced with the production function Q = f(K,L), where K is the number of machines used, and L the number of workers used. Assuming that the price of output p and the wage w and rental rate of capital r are all constant, what would the proﬁt maximizing rules be for the hiring of L and K? (b) What is the MRTSK,L for the following production function: Q = 10K4L2? Is this technology CRS, IRS...

Assume that output is given by Q(L,K)=50 K^0.5 L^0.5 with price of labour L = w...

Assume that output is given by Q(L,K)=50 K^0.5 L^0.5 with price of labour L = w and price of capital K = r 1.If capital in the short run is fixed at K what is the short-run total cost? 2.Write the values for the derivatives of the Total cost with respect to w and r. Does Shephard’s lemma hold in this case?

A firm produces output according to the following function: q = f (L, K) = L^1/2...

A firm produces output according to the following function: q = f (L, K) = L^1/2 K^1/4 . The cost of labor is $8 per hour and the rental cost of capital is $2 per hour. a. Determine the returns to scale for this function. b. Suppose the firm wishes to produce at cost $96. How much capital and how much labor does the firm employ? c. Derive the short-run cost function with optimal amount of K from part b....

Suppose your firm uses 2 inputs to produce its output: K (capital) and L (labor). the...

Suppose your firm uses 2 inputs to produce its output: K (capital) and L (labor). the production function is q = 50K^(1/2)L^(1/2). prices of capital and labor are given as r = 2 and w = 8 a) does the production function display increasing, constant, or decreasing returns to scale? how do you know and what does this mean? b) draw the isoquants for your firms production function using L for the x axis and K for y. how are...

A firm produces output y using two factors of production (inputs), labour L and capital K....

A firm produces output y using two factors of production (inputs), labour L and capital K. The firm’s production function is ?(?,?)=√?+√?=?12+?12. The wage rate w = 6 and the rental price of capital r = 2 are taken as parameters (fixed) by the firm. a. Show whether this firm’s technology exhibits decreasing, constant, or increasing returns to scale. b. Solve the firm’s long run cost minimization problem (minimize long run costs subject to the output constraint) to derive this...

Output is produced according to Q=4LK, where L is the quantity of labor input and K...

Output is produced according to Q=4LK, where L is the quantity of labor input and K is the quantity of capital input. If the price of K is $10 and the price of L is $5,then the cost minimizing combination of K and L capable of producing 32 units of output is:

Suppose output, Q, is produced by labor, L, and capital, K, according to the following function:...

Suppose output, Q, is produced by labor, L, and capital, K, according to the following function: Q = K ½ L½.. Suppose the firm sells each unit of output in a competitive market for a price P = $100. Suppose the firm hires each unit of labor in a competitive market for a wage W = $25. Suppose the firm has to make do for now with a stock of capital K = 49; moreover, suppose each unit of capital...

Assume that output is given by Q(L,K)=50L^0.5K^0.5 with price of labour L = w and price...

Assume that output is given by Q(L,K)=50L^0.5K^0.5 with price of labour L = w and price of capital K = r a Use the primal formulation of minimising costs to obtain the demand for Labour L and capital K 2 b Using the values of L & K obtained above, verify whether the output Q equals the one given in the question by eliminating the values of w and r. Are the primal and dual problems leading to the same...

A firm produces output according to the production function: Q= F(K, L) = 4K + 8L.

A firm produces output according to the production function: Q= F(K, L) = 4K + 8L. a. How much output is produced when K= 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 units of output? c. If the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour, what is the...

Subjects