Futons Inc. produces futons using only two inputs – capital (wood, nails, and ha
ID: 1200708 • Letter: F
Question
Futons Inc. produces futons using only two inputs – capital (wood, nails, and hammers) and labor (measured in worker hours) – with a technology characterized by the following function:
q = 2ln(K + 3L)
Futons Inc. spent $100 on 100 units of capital at the beginning of the period. They can neither purchase nor sell units of wood, nails, and hammers until the end of the period, but the material does not lose any value over time.
a) Solve for the average product of labor and the marginal product of labor.
b) Assuming that futon makers earn a wage of $9 per hour and the prevailing interest rate in the economy is 10 percent, solve for short run costs as a function of the numbers of futons produced.
Explanation / Answer
q = 2ln(K + 3L) , K =100
MPL = dq/dL = [2/(k + 3L)]*3 = 6/100 +3L
Average product of Labour = q/L = 2ln(100 + 3L)/L
b. Total Cost = Wage*L + Interest rate*K = 9*L + 0.10K
Setting up the lagrange function
G = 9*L + 0.10K + (q - 2ln(K + 3L))
dG/dL = 9 - 6/k+ 3L
dG/dK = 0.10 - 2/k + 3L
dG/d = q - 2ln(K + 3L)
Putting dG/dL =dG/dL = dG/d = 0
Solve these equations and put the values in the Cost function
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